MODELING INACTIVATION OF SALMONELLA DURING SPRAY DRYING OF SOY PROTEIN ISOLATE By Philip Steinbrunner A THESIS Submitted to Michigan State University in partial fulfillment of the requirements for the degree of Biosystems Engineering Master of Sc ience 2019 ABSTRACT MODELING INACTIVATION OF SALMONELLA DURING SPRAY DRYING OF SOY PROTEIN ISOLATE By Philip Steinbrunner Foodborne illness o utbreaks linked to spray dried foods like infant formula and protein powders demonstrate a need for greater unders tanding of bacterial inactivation kinetics during spray drying . However, despite extensive research regarding the mechanisms of the spray drying process, the su rvival of bacteria during spray drying is not well understood. Therefore, the objectives were to : (1) measure the inactivation rate s of Salmonella within a spray drying droplet, (2) develop a model that relates droplet drying kinetics to Salmonella inactiv ation rate, and (3) assess the surviva bility of Salmonella and Enterococcus faecium throughout a pilot - scale spray dryer . In t he first study , a thin layer of soy protein slurry inoculated with Salmonella was dried in a convection oven using actual s pray dr ying conditions to measure the inactivation rate of Salmonella within droplet s . Thereafter , a he at - mass coupled droplet drying model and secondary bacterial inactivation models using droplet temperature and moisture content were developed . Lastly, the survival and spatial distribution of Salmonella and Enterococcus faecium throughout a pilot - scale sp ray dryer were evaluated at various process temperatures . Bacterial inactivation rate was successfully modeled, with the best fitting secondary model including parameters for both droplet temperature and moisture content , which were coupled with the dropl et drying model and validated . Although t he spray drying process was able to reduce b o th organism s , survivors were found both in the final powder as well as the interior dryer surfaces, which indicat es a potential health risk if the spray dryer is contamin ated. iii ACKNOWLEDGMENTS The work presented in this thesis would not have been possible without the help of many people along the way. Thus, I would like to thank these people for their support in helping me reach this goal. First , thank you to Dr. Jeong f or advising me during both my undergraduate and graduate research. His co nstant support and guidance were what made my work possible, and I greatly appreciate all the opportunities and advice he has given me over the years. Additionally, I would like to th ank to my committee members, Dr. Marks, Dr. Ryser, and Dr. Dolan, for add itional help and guidance with research problems along the way. I would also like to acknowledge the immense help given to me by my coworkers during my time at MSU. My lab managers Mi ke James and Nicole Hall offered great laboratory expertise and were alwa ys willing to help with my research when needed. My fellow graduate students (Nurul Ahmad, Ian Hildebrandt, Pichamon Limcharoenchat, Francisco Garces - Vega, and Beatriz Mazon) were exc ellent sources of expertise in many varying research subjects and were gr eat sources of comradery and kindness when I felt discouraged. I also greatly appreciate all the work done by the undergraduate students in the lab I know how much work goes on behi nd the scenes to keep our lab running, and this effort means a great deal to me. I would like to thank my friends and family, especially my parents, for their undying support and belief in my abilities. Their love was much needed in difficult times, and I am glad I could always count on them to encourage me to keep working and not give up. Finally, I would like to thank my wife, Victoria Steinbrunner. She has always been the first person I turn to throughout my graduate studies and has offered invaluable lo ve and support iv through all the difficult times of graduate sc hool. I am grateful for her never giving up on me and responding to all my frustration, discouragement, and anxiety with love and understanding. I could not have reached this point without her. T he work presented in this thesis was supported by USDA NIFA A griculture and Food Research Initiative (AFRI) grant number 2017 - 67017 - 26528 Salmonella Control Strategies for Spray - v TABLE OF CONTENTS LIST OF TABLES ................................ ................................ ................................ ........................ vii LIST OF FIGURES ................................ ................................ ................................ ..................... viii KEY TO SYMBOLS ................................ ................................ ................................ ...................... x 1. INTRODUCTION ................................ ................................ ................................ ................... 1 1.1. Spray Drying Process and Products ................................ ................................ ................. 1 1.2. Food Safety Impact and Regulation ................................ ................................ ................. 2 1.3. Objectives ................................ ................................ ................................ ......................... 3 2. LITERATURE REVIEW ................................ ................................ ................................ ........ 5 2.1. Spray Drying Process ................................ ................................ ................................ ....... 5 2.1.1. F eed material pre - treatment ................................ ................................ ...................... 5 2.1.2. Atomization ................................ ................................ ................................ ............... 6 2.1.3. Droplet dr ying ................................ ................................ ................................ ........... 9 2.1.4. Parti cle residence time ................................ ................................ ............................ 11 2.2. Droplet Drying Kinetics Modeling ................................ ................................ ................ 13 2.2.1. Introduction ................................ ................................ ................................ ............. 13 2.2.2. Experimental methods and results ................................ ................................ .......... 18 2.2.3. Theoretical methods and results ................................ ................................ .............. 21 2.2.4. Conclusions ................................ ................................ ................................ ............. 22 2.3. Bacterial Inactivation Modeling ................................ ................................ ..................... 23 2.3.1. Introduction ................................ ................................ ................................ ............. 23 2.3.2. Spray d rying inactivation studies ................................ ................................ ............ 24 2.3.3. Low - moisture inactivation studies ................................ ................................ .......... 30 2.3.4. Surrogate organisms ................................ ................................ ................................ 32 2.3.5. Conclusion ................................ ................................ ................................ .............. 33 2.4. Summary ................................ ................................ ................................ ........................ 33 3. MODELING BACTERIAL INACTIVATION KINETICS DURING THIN - FILM DRYING OF SOY PROTEIN POWDER SOLUTION ................................ ................................ ................ 34 3.1. Introduction ................................ ................................ ................................ .................... 34 3.2. Ob jectives ................................ ................................ ................................ ....................... 34 3.3. Materials and Methods ................................ ................................ ................................ ... 34 3.3.1. Spray dryer air temperature measurement ................................ .............................. 34 3.3.2. Materials and properties ................................ ................................ .......................... 36 3.3.3. Lab - scale oven simulation ................................ ................................ ...................... 38 3.4. Results and Discussion ................................ ................................ ................................ ... 41 3.4.1. Spray dryer chamber temperature results ................................ ............................... 41 3.4.2. Thin - layer drying droplet inactivation results ................................ ......................... 43 3.5. Conclusion ................................ ................................ ................................ ...................... 47 vi 4. SIMULATED DROPLET DRYING KINETICS AND APPLICATION OF BACTERIAL INACTIVATION MODELS ................................ ................................ ................................ ........ 48 4.1. Introduction ................................ ................................ ................................ .................... 48 4.2. Objectives ................................ ................................ ................................ ....................... 48 4.3. Materials and Methods ................................ ................................ ................................ ... 49 4.3.1. D roplet drying modeling methods ................................ ................................ .......... 49 4.3.2. Bacterial inactivation modeling methods ................................ ................................ 51 4.3.3. Model evaluation and selection ................................ ................................ .............. 53 4.4. Results and Discussion ................................ ................................ ................................ ... 54 4.4.1. Droplet drying simulation results ................................ ................................ ............ 54 4.4.2. Inactivation modeling ................................ ................................ ............................. 56 4.5. Conclusion ................................ ................................ ................................ ...................... 61 5. PILOT - SCALE VALIDATION OF COMBINED SPRAY DRYING AND BACTERIAL INACTIVATION MODELS ................................ ................................ ................................ ........ 62 5.1. Introduction ................................ ................................ ................................ .................... 62 5.2. Objectives ................................ ................................ ................................ ....................... 62 5.3. Materials and Methods ................................ ................................ ................................ ... 62 5.3.1. Materials and properties ................................ ................................ .......................... 62 5.3.2. Inactivation study methods ................................ ................................ ..................... 63 5.3.3. Spray dryer operational safety ................................ ................................ ................ 66 5.4. Results and Discussion ................................ ................................ ................................ ... 67 5.4.1. General properties ................................ ................................ ................................ ... 67 5.4.2. Effect of sampling location ................................ ................................ ..................... 67 5.4.3. Effect of inlet air temperature ................................ ................................ ................. 75 5.4.4. Comparison of survival be tween organisms ................................ ........................... 75 5.4.5. Validation of inactivation model ................................ ................................ ............ 76 5.5. Conclusion ................................ ................................ ................................ ...................... 79 6. CONCLUSIONS ................................ ................................ ................................ ................... 80 6.1. Overall Conclusions ................................ ................................ ................................ ....... 80 6.2. Commercialization Potential ................................ ................................ .......................... 81 6.3. Future Work ................................ ................................ ................................ ................... 81 6.3.1. Experimental work ................................ ................................ ................................ .. 81 6.3.2. Modeling improvements ................................ ................................ ......................... 83 APPENDIX ................................ ................................ ................................ ................................ ... 85 REFERENCES ................................ ................................ ................................ ............................. 99 vii LIST OF TABLES Table 1. Average drying chamber air tem perature (°C ± standard deviation) measured at 7, 45, and 90 cm from the chamber ceiling (top, middle, bottom, and average of entire chamber, respectively) during normal spray drying oper ation at inlet air temperatures (T inlet ) of 180, 200, and 220°C. ................................ ................................ ....................... 42 Table 2. D - values (± 95% confidence intervals) for Salmonella En teritidis PT30 in soy protein isolate inoculated onto nylon mesh discs treated in a convection oven at 80 - 200°C. .... 45 Table 3. Boundar y and initial conditions used in the simulated droplet drying model. ............... 51 Table 4. Parameter estimates and model evaluation for secondar y models of Salmonella inactivation in drying soy protein isolate droplets, using T ref = 77°C and X ref = 1 kg H 2 O/kg total. ................................ ................................ ................................ ................... 57 Table 5. Inactivation of E. faecium and Salmonella (± 95% confidence interval) in soy protein isolate powder sampled from the primary and secondary collectors after spray drying at various inlet air temperatures. Initial concentrations of E. faecium and Salmonella in the inoculated soy protein solution wi th 95% confidence interval were 9.73 ± 0.18 and 8.86 ± 0.18 CFU/g solids. ................................ ................................ ................................ ....... 69 Table 6. Population of E. faecium and Salmonella (± 95% confidence interval) in soy protein isolate powder swab samples from the nozzle shield, drying chamber, cyclone, and exhaust pipe after spray drying at various inlet air temperatures. ................................ .. 72 viii LIST OF FIGURES Figure 1. Theoretical characteristic drying curve and cross - section of a droplet of dissolved solids in water (Mezhericher, Levy, and Borde 2015). ................................ .................. 14 Figure 2. FT80 Tall - form Spray Drier housed in the Biosafety Level 2 pilot plant facilit y at Michigan State University. ................................ ................................ ............................. 35 Figure 3. Separation of a 10% w/w soy protein isolate (SPI) solution into watery and paste - like phases after blending. ................................ ................................ ................................ ..... 37 Figure 4. Nylon mesh on a wire rack before inoculation and drying in a convection oven (top), side view cross - section representati on of droplets suspended in a single - layer within the nylon mesh (bottom). ................................ ................................ ................................ ...... 39 Figure 5. Nylon mesh attached to wire rack placed insi de a convection oven sampling port. Arrows indicate the direction of heated airflow. ................................ ............................ 40 Figure 6. Surviva l of Salmonella Enteritidis PT30 in soy protein isolate inoculated on nylon mesh disc after low (80 - 110°C, top) and high - temperature (180 - 200°C, bottom) treatment in a convection oven. ................................ ................................ ...................... 44 Figure 7 . Droplet temperature ( T d ) and moisture content ( X ) of simulated droplets of diameter 10, 20, 40, 80, 160, and 320 µm at air temperatures of 80°C (top) and 200°C (bottom) using the drying model described in section 4.3 .1. ................................ ................................ .. 55 Figure 8. Scaled sensitivity coefficients and predicted log reductions for Eq. (17) and (20) using an air temperature of 80°C, and droplet diameter of 160 µm after optimizing parameter estimates. ................................ ................................ ................................ ........................ 56 Figure 9. Measured bacterial inactivation, model prediction, and 95% confidence and prediction intervals using Eq. (20) (markers, solid lines, dashed lines, and dotted lines, respectively) for inactivation of Salmonella i n a 160 µm diameter soy protein droplet during drying at various temperatures (80 - 200°C) ................................ ......................... 59 Figure 10. Residual analysis for obser ved versus predicted survival of Salmonella in a 160 µm diameter soy protein droplet during drying at various temperatures (80 - 200°C) using Eq. (20) . ................................ ................................ ................................ .......................... 60 Figure 11. Diagram of the sampling locations within the FT80 Tall Form Spray Dryer used in the pilot - scale v alidation study. ................................ ................................ ............................ 65 Figure 12. Typical appearance of fine soy protein powder accumulated in the secondary collector after spray drying. ................................ ................................ ................................ ........... 70 ix Figure 13. Typical appearance of accumulated coarse soy protein powder in the primary collector after spray drying. ................................ ................................ ................................ ........... 70 Figure 14. Top - down view of the spray drying chamber with deposited soy protein powder after spray drying. ................................ ................................ ................................ ................... 71 Figure 15. Nozzle shield with deposited soy protein powder after spray drying. ........................ 74 Figure 16. Cy clone connecting pipe with deposited soy pr otein powder after spray drying. ....... 74 Figure 17. Predicted inactivation of Salmonella in a droplet drying at constant air temperatures of 104, 119, and 13 2°C using Eq. (20) (lines) and observed inactivation (with 95% confidence intervals) of Salmonella in powdered soy protein isolate in the primary/secondary collectors of the pilot scale s pray dryer after drying at inlet air temperatures of 180 and 200°C fo r their assumed residence times (markers). .............. 78 x KEY TO SYMBOLS A surface area of droplet (m 2 ) a fitting parameter a w water activity b fitting parameter c p specific heat of droplet material (J/kgK) D decimal reduction time (s) D ref reference decimal reduction time (s) E d inactivation energy (J/mol) f dimensionless moisture content (f = 1 during constant rate drying period, f < 1 during falling rate drying period) h heat transfer coefficient (W/m 2 K) h m mass transfer coeffic ient (m/s) k 0 reference inactivation rate constant (s - 1 ) k d inactivation rate constant (s - 1 ) m mass of droplet (kg) m s mass of solids in droplet (kg) n evaporation hindering shape factor (convex drying rate if n < 1, concave drying rate if n > 1) N bacteri al load (CFU /g ) N 0 initial bacterial load (CFU /g ) Nu Nusselt number Pr Prandtl number p v , ambient vapor concentration (kg/m 3 ) p v ,sat saturated surface vapor concentration (kg/m 3 ) xi R universal gas constant (J/mol K) Re Reynolds number RH r elative humidity Sc Schmidt number Sh Sherwood number t time (s) T t emperature (K) T a air temperature (K) T d droplet temperature (K) T ref reference temperature (K) T wb wet bulb temperature (K) X moisture content of droplet, wet basis (kg H 2 O/kg total) X cr critical moisture content of droplet, wet basis (kg H 2 O/kg total) X eq equilibrium moisture content of d ro plet, wet basis (kg H 2 O/kg total) z Td Temperature change required for one log change in decimal reduction time (°C) z X Moisture content change required for one log change in decimal reduction time (kg H 2 O/kg total) E V apparent activation energy (J) H evap latent heat of vaporization (J/kg) with water, approaches 0 as droplet reaches equilibrium moisture) 1 1. INTRODUCTION 1.1. Spra y Drying Process and Products Spray drying is a process used to manufacture food , pharmaceutical , and industrial powders by atomizing a liquid solution int o droplets within a chamber containing high - temperature, high - velocity air to rapidly evaporate moist ure, forming very fi ne particles from a solid - liquid mixture or slurry . This process is commonly used to manufacture low - moisture food powders such as powdered milk, various protein powders, instant coffee and tea, dried flavorings, and encapsulated probio tic cultures (Chegini and Taheri 2013; Slavutsky et al. 2017) . Spray drying is favored over other drying methods (freeze drying, drum drying, conveyor drying) for many products due to its unique drying characterist ics (Handscomb 2008) . Although spray drying uses high - temperature air , droplets experience very short residence times (< 10 s ) and relatively low wet - bulb temper atures , so heat - sensitive products can be dried without reduction in quality (Sinnott 2005; Kuye et al. 2009; Zbicinski, Strumillo, and Delag 2002) . Thus, s pray drying can be used to encapsulate desired products like probiotic microorganisms in carrier materials. This allows manufacturers of pr obiotic products to dry microorganisms and extend their shelf life while maintaining high cell viability (Slavutsky et al. 2017; Tang and Li 2013) . Because spra y drying is a high - temperature drying process, it also has the potential to inactivate undesirable microorganisms that may lead to spoilage or contamination in the finished dry product (Lievense et al. 1990) . Th e market for spray dried foods has grown substantially in recent years. Global production of dry milk powders grew from 3.7 million tons in 2009 to 4.5 million tons in 2013, with spray drying being the most common method of production (Lagrange, Whitsett , and Burris 2015) . One of the fastest growing dry milk products is infant formula, for which global sales volume 2 gr e w by 40.8% between 2008 and 2013, and is projected to continue at a rate of 9% annually between 2016 and 2020 (Affertsholt and Pedersen 2017; Baker e t al. 2016) . Additionally, the global soy protein market value has been projected to increase from $4.8 bill ion in 2015 to $7.8 billion in 2024 (Transparency Market Research 2018) . G lobal reve nue from spray dried whey protein powder was $8.2 billion in 2015 (Zion Market Research 2016) . 1.2. Food Safety Impact a nd Regulation Salmonella is a common cause of foodborne illness worldwide , with an estimated 1.4 million cases, 415 fatalities, and cost of $3.1 billion per year in the United States alone (Roos, 2010) . Infection by Salmonella causes symptoms typical of ga stroenteritis , including fever, nausea, vomiting, abdominal pain, and diarrhea (Centers for Disease Control and Prevention 2019) . In severe infections, symptoms can lead to dehydration and hospitalization. As is true of many foodborne illnesses, all people are vulnerable to infection by Salmonel la , but illness is more frequent and severe in the elderly, very young, and immunocompromised populations. Salmonella spp . is commonly associated with poultry, eggs, and produce, but ha s been increasingly linked to outbreaks in low - moisture products such a s almonds and pine nuts (Centers for Disease Control and Prevention 2004, 2011) , nut butters (Centers for Disease Control and Prevention 2014, 2017 a, 2016c) , flour (Centers for Disease Control a nd Prevention 2016a) , and dried coconut (Centers for Disease Control and Prevention 2018) . S everal spray - dried products have also been the subject of recalls due to bacterial contamination, including meal - replacement shake powder (Centers for Disease Control and Prevention 2016b) , and infa nt formula (Brouard et al. 2007; Cahill et al. 2008; Usera et al. 1996; Van Acker et al. 2001; Forsythe 2005) . Outbreaks linked to spray - d ried food s are most often caused by either Salmonella or Cronobacter sakazakii , and while most infected people recover on their own, 3 some severe infections due to these pathogens can be fatal (Drudy et al. 2006; Centers for Disease Control and Prevention 2017b) . Beyond health impacts, foodborne illnesses have a tremendous economic impact, with the total burden of all foodborne illness in the United States estimated to have had a total burden of $77.7 billion in 2012 (Scharff 2012) . These outbreaks and economic burdens have led the US government to pass the Food Safety Modernization Act (FSMA) in 2011 , with the main goal of improving food safety nationwide and transform ing government food safety regulation from being reactive to preventative (Strauss 2011) . A major portion of this prevention - based approach is the mandate for written preventative control plans that include evaluation of food safety hazards, implementation of control steps put in place to reduce those hazards, and validation and verification of the (U.S. Food and Drug Administration 2011) . Therefore, a greater understanding of the efficacy of food processing techniques is needed to both meet these new reg ulations and improv e food safety. 1.3. Objectives Increased food safety regulation , as well as the health and economic impacts of foodborne illness , ha ve led to an increased research effort focused on b acterial inactivation and survival in low - moisture food pr ocessing and storage (Osaili et al. 2008; Podolak et al. 201 0; Limcharoenchat, James, and Marks 2019; Uesugi, Danyluk, and Harris 2006; Danyluk, Uesugi, and Harris 2005; Smith and Marks 2015; Ceylan and Bautista 201 5; Farakos, Frank, and Schaffner 2013; Farakos et al. 2014; Villa - Rojas et al. 2013) . Spray drying is one such process , being that it is used for manufacturing low - moisture food powders and involves complex drying mechanics . Although spray drying uses hot air, it s fundamental principle is evaporative drying which is not enough to achieve pasteurization . Therefore , potential contamination of spray 4 drying systems , as evidenced by previous outbreaks and recalls , can pose a health risk for consumers . Neverthel ess, b acterial inactivation and survival kinetics during spray drying are not currently well understood in the literature. If the reductio n of bacteria can be maximized by modifying process conditions while still achieving quality goals , then final product s will be improved through additional safety . Therefore, research o n modeling bacterial inactivation during spray drying is highly valuabl e for understanding the risks involved with the process in the event of bacterial contamination , and will ultimately h elp the food industry to validate the safety of spray dr ied food products , remain compliant with new safety regulations , and reduce the risk of outbreaks . With this motivation in mind, the research that follows included the following objectives: 1. To m odel t he inactivation kinetics of Salmonella in droplets via a thin layer of Salmonella - inoculated soy protein slurry under conditions relevan t to spray drying . 2. To d evelop a droplet drying model to simulate droplet properties during spray drying and a bacterial inactivation model that incorporates the effects of such properties on inactivation rate . 3. To v alidat e the previously developed bacterial inactivation model using a pilot - scale spray dryer and c ompar e the surviva l of Salmonella and Enterococcus faecium duri ng the spray drying process under various processing conditions . 5 2. LITERATURE REVIEW 2.1. Spray Drying P rocess The spray drying process consists o f several key steps : pre - treatment of the feed solution , atomization of the feed solution , mixing of droplets in the hot air stream and subsequent droplet drying, and separation of powder from the drying air (Kuye et al. 2009) . Considerable research has been conducted in an effort to understa nd how these steps impact dryer operation and product quality. Thus, previous research regardin g these steps will now be reviewed along with the most relevant information for the objectives of this thesis. 2.1.1. Feed material pre - treatment The characteristics of the feed material have a significant impact on the drying process and qualit y of the final pow der product. The solids content of a liquid feed is one such critical factor that affects feed rate, droplet and particle size ( droplets are frequently defined a s particles once they have dr ied to the point of solid crust formation) , and overall drying eff iciency. Each food product has an optimal solids content for use as a liquid feed in spray drying which generally range s from 1 0 % (soy protein isolate) to 65 % so lids (coffee creamer) (Armfield Engineering Teaching Equipment 2013; Masters 1972) . This product - specific optimum value is based on the desired final product texture ( increase in solids content leads to increased droplet size ) as well as drying eff iciency (higher solids content leads to high viscosity, which may be difficult to pump and atomize without the use of specialized rotary atomizers ) (Kuye et al. 2009) . Many liquid feed mixtures are conc entrated by evaporation of water , often by boiling the liquid under a vacuum before spray drying to increase the concentration of solids (Rotronic 2015; Ramirez, Patel, and Blok 2006) . 6 In the industry, liquid feeds are typically pasteurized in an attempt to eliminate all pathogenic microorganism s before spr ay drying (Chegi ni and Taheri 2013; Coperion 2015; Scott et al. 2007; Ramirez, Patel, and Blok 2006; Rotronic 2015; Mullane et al. 2008) . However, protecting a pasteurized food from recontamination can be difficult , as environmental bacteria are frequently present in food processing facilities and are extremely difficult to control. Mullane et. al. (2008) studied the environmental prevalence of Crono bacter sakazakii in a powdered milk protein facility in an attempt to better understand how previous powdered milk products have become contaminated (Mullane et al. 2008) . The results showed that all air filter s in the facility were positive for Crono bacter sakazakii , along with swabs from the drying air outlet, which contacted the dried milk powder. Mullane et. al (2007) also completed another similar study to detect and identify Cronobacter sakazakii in a powd ered infant formula facility (Mu llane et al. 2007) . Cronobacter was detected in multiple areas of the facility including the bag - filling platf orm, dryer floor, and packing vacuum. Th e s e stud ies show the difficulties of maintaining a processing environment free of bacterial contaminati on, and the risk of recontamination for liquid feed intended for spray drying after pasteurization. 2.1.2. Atomization L iquid feeds that have been pre - treated are pumped into the atomizer, where the feed is split into small droplets with diameters generally in the range of 50 - 350 µm (Masters 1972; Kuye et al. 2009) . There are two main types o f atomizers used in spray drying. The first is the rotary atomizer, which spins the liquid feed on a disc rotating at high angul ar velocity to break up the flow into small droplets of mean diameter s of 20 - This type of atomizer is capable of atomiz a tion at high feed rates, but is only applicable in dryers with sufficiently large chamber s , as droplets are propelled outward an d must have enough radial space to redirect the droplets 7 away from the wall (Kuye et al. 2009) . The alternative is the pneumatic nozzle atomizer, which uses pressurized gas to disr upt a narrow stream of liquid feed . This produces a con ical spray of small dropl et s with mean diameter s of 15 - , depend ing on the properties of the feed, pressurized gas, and dimensions of the nozzle (Masters 1972) . Thoug h this type of atomizer cannot atomize at feed rates as high as rotary atomizers, they are more common in lab and pilot - scale spray dryers that do not have the required chamber diameter to properly utilize a rotary atomizer. There are two options for the o rientation of atomization within the drying chamber: co - current or counter - current. In co - current atomization, the liquid feed is atomized at the top of the chamber and droplets travel downward in the same direction as the inlet air. In counter - current ato mization, liquid feed is atomized from the lower portion of the chamber in an upward direction , with inlet air being supplied either upwar ds or downwards (Armfield Engineering Teaching Equipment 2013; Jaskulski, Wawrzyniak, and Zbicinski 2015; Jaskulski, Wawrzyniak, . This orientation increases the residence time for particles in the drying chamber , as the particles are sprayed upward, t hen fall downward into collectors after being sufficiently dried . This is useful for feeds with low solids content due to their longer required drying t imes . However, counter - current drying is only suitable for thermally stable products, as particles are m ore likely to burn and undergo quality degradation due to longer exposure to high temperature inlet air . Therefore, most spray dried food products are d ried using co - current atomization (Masters 1972; Kuye et al. 2009) . The size of droplets produce d by the atomizer is a highly variable parameter that is dependent on both atomizer design and operation as well as the properties of the liquid feed being atomized. Several factors can strongly impact the size of atomized droplets. D roplet size 8 decreases proportionally with increased atomizer pressure or rotational speed (using pressure or rotary atomizers, respectively) , and increases proportionally with feed rate and feed viscosity (Kuye et al. 2009) . Because the size of droplets of various materials created under different atomiza tion conditions varies widely and has a large impact on their drying kinetics and powder properties , spray dryer droplet size has been researched extensively. Experimental efforts have provided data regarding droplet size distributions for various spray dr ied products. Li C ari and Potter (1970) measured the distribution of spray dried skim milk particles using a pneumatic nozzle at varying atomizing air pressures, and found average particle diameters of 9.43, 7.67, and 6.10 µm at atomizing pressures of 5.27, 7.03, and 8.79 kg/cm 2 (LiCari and Potter 1970 b ) . However, initial wet droplet size was not measured in this experiment. Zbici n ski, S trumillo, and Delag (2002) reported mean diameter of 44.9 µm for atomized maltodextrin droplets during the drying process using a l aser measuring device (Zbicinski, Strumillo, and Delag 2002) . Spray drying simulation studies often u tilize a distribution of droplet sizes t o assess the effects of variable droplet size on other conditions within the simulation . These simulations frequently use th e Rosin - Rammler distribution for creating a continuous distribution of droplet sizes. This distribution has been found to appl y well to the break - up of flowing liquid in spray dryer atomization (Djamarani and Clark 1997) . Mezhericher, Levy, and Borde (2015) used droplet diam eters of 10 - 138 µm in computational fluid dynamics (CFD) simulations by assuming the diameters obey the Rosin - Rammler distribution to study droplet drying and particle trajectories for a silica suspension (Mezhericher, Levy, and Borde 2015) . Jin and Chen (2009) used the Rosin - Rammler distribution wit h minimum, mean, and maximum diameter s of 100, 200, and 500 µm, respectively, for their study in applying the reaction eng ineering droplet drying 9 approach in CFD spray drying simulations of milk powder (Jin and Chen 2009) . Kieviet and Kerkhof (1995) measured the size of dried maltodextrin particles after spray drying (134 µm mean diameter), then fitted the data to a Rosin - Rammler distribution (Kieviet and Kerkhof 1995) . This met hod allows for the creation of a complete distribution of droplet sizes using a small set of experimental data. Several models of varying complexity have been developed to estimate average droplet size based on atomization and feed properties. Models for p neumatic nozzles often involve combinations of properties like surface tension, density, and viscosity of feed, relative flow rates and velocities of air and feed, and dimensions of the nozzle in order to estimate average droplet size (Kuye et al. 2009; Masters 1972; Dobry et al. 2009) . These models have only been validated as accurate for a few products and can be unreliable without such validation. As the previously described experimental, theoretical, and simulat ed results have shown , droplet size varies widely based on atomization conditions and feed properties , and can be difficult to accurately measure without specialized equipment. In general, the best approach is to obtain droplet size data from the atomizer manufacturer and confirm the r esults for the intended conditions using an appropriate model and data from the literature (Masters 1972) . 2.1.3. D roplet drying The atomizer sprays the droplets into the main cylindrical chamber of the spray dryer, where drying takes place. To create an environment suitable for droplet drying, a ir is filtered, heated to a high temperature (170 - 240°C), and blown into the main chamber using fans (Masters 1972; Ozmen and Langrish 2003; Kieviet et al. 1997) . This swirling a ir creates a vortex of highly convective air that supplies the energy needed to rapidly evaporate the moisture in the atomized droplets. 10 While the inlet air temperature can be precisely controlled, the air temperature will drop rapidly and form a fairly co nstant temperature p rofile once entering the drying chamber. This temperature dr op is due to evaporative cooling of the droplets being dried, as well as heat losses through the walls of the chamber. This temperature drop has been observed in multiple dryin g studies , with differences between inlet and outlet air temperature as large as 132°C (Doyle, Meske, and Marth 1985; Miller, Goepf ert, and Amundson 1972; Birchal et al. 2006; Li C ari and Potter 1970a) . CFD simulations have been helpful in profiling the air temperatures within the drying chambe r , as such temperature profiles can be difficult to accurately measure using experimental methods. This is because of the rapidly changing air temperature s that oc cur near the atomizer, where evaporation from droplets rapidly cools the heated inlet air. Ha rvie, Langrish, and Fletcher (2002) used CFD to simulate spray drying of skim milk and reported the air temperature profile within the drying chamber (Harvie, Lang rish, and Fletcher 2002) . This simulation showed a high temperature (~217°C) where inlet air enters the drying chamber, but rapid cooling as the air moves downward in the chamber. Most of the air inside the chamber range d from 97 - 127°C. Overall, studies in volving measurement of air temperature within the drying chamber agree that temperature decre ases rapidly as air moves away from the inlet, both vertically and radially (Montazer - Rahmati and Ghafele - Bashi 2007; Kieviet and Kerkhof 1997) . This creates zones of varying air temperatures that are experienced b y circulating particles, making predictions of environmental temperature difficult for droplet drying models. After particles hav e dried to the equilibrium moisture level , hot air then carries the dried particles into the cyclone sep aration stage, where th e particles fall into a collector or conveying system, depending on the scale of the operation (Masters 1972) . Drying air exits the cyclone and 11 is filtered before being exhausted to the environment or recycled back into the system to be used again as heating air (Masters 1972) . 2.1.4. Particle residence time Droplets remain in the drying chamber until they reach their equilibrium moisture content , which is dependent on both dryer design and conditions , feed composition, and droplet properties . After reaching t he equilibrium moisture content, particles spend varying amounts of time swirling inside the drying chamber before dropping into a collector (Mezhericher, Levy, and Borde 2015) . Similar to droplet size, particle r esidence time var ies widely based on dryer design, drying conditions, and properties of the liquid feed and droplets . This residence time has been studied using a variety of methods, both experimental and theor etical. Kieviet and Kerkhof (1995) experimentally measured residence time by injecting a tracer material into a maltodextrin solution being pumped into a pilot - scale co - current spray dryer and measuring the concentration of the tracer in the final product over time (Kieviet and Kerkhof 1995) . This resulted in a roughly log - normal distribution of particle residence times with a median of 58.5 s , minimum of less than 3 s and a maximum time of ove r 10 min . However, it was reported that concentration of the tracer became more difficult to measure accurately as treatment time increased and contributed to a high variance overall . This method was not able to correlate residence time with particle size, which varied between ~53 - 250 µm diameter. Zbicinski, Strumillo, and Delag (2002) experimentally tested the residence time of (Zbicinski, Strumillo, and Delag 2002) . Drying a ir temperatures varied fro m 175 - 220°C, air velocities varied from 0.6 - varied from 10% to 30%. These conditions gave a distribution of average residence times, with a 12 minimum of ~2 s and ma ximum of ~5 s . The results also showed that residence time is reduced with increased temperature and air velocity, and increases at higher air to liquid atomization ratio s . Masters (1972) presented a rough calculation to determine the minimum particle resi dence time by assuming it to be equal to the average residence time of air (Masters 1972) . This can be calcu lated by dividing the volume of the drying chamber by the flow rate of air into the drying chamber. This is only a rough estimate of minimum particle residence time, and it was noted that most particles have a much greater residence time than this due to r ecirculating air flow patterns and particles remaining suspended on dryer w alls or in low air velocity sections of the drying chamber. It is also mentioned that dryer designs can range in residence times from 5 s up to several minutes, but for co - current d ryers a normal residence time is in the range of 20 - 40 s. Kuye et. al. (20 09) recommended a set of equations to estimate particle residence times based on feed, droplet, and drying air properties (Kuye et al. 2009) . These equations were used to calculate the residence time of starch particles in a pilot - scale spray dryer and were reported in the range of ~1.5 - 2.5 s . Mezhericher also simulated drying of silica suspension droplets in an industrial - scale spray dryer using computational fluid dynamics (CFD) s oftware (Mezhericher, Levy, and Borde 2015) . Results from this simulation gave an averaged p article residence time in the range of 1.0 - 3.9 s , depend ing on the modeling parameters and initial droplet diameter. The wide range of particle residence times is likely due to a few different factors. Each experimental test was carried out on a unique spr ay dryer, leading to much variability in terms of the size of the drying ch amber, airflow patterns within the chamber, temperature and humidity conditions, droplet size , and droplet composition. These conditions are unique to each test and 13 can greatly impa ct residence times . Additionally, due to the complexity of spray drying as a process, wide distributions can be observed for residence time even within a single dryer. This makes comparisons between dryers difficult and leads to the conclusion that residen ce time should be measured or estimated for each unique system and set of o perating conditions . Despite the complexity of the process, t he operating principles of spray drying are well understood, and th e properties of droplet size, drying temperature, and particle residence time have been well researched. These principles can be used to better understand and model the drying process for individual droplets. 2.2. Droplet D rying Kinetics Modeling 2.2.1. Introduction T he field of drying kinetics seeks to describe complex drying processes using a series of heat and mass transfer equations. Droplet drying kinetics modeling is used to describe attributes of liquid droplets such as temperature, moisture content, crust forma tion, and stickiness during the process of drying int o solid particles . There are several methods used to model droplet drying kinetics , the most common methods being the characteristic drying curve method (CDC), the reaction engineering approach (REA), an d deterministic analytical models (M ezhericher, Levy, and Borde 2010; Mondragon et al. 2013) . The characte ristic drying curve approach assumes that droplet drying occurs in two distinct periods: the constant rate drying period, where the droplet moisture content is a bove a critical moisture which is specific to each feed material, and the falling rate drying p eriod, where the droplet moisture content is below the critical moisture ( Figure 1 ) (Mezhericher, Levy, and Borde 2010) . 14 Figure 1 . Theoretical characteristic dryin g curve and cross - section of a droplet of dissolved solids in water (Mezhericher, Levy, and Borde 2015) . This model is represented in the following form: ( 1 ) ( 2 ) ( 3 ) where X , X eq , and X cr ar e the moisture content , equilibrium moisture content, and critical moisture content of the droplet, respectively, t is time, f is a dimensionless moisture content, A is the surface are of the droplet, h is the heat transfer coefficient, m s is the mass of s o lids in the droplet, evap is the latent heat of vaporization of water, T a is the air temperature, and T wb is the wet bulb temperature. 15 During the constant rate drying period, moisture content is greater than the critical moisture value, and evaporation of moisture is unhin dered and occurs at a constant rate . The t emperature of droplets made of solids suspended in liquids do es not exceed the wet bulb temperature during this stage (Chen and Lin 2005) . However, the temperature of droplets made of solids dissolved in solutions follows a smooth curve that can excee d the wet bulb temperature during this stage (Mezhericher, Levy, and Borde 2015) . When the droplet moisture content reaches the critical moisture level, an initial sol id crust is formed around the exterior of the droplet that inhibits evaporation, and the droplet enters the falling rate drying period (Mezhericher, Levy, and Borde 201 5) . During this period, drying rate decreases proportionally with droplet moisture content due the growth of the dry crust surrounding the wet core which inhibits vapor d iffusion (Cheong, Jeffreys, and Mumford 1986 ; Mezhericher, Levy, and Borde 2008) . The temperature of the particle also increases above the wet bulb temperature in this stage ( Mezhericher, Levy, and Borde 2015) . The particle continues drying in the falling rate period until it reaches the equilibrium moisture content, where mass transfer between the particle and the environment reaches equilibrium. A common assumption when us ing the CDC model for food products is initial moisture content is equal to the critical moisture content, which means the entire drying process occurs during the falling rate period (Woo et al. 2008; Langrish and Kockel 2001) . This as sumption is acceptable since these products generally hav e a very short or non - existent first drying period where droplet temperature cannot exceed the wet bulb temperature , mak ing the CDC model highly suitable (Mondragon et al. 2013) . The reaction engineering approach assumes there is a required activation energy necessary for moisture removal to occur in drying droplets , and considers the vapo r 16 concentration gradient to be the driving force for drying (Mondragon et al. 2013) . This model is represented in the following form: ( 4 ) ( 5 ) where m is the mass of the droplet, t is time, h m is the mass transfer coefficient, A is th e surface area of the droplet, m s is the mass of solids in the droplet, is the interface moisture content fractionality, p v,sat is the saturated surface vapor concentration, T d is the droplet temperature, p v, is the ambient vapor concentration, V is the apparent activation energy, R is the universal gas constant, and T a is the air temperature. Th e activation energy is close to zero when surface moisture is high and increases a s moisture content decreases due to the increased energy required to diffus e moisture through the solid outer crust. This activation energy is specific to each material being dried, making this approach ideal for materials that have already been researched extensively (Woo et al. 2008; Woo , Mujumdar, and Daud 2010; Mezhericher, Levy, and Borde 2010; Chen and Lin 2005) . Deterministic analytical models simultaneously solve continuity, momentum, energy, and species conservation differential equations with initial and boundary conditions deter mined by droplet properties and drying conditions (Mondragon et al. 2013) . Th ese m odels accurate ly reflect experimental data , at the cost of greater complexity than the CDC or REA models . This complexity is due to the moving boundaries of the shrinking droplet surface and the interface between the wet core and solid crust , as well as th e required knowledge of parameters such as particle porosity, thermal and mass diffusivity of droplets, and critical moisture content (Mezhericher, Levy, and Borde 2010; Mondragon et al. 2013) . Due to the complexit y of these 17 models and the computational resources required to us e them , the CDC or REA models are utiliz ed for most applications. A common heat transfer model is typically used for droplet temperature regardless of the moisture content model, following th e form (Woo et al. 2008) : ( 6 ) where m is the mass of the droplet, c p is the specific heat of the droplet material, T d is the droplet temperature, t is time, h is the heat t ransfer coefficient, A is the droplet surface area, T a is the air temperature, T d is the droplet temperature, evap is the latent heat of vapori zation of water, m s is the mass of solids in the droplet, and X is the moisture content of the droplet. Th is model assumes a homogeneous temperature profile throughout the droplet . The heat and mass transfer coefficients used in the heat transfer or drying rate models are calculated using the Ranz - Marshall correlations (Woo et al. 2008) : ( 7 ) ( 8 ) where Nu, Re, Pr, Sh, and Sc are the Nusselt, Reynolds, Prandtl, Sherwood, and Schmidt numbers, respectively. Whil e drop let drying models follow t hese general methods , usage of each model can vary in complexity based on the assumptions that are made, as well as the initial and bounda ry conditions applied to the droplets and their environments . Several of these assumptions a re commonly used in droplet drying kinetics modeling to simplify calculations and reduce computational resource requirements. One such common assumption is temperat ure homogeneity within the droplet . This assumption is based on the Biot number for drying d roplets 18 being very small ( < 0.1 ) due to the diameter of a droplet generally being in the range of 50 - 150 µm (Chen 2005; Chen and Peng 2005) . This assumption significantly simplifies the modeling process at the cost of differentiati ng the temperature profile between the wet core and solid crust . Another common assumption is homogeneous moisture content throughout individual droplet s . While using this assumption is not accurate for droplet s that contain a wet core and solid crust , it opts to use the average moisture content of a droplet in order to simplify the modeling process (Chen and Patel 2007; Che and Chen 2010; Chen 2008; Chen and Lin 2005) . 2.2.2. Experimental m ethods and r esu lts Although m uch of droplet drying modeling is theoretical, there ha ve been numerous attempts at understanding droplet drying kinetics experimentally. Three main methodologies have been used for experimental single droplet drying studies: free - falling dro plets in a tow er, droplets suspended in air using aerodynamic or acoustic fields, and droplets suspended on the tip of a filament (Fu, Woo, and Chen 2012) . Of these, the most commonly used for accurate measurement of temperature and moisture content changes during droplet drying is the filamen t method. Charlesworth and Marshall (1960) developed a methodology using the filament method, which was later used and modified in multiple studies on droplet drying (Cheong, Jeffreys, and Mumford 1986; Charlesworth and Marshall 1960; Lin and Chen 2002; Che and Chen 2010) . T h ese stud ies involve suspending a slurry droplet on a filament within a chamber that supplie s hot drying air . A thermocouple is placed inside the filament to measure the droplet core temperature during drying is measured based on the , and this change in mass of water within the droplet can then be correlated with the moisture c ontent of 19 the droplet . Physical restrictions based on the size of the filament r equire the droplet diameter to be ~1.5 mm or larger , which is substantially larger than droplets created b y spray dryer atomizers. However, this methodology allows for simultan eous collection of temperature and moisture content data during droplet drying, which is highly valuable for the advancement of droplet drying modeling. In this study , droplets containing inorganic salts similarly showed distinct periods of constant temper ature, while dropl ets containing coffee extract had smooth temperature curves wit hout stalling at the wet bulb temperature , indica ting only one drying period (Charlesworth and Marshall 1960) . This supports the commonly used assumption that dissolved solutions of food products have very s hort or nonexisten t constant rate drying periods. Cheong, Jeffreys, and Mumford (1986) u sed the filament method to observe the temperature and moisture content characteristics of drying droplets containing suspended sodium sulfate decahydrate at various ai r temperatures (Cheong, Jeffreys, and Mumford 1986) . The core temperature results at various drying air temperatures showed a general trend upon exposure to air dr ying , droplets initially cooled to the wet bulb temperature. Droplet temperature then rose to the melting point of sodium sulfate decahydrate (~33°C), at which point the core temperature dropped due to absorption of heat by the crystal. C ore temperature th en rose aga in, plateau ing at the drying air temperature. Th ese results are similar to the trend found by Charlesworth and Marshall for droplets containing suspended inorganic materials (Charlesworth and Marshall 1960) . Lin and Chen (2002) used a modified version of this methodology to study the drying kinetics of milk droplets (Lin and Chen 2002; Chen and Lin 2005) . The system was modified by adding a camera to measure the change in droplet weight based on deflection of the filam ent, as well as the change in droplet diameter during drying. The droplets observed in this stud y were of 20 similar diameter to the previous study (~1.5 mm ) but showed substantially different trends in droplet temperature during drying. While droplets contai ning insoluble solids displayed distinct drying periods (droplet core temperature plateau ed at t he wet - bulb temperature, drop ped at melting point of solute, then final ly plateau ed at air temperature), droplets containing dissolved solids displayed smooth s igmoidal curves from wet bulb to ambient air temperature, without indication of temperature plat eaus during drying. This finding also agree s with the results of Charlesworth and Marshall (Charlesworth and Marshall 1960) . When comparing the fit of the REA and CDC models to the experimenta l data collected in this study, the REA had a n overall better fit at the cost of increased knowledge required regarding the activation energy for each material tested. Adhikari, Howes, Bhandari, and Troung (2003) used the glass filament method to observe t emperature and moisture profiles as well as stickiness properties of drying droplets containing carbohydrates and organic acids (Adhikari et al. 2003) . This data was used by Woo et. al (2008) to compare the accuracy of the CDC and REA models (Woo et al. 2008) . The results showed that the CDC model overestimated the drying rate of the droplets in the expe rimental data by inaccurately following a linear drop in drying r ate during the falling rate period. A modified CDC model was proposed to better fit the drying rate curve, which added a shape parameter to the evaporation hindering factor to allow for a non linear change in the drying rate during the falling rate period: ( 9 ) where f is the dimensionless moisture content, X , X eq , and X cr are the moisture content, equilibri um moisture content, and critical moisture contents of the droplet, respectively, and n is the evaporation hindering shape factor. 21 Using this modified model, the drying rate change will be convex if n is less than 1, and concave if n is greater than 1. Thi s parameter should be fit for each material, but it was theorized that convex falling rates are suitable for materials that form a solid crust due to their increased inhibition of vapor diffusion as the crust thickens. T his modified model had a better fit to the experimental data as compared to the standard CDC model , and was comparable to the accuracy of the REA model. 2.2.3. Theoretical m ethods and r esults Droplet drying models have also been used extensively for theoretical p urposes . This research is largely us ed to incorporate droplet drying information into computational fluid dynamics (CFD) models of spray drying systems . Woo et. al. (2008) used CFD simulation of a spray drying system to compare the characteristics of three droplet drying models: CDC, modifie d CDC, and REA (Woo et al. 2008) . The results indicated that the CDC and REA models were similar , while the modifie d CDC model was different from the other models in terms of final moisture content. However, these were only comparisons between the characteristics of the models and cannot be validated, as no experime ntal data for the drying curve of droplets this size ( 19.2 65.8 µm) was collected. In addition, these simulations revealed that var ying ambient conditions in specific regions of the dryer ( air temperature, velocity, and humidity ) had little effect on the drying curves of droplets traveling through the dryer . Mezhericher, Levy, and Border (2015) utilized the CDC drying model in various CFD simulations to study drying properties of droplets containing a silica suspension such as particle residence time, tem perature, and moisture content as a factor of particle diameter, as well as droplet - droplet and particle - particle collisions during the drying process (Mezhericher, Levy, and 22 Borde 2015) . Th ese models estimate that spray dried silica droplets experience an a verage residence time ratio of approximately 3:1:12 for each drying period . This means that a theoretical silica droplet with a particle residence time of 16 s would spend 3 s in the constant rate drying period, 1 s in the falling rate drying period, and 12 s as a dry particle at equilibrium moisture content before exiting the drying chamber . The notably long period of time spent at equilibrium moisture was not observed in previous particle residence time studies. This r atio is likely not entirely accurate for particles containing a dissolved solid solution , however, based on the very short or nonexistent first drying period observed in experimental drying data of these particles. Jaskulski, Wawrzyniak, and Zbicinski (20 15) created a three - dimensional CFD model of a spray dryer using the CDC method to predict agglomeration in maltodextrin and detergent particles (Jaskulski, Wawrzyniak, and Zbicinski 2015; Jaskulski, Wawrzyniak, and 2018) . The Guggenheim - Anderson - de Boer ( GAB ) model was used with previous experi mental data to determine the equilibrium moisture content in the maltodextrin study . The CDC model showed good agreement with experimental data for particle moistur e content of both products . 2.2.4. Conclusions Overall, both the CDC and REA methods have been shown to fit well to experimental data and appear to be good options for modeling droplet drying during spray drying . Previous use of these models suggests that the REA method is preferred for products with properties tha t are well understood and have been extensively researched, while the CDC requires less prior The largest problem with validation of these models i s the lack of experimental drying data for droplets o n the scale of spray dried droplets ( ~50 - 150 µm), due to the difficulty of creating and measuring the properties of such small droplets. 23 Several useful assumptions have been used in droplet drying models for particles made up of dissolved food solids , such as the assumption of homogeneous temperature and moisture content within a particle, and the assumption that food droplets begin the drying process at the ir critical moisture content and do not have a c onstant rate drying period. These assumptions can gre atly simplify the modeling process for food droplet drying. Droplet drying model s combined with CFD modeling can provide valuable estimations of droplet properties like residence time, moisture content, and temperature at all times during the spray drying process. Such properties would be difficult or impossible to measure to the same degree using experimental methods. However, these results should be validated using the closest possible experimental resu lts . 2.3. Bacterial Inactivation Modeling 2.3.1. Introduction Bac terial inactivation models have been extensively researched in the food safety field to predict the survival of pathogenic bacteria for various processing techniques and environmental conditions. Inactiv ation models relate the survival of bacteria within a food to the critical parameters of that food and the environment. These models are represented as primary models, which determine bacterial inactivation over time, and secondary models, which determine the effect of processing condition variables ( temperature, moisture content, surface moisture, etc.) on the inactivation rate parameter in the primary model . Bacterial inactivation rate is often described using decimal reduction times (or D - values) and z - v alues. D - values are defined as the time requir ed for a 1 - log (or 90%) reduction in bacterial population at a given condition , while z - values are defined as the change in a processing condition required for a 1 - log change in D - value. Z - values have been esti mated in previous secondary models for various processing 24 conditions, such as treatment temperature, moisture content, water activity, and surface moisture (Jeong, Marks, and Orta - Ramirez 2009; Casulli 2016) . Impor tant variables within a food or its environment that have been researched for their impact on bacterial inactivation include treatment temperature, water activity (a w ), and humidity (Jeong, Marks, and Orta - Ramirez 2 009; Casulli 2016; Farakos, Frank, and Schaffner 2013; Mattick et al. 2001) . Developing and validating these models allows food processors to better understand their process and be confident in the safety of the food being produced. Since the final moistu re content of spray dried foods is generally very low (~ 2 - 5% wet basis) , the f inal pro duct can be classified as a low - moisture food powder . Other low - moisture foods that have been researched for bacterial inactivation modeling include almonds (Limcharoenchat, James, and Marks 2019; Jeong, Marks, and Orta - Ramirez 2009; Villa - Rojas et al. 2013) , pistachios (Casulli 2016) , wheat flour (Smith et al. 2016) , and milk powder (Lian et al. 2015) , among many others . However, because the beginning product is a liquid solution, spray drying involves highly dynamic moisture and is uni que from many other low - moisture processing techniques. 2.3.2. Spray drying inactivation studies Research related to bacterial inactivation during low - moisture food processing is active and has produced an extensive understanding of processes such as dry roasting , oil roasting, blanching (Almond Board of California 2017) , steaming (Chang et al. 2010; Cenkowski et al. 2007) , chemical immersion (DiPersio , Kendall, and Sofos 2004) , gas treatment (Almond Board of California 2008; Oztekin, Zorlugenc, and Zorlugenc 2006) , and irradiation (Jeong et al. 2012; Osaili et al. 2008; Prakash et al. 2010; Cuervo, Lucia, and Castillo 2016; Karagoz, Moreira, and Castell - Perez 2014) . However, research on the safety of the spray drying process is scarce , and 25 there is much still unknown about bacterial survival during the process. Neverthe less, t he research that has been conducted related to the survival of bacteria during spray drying will be reviewed in the fo llowing section. Li C ari and Potter (1970) studied the survival of multiple strains of Salmonella during spray drying and storage of skim milk powder (Li C ari and Potter 1970 a ; Li C ari and Potter 1970b) . Pasteurized and condensed skim milk was inoculated with Salmonella and dried in a co - current pilot - scale spray dryer equipped with a pneumatic n ozzle. The controlled conditi ons of drying included outlet air temperature ( set at 65.6, 93.3, and 121.1°C ) and particle size controlled by the atomization air pressure (set at 5.27, 7.03, and 8.79 kg/cm 2 ). Reduction in bacteria was quantified in the dried milk as colony forming units per gram of powder ( C FU/g ) , and was found to be within the range of 0. 6 - 4.9 log, depending on the drying conditions and bacterial strain used. Increased temperature proportionally reduc ed Salmonella , but the dried particle siz e had no significant effect on bacterial reduction. While significant reductions were observed for all drying conditions, no conditions were able to eliminate Salmonella . The treated milk powders were also stored at varying temperatures (25, 35, 45, and 55 °C) for u p to 8 weeks to determine the long - term survival of Salmonella . R apid death was observed during the first two weeks of storage, with a reduced rate observed afterwards. In this s tudy , Salmonella was recovered after 8 weeks of storage regardless of storage conditions . Miller, Goepfert, and Amundson (1972) completed a similar study on the survival of both Salmonella and E. coli during spray drying of skim milk, whole milk, whey, whole egg, egg white, egg yolk, and Torula yeast (Miller, Goepfert, and Amundson 1972) . These products were i n oculated with bacteria and dried in a portable spray dryer equipped with a rotary atomizer at various inlet air temperatures (165 and 225°C , giving 93 and 67°C outlet air temperature, 26 respectively ) . T he dried powders were then collected for enumeration of surviv ing bacteria . Skim milk showed a similar reduction in Salmonella compared to the previous study, with spray drying achieving 1.1 - 6.0 log reductions depending on the drying conditions and bacterial strain. H igher temperature s resulted in significantl y lower moisture content in the powdered product, as well as greater reduction of Salmonella . Whey powder had very similar survival to skim milk after spray drying at 225°C (3.5 and 3.3 log reductions, respectively). Doyle, Meske, and Marth (1985) complete d a similar study on the survival of Listeria monocytogenes in nonfat milk during spray drying and subsequent storage (Doyle, Meske, and Marth 1985) . Skim milk was inoculated with L . monocytogenes and spray dried in a portable spray dryer at an inlet air temperature of 165°C (outlet air temperature of 67°C). The dried m ilk was collected, enumerated for surviving Listeria , and additional treated samples were stored for up to 16 weeks at 25°C. The results showed an approximate 1 - 1.5 log reduction in L. monocytogenes due to spray drying , lower than the reduction of E. coli or Salmo nella in skim milk under similar drying conditions (LiCari and Potter 1970 a ; Miller, Goepfert, and Amundson 197 2) . Both strains tested decreased by > 4 log s after 16 weeks at room temperature. Arku et. al (2008) st udied the survival of Cron obacter sakazakii during the spray drying of powdered infant formula (Arku et al. 2008) . Reconstituted skim milk was inoculated with high and low concentrations of Cron obacter sakazakii (~7 and 2 log CFU/g solids, respectively), spray dried at an outlet temperature of 90°C , with t he resulting powder sampled for survivors . Results showed that while the bacterial population significant ly decreased (~2.5 log CFU/g solids), surviving Cron obacter was found in all milk powder samples that w ere inoculated at the high concentration , and in some samples inoculated at the low concentration. These results are 27 similar to previous studies for spray dried products, and it was emphasized that introduction of Cron obacter into the spray drying process must be avoide d. In addition to research on path ogenic bacterial survival during spray drying, a significant amount of research has been conduct ed on the retention of beneficial microorganisms and bioactive materials during spray drying. These materials include various drugs, nutraceuticals, biochemicals, and biologically active materials such as enzymes, proteins, antibodies, and vitamins, which are commonly spray dried to preserve their activity f or a longer shelf - life at low cost (Chen and Patel 2007; Huang et al. 2017) . While the goal of spray drying these materials is to preserve as much of the microbial viability as possible, the res ults found from these studies can still be applied to pathogen inactivation and the field of food safety (Goderska and Czarnecki 2008) . Lievense et. al. (1990) assessed the inactivation of Lactobacillus plantarum during fluidized bed drying by incorporating a drying kinetics model with a therma l inactivation model (Lievense et al. 1990) . The re sults of the study showed that inactivation of L. plantarum was due mainly to dehydration during the initial constant rate drying stage. In the falling rat e stage, when temperature increases rapidly above the wet bulb temperature, thermal inactivation beco mes more impactful than dehydration. Thus, a model was created that determine d the inactivation rate constant for L. plantarum at each time step of drying based on the temperature and moisture content of the fluid. The model parameters were fitted using ex perimental data on the inactivation of L. plantarum under various drying conditions. Although t his model worked well with fluidized bed drying , its applica tion to droplet drying during the spray drying process is limited. 28 Li et. al (2006) created a probiot ic bacteria inactivation model for use in single droplet drying (Li et al. 2006) . This model describes the inactivation of microorganisms w ith first - order reaction kinetics, using the form: ( 10 ) where N is the bacterial load, N 0 is the initial bacterial load, t is time, and k d is the inactivation rate constant. In this equation, the inactivation rate constant k d is temperatu re dependent accordin g to the Arrhenius equation: ( 11 ) where k d is the inactivation rate constant, k 0 is the reference inactivation rate constant, E d is the inactivation energy, R is the un iversal gas constant, and T is the temperature. In addition to temperature dependen cy, the current moisture content is incorporated into the calculation of the inactivation rate constant by using the following equation (Meerdink and VantR iet 1995 ) : ( 12 ) where k d is the inactivation rate constant, k 0 is the reference inactivation rate constant, a and b are fitting parameters, X is the droplet moisture content, E d is the in activation energy, R is the universal gas constant, and T is the temperature. This model was fitted to experimental data for milk droplet drying at air temperatures of 70, 90, and 110°C using the filament met hod. These droplets were inoculated with Bifidob acterium infantis or Streptococcus thermophilus, and survivors were enumerated after the droplets were dried. Since Eq. ( 12 ) fit the bacterial survival data poorly , additional parameters 29 were added to the model in order to make the inactivation rate constant dependent on the drying rate and/or heating rate (Chen and Patel 2007; Li et al. 2006) . T he following equation s were formed : ( 13 ) ( 14 ) ( 15 ) where k d is the inactivation rate constant, k 0 is the reference inactivation rate constant, a and b are fitting parameters, X is the droplet moisture content, t is time, E d is the inactivation energy, R is the universal gas constant, and T is the temp erature. Th e s e equation s for inactivation can be coupled with heat and mass transfer equations to determine the inactivation rate at any given temperature , heating rate, moisture content, and drying rate con dition within a droplet. These models were fitted to the previously mentioned bacterial survival data and compared to see which model had the best fit. Based on this approach, Eq. ( 15 ) , which included parameters for changing drying rate, had the best overall fit. The parameter for heating rate added in Eq. ( 14 ) d id not significantly improve the fit of the model, so it was ignored. For the two probiotic bacteria strains tested, the most relevant parameters for modeling inacti vation were droplet temperature and drying rate. While some research has been done on bacterial survival during the spray drying process, there is still much unknow n. All previous studies involving pathogenic bacterial inactivation have been concerned only with the survival of bacteria in the final powdered product after drying, but little is known about the survival of bacteria remaining within the spray dryer. Addi tionally, no attempt has been made to combine pathogenic bacterial inactivation modeling 30 wit h droplet drying kinetics modeling, which would be highly relevant for ensuring spray drying safety. 2.3.3. Low - moisture inactivation studies As described in the previous section, d roplet temperature, heating rate, moisture content, and drying rate have been the most researched variables studie d for their effect on bacterial inactivation during spray drying. O ther variables such as water activity, process humidity, surface moisture, and food composition have been researched in laboratory settings and found to have significant effects on bacterial inactivation in low - moisture foods (Jeong, Marks, and Orta - Ramirez 2009; Smith et al. 2016) . Therefore, a review of the understanding of each of these variables is important to det ermine their applicability to modeling bacterial inactivation during spray drying. Water activity is defined as the ratio of vapor pressure of water in a food to vapor pressure of pure water , and foods with water activity below 0.85 are generally considere d to be low - moisture foods (Beuchat et al. 2013; Caurie 2011) . Water activity is an important factor in bacterial growth and survival, and growth of Salmonella has been found to be inhibited below water activity of ~0.92 (Ste ncl 1999) . Though inhibited under these conditions, Salmonella is capable of surviving 8 weeks or longer in low - moisture foods (Lian et al. 2015; Farakos, Frank, and Schaffner 2013) . Additionally, i ts thermal resi stance has been found to increase with decreasing water activit y in a variety of low - moisture foods . Studies using multiple Salmonella serovars (Mattick et al. 2001) , Salmonella in whey protein powder, non - fat dry milk, peanut meal, cocoa powder, and wheat flour (Farakos, Frank, and Schaffner 2013) , and Salmonella in almond kernel flour (Villa - Rojas et al. 2013) all found that thermal resistance increased significantly with d ecreasing water activity under isothermal conditions. Thermal resistance of 31 Salmonella in powdered foods is extremely high at water activities of 0.2 and below (Archer et al. 1998) . This i s in the lower range of water activit y that s pray dried powder s reach during drying, so even though th ey begin the process as a liquid at very high water activity, this information is relevant for spray dried powders (Sten cl 1999) . D ynamic moisture conditions of a food product can also influence bacterial inactivation rates . M odels that take complex moisture phenom ena (surface moisture content, pre - treatment desiccation rate, drying rate) into account can significantly improve the accuracy of previous models that only consider overall moisture content of a food product . Jeong , Marks, and Orta - Ramirez (2009) created a bacterial inactivation model with an added parameter to account for surface moisture rather than overall moisture content of almonds being roasted in a moist - air convection oven (Jeong, Marks, and Orta - Ramirez 2009) . Smith and Marks tested the effect of rapid desiccation (0.6 to 0.3 a w ) and hy dration (0.3 to 0.6 a w ) just before isothermal treatment on thermal resistan ce of Salmonella in wheat flour (Smith and Marks 2015) . Neither desiccation nor hydration had a significant effect on thermal resistance. However, these results may not be applicable to spray drying as droplets begin the drying process at a much higher water activity than 0.6, and the desiccation process occurs during treatment in spray drying as opposed to before treatment as in this study. As mentioned previously, Li et . al. found that a model containing droplet drying rate ( 15 ) had a better fit to experimental data of milk drying (Li et al. 2006) . The spray drying of droplets yields highly dynamic moistur e conditions during both the constant and falling drying rate s tages. Therefore, the impact of dynamic moisture conditions on thermal resistance of Salmonella will likely play a large role in the modeling of Salmonella inactivation during spray drying. 32 Sol ids content of liquid foods should also be considered for poten tial effects on inactivation of Salmonella . I ncreased solids content has been shown to increase Salmonella resistance to thermal inactivation in milk concentrates at isothermal conditions (Dega, Amundson, and Goepfert 1972) . This is lik ely correlated with the effect of increased resistance at low moisture, as a higher solids content in the feed solution will lead to lower overall moisture content in the milk. Because liquids intended for spray drying frequently undergo an evaporation pro cess to concentrate the solids within the liquid, understanding the effect that the solids content ha s on moisture content and bacterial resistance could be beneficial (Kuye et al. 20 09) . 2.3.4. Surrogate organisms Surrogate organisms ar e non - pathogenic organisms with similar characteristics to a pathogen of concern. In research involving bacterial inactivation, this means that a surrogate organism has similar inactivation kinetics to the pathogen, and so it can be used to predict the inactivation of the pathogen in various processes. Once an organism has been determined to be a suitable surrogate for a pathogen, food manuf actur ers can validate their processes by introducing the surrogate into a product, determining its survival through the process, and finally predict ing the survival of the pathogen of concern based on the survival of the surrogate . This way the manufacture r nev er has to purposefully contaminate their process with a pathogen, which would cause major safety risks (Kopit et al. 2014) . Enterococcus faecium ( E. faecium) is a commonly used surro gate organism for Salmonella Enteritidis phage type 30 (SE PT30) in low - moisture foods due to its similar thermal tolerance (Kopit et al. 2014) . Its inactivation kinetics and su itabi lity as a surrogate have been tested in several low - moisture food products, including almonds (Jeong, Marks, and Ryser 2011) , pet food (Cey lan and Bautista 2015) , and an extruded meal mixture (Bianchini et al. 33 2014) . While E. faecium has been determined to be a suit able surrogate for Salmonella in a variety of similar food products and processes, it should still be validated for its applicability to spray drying before it is implemented in a commercial process. 2.3.5. Conclusion Many models are available to predict bacteria l inactivation for various microbial reduction processes. Each model has pros and cons, and model selection is an important step in accurately predicting bacterial inactivation during droplet drying . While there are many factors that can im pact bacterial i nactivation during spray drying, the literature has indicated a few critical variables related to droplet conditions: droplet temperature, heating rate, moisture content, and drying rate. By fitting a model containing these variables to exp erimental inacti vation data, the optimal model for predicting inactivation in a drying droplet can be de veloped . 2.4. Summary Spray drying is a n efficient and unique food manufacturing technology , but its efficacy for pathogenic bacterial inactivation is not fu lly understood. While knowledge about spray dry er design and operation allows for a general understanding of the process, dryer properties can differ greatly and will have a large impact on drying conditions that should be evaluated for each unique process . Similarly, whi le bacterial inactivation during various processes has been well - researched, the survival and inactivation of bacteria during the spray drying process has some significant knowledge gaps. Understanding these inactivation kinetics through a combination of b oth bacterial inactivation and droplet drying modeling can lead to an integrated model that predicts the inactivation of pathogens during spray drying . Such a model can be used to improve dryer design, operation, and safety of spray dried foods. 34 3. MODELING BACTERIAL INACTIVATION KINETICS DURING THIN - FILM DRYING OF SOY PROTEIN POWDER SOLUTION 3.1. Introduction Obtaining data for bacterial inactivation as a function of drying time and temperature is the first step in develop ing a complete process model for predicti ng bacterial survival in a spray drying system . However, due to the complexity of the spray drying process, it is not feasible to locate and retrieve particles of specifi c residence times while the system is running . Therefore, a simulate d spray drying pro cess that can be more easily controlled and accessed during operation is imperative to collect such data. In t his study, a convection oven was used to simulate spray dr ying conditions , such as air temperature, humidity, and velocity. Samp les of droplets in oculated with Salmonella were placed inside the oven for specified times under controlled conditions to obtain data representing bacterial inactivation during drying. T his simulation attempted to re plicate the conditions of an actual spra y drying process e xperienced by a droplet , with the inactivation data collected represent ing inactivation within droplets during spray drying. 3.2. Objective s The objective of this study was to quantify the inactivation kinetics of Salmonella under simulated spray drying conditi ons. 3.3. Materials and Methods 3.3.1. Spray dryer air temperature measurement To determine proper treatment temperatures for the spray dryer simul ation, the air temperature profile within a pilot - scale spray dryer was measured during operation. These measurements we re carried out using an FT80 Tall Form Spray Drier (Armfield Inc., Clarksburg, NJ) ( Figure 2 ). This dryer includes an air heater that supplies inlet air at temperatures in the 35 range of 25 - 250°C. Air pressure within the drying chamb er was controlled by both the inlet and exhaust fans, which were set to co nstant speeds to maintain a slight negative pressure in the drying chamber (0 to - 1 mbar). A pneumatic nozzle was used to atomize feed droplets from the top of the drying chamber in a co - current manner. The compressed air in the nozzle used to atomize the liquid feed in the nozzle was set to 0.8 bar for all experiments, giving an average droplet diameter of ~55 µm in a hollow cone arrangement (DeMaria 2019) . This nozzle was surrounded by a shield that allowed inlet air to enter the main drying chamber in an annular fashion around the nozzle. Sensor s built into the dryer measured and displayed the current inlet and exhaus t air temperatures, exhaust air relative humidity, chamber air pressure, and differential air pressure between the cyclone and chamber. Figure 2 . FT80 Tall - form Spray Drier housed in the Biosafety Level 2 pilot plant facility at Michigan State University. 36 This dryer was fitted with an ultra - low flow variable - flow peristaltic pump ( Cole - Parmer, Vernon Hills, IL) to pump the liquid concentrate into the dryer nozzle. The variable speed on the pump was set to 38 on a scale from 0 - 100, which provided a flow rate of ~10 mL/min to the nozzle. This low speed was chosen to allow for maximum drying while maintaining a steady stream into the nozzle. Three K - type thermo couples were taped to the drying chamber walls of the pilot - scale spr ay dryer at distances of 7, 45, and 90 cm from the chamber ceiling. The spray dryer was then operated at an inlet air temperature 180, 200, and 220°C (±1°C) using filtered water as the dr ying medium with a feed rate of ~10 mL/min and nozzle pressure of 0.8 bar. These conditions replicate those used in the pilot - scale spray drying study (chapter 5 ), with the exception of using water instead of soy prote in isolate (SPI) solution , which was done to prevent powder deposition on the thermocouples that could cause errors in data collection. The dryer was run under these conditions for 20 min, which was sufficiently long for the temperature to stabilize, with measurements recorded every 2 s. Data from the final 200 s of each inlet air temperature were used for statistical analysis, as the air had reached equilibrium and represents the conditions of the dryer after the appropriate warm - up period. 3.3.2. Materials and p ropertie s Salmonella Enteritidis Phage Type 30 was chosen for all experiments because of its frequent usage in many low - moisture food safety studies (Smith and Marks 2015; Cuervo, Lucia, and Castillo 2016; Lim charoenchat et al. 2018; Shachar and Yaron 2006; Limcharoenchat, Jame s, and Marks 2019; Danyluk, Uesugi, and Harris 2005) . This strain was originally obtained from Dr. Linda Harris (University o f California Davis) and kept in vials at - 80 °C in Tryptic S oy Broth (TSB) ( Difco, Becton Dickinson, Sparks, MD) containing 20% glycerol . After two 37 24h/37°C transfers in TSB, this strain was used to inoculate unflavored SPI (NOW Foods, Bloomingdale, IL), which was stored at 4°C in a sealed canister. A 10% w/w SPI s lurry was created by adding 90 mL of water to 10 g of unflavored SPI and blended in a laboratory blender (Waring, Torrington, CT) for 5 min ( Figure 3 ). This was done to create a slurry similar to the liquid feed used in industrial spray drying (Miller, Goepfert, and Am undson 1972) . The slurry was then stirred at 200 RPM on a stir plate for 24 h to fully hydrate the protein, resulting in a more homo genous mixture without phase separation (Tang and Li 2013) . On the day of testing, 6 mL of the inoculated TSB culture (~10 9 CFU/mL) was pipetted into the slurry and stirred at 200 RPM for 5 min to achieve a population of ~10 7 CFU/mL). Figure 3 . Separation of a 10% w/w soy protein isolate (SPI) solution into watery and paste - like phases a fter blending. 38 3.3.3. Lab - scale oven simulation For each sample, 0.04 mL of inoculated SPI slurry was pipetted onto the surface of a nylon mesh filter dis c (25 mm dis c diameter, 160 µm mesh opening size, 43% open area, 109 mesh count, 80 µm thread diameter , part number CMND - 160 ) (Component Supply Company, Sparta, TN) and spread using a plastic spreader to allow maxim um absorption into the mes h openings . This amount of inoculum completely filled the voids in the mesh with minimal extra inoculum . Therefore , the disc can be considered a single layer of droplets of inoculated SPI slurry with a diameter equal to the void size (160 µm ), which approx imates the size of a droplet formed by a pneumatic nozzle atomizer used in spray drying. Th e disc was placed on a small wire rack and clipped into place to allow maximum contact between the air and disc ( Figure 4 ) . Treatment was ca rried out in a lab - scale, computer - controlled, moist - air convection oven under controlled temperature and air velocity conditions. Humidity was not controlled by steam injection for this experiment , as the humidity conditions within the oven ( <1% relative humidity) were similar to those inside the pilot - sca le spray dryer used in chapter 5 . The disc and cage w ere placed into a lab - scale convection oven with the surface of the disc parallel to the direction of airflow for the treat ment time (0 - 60 s ) , attempting to replicate the conditions experienced by drying droplets with varied residence times ( Figure 5 ) . 39 Figure 4 . Nylon mesh on a wire rack before inoculation and drying in a c onvection oven (top), side view cross - section representation of droplets suspended in a single - layer within the nylon mesh (bottom). 40 Figure 5 . Nylon mesh attached to wire rack placed inside a convection oven sampling port. Arro ws indicate the direction of heated airflow. After heating , the disc was removed from the oven and placed into a plastic bag containing 4 mL of chilled 0.1% buffered peptone water (BPW) (Difco) to rapidly chill the disc and prevent any further bacterial i nactivation. Bags were then sonicated for 2 min to recover the bacteria ( FS30, Fis her Scientific, Waltham, MA) , serially diluted, and plated on modified Tryptic Soy Agar (Difco) supplemented with 0.6% (w/v) yeast extract (Difco) , ferric citrate (0.05%) (Si gma Aldrich, St. Louis, MO) , and sodium thiosulfate (0.03%) (Sigma Aldrich ) , also known as mTSA . A fter 48 h of incubation at 3 7 °C, all black colonies were counted as Salmonella (Jeong, Marks, and Orta - R amirez 2009) . After the experiment , meshes were sanitized by immers ion in a 75 % ethanol solution for 30 min before reuse . 41 Initial temperature conditions for the convection oven were set at 180, 190 or 200°C ( referred to as high temperature treatment s ) with treatment times of 0, 5, 10, 15, 20, and 25 s . These temperatures were chosen because they are common inlet air temperatures used in spray drying (Armfield Engineering Teaching Equipment 2013; LiCari and Potter 1970 a ; Tang and Li 2013) . However , as discussed in s ection 2.1.3 , air temperature rapidly drops upon entering the drying chamber. This lower temperature air is the environment to which drying droplets are exposed in the drying chamber, so these high temperature treatments do not accurately describe the environment for such droplets. To account for this , a second experiment was condu cted with oven temperatures set at 80, 95 and 110°C (referred to as low temperature treatments) and extended treatment times of 0, 10, 20, 30, 40, 50, and 60 s in order to achieve meaningful inactivation for modeling purpose s. These temperatures were chose n based on the results discussed in s ection 3.4.1 . 3.4. Results and Discussion 3.4.1. Spray dryer chamber temperature results While the inlet air temperatures used in this study were in the range of 180 - 220°C, air temperatur e s inside the drying chamber were substantially lower ( Table 1 ) . Drying chamber temperatures with inlet air temperature s of 180 - 220°C were 98 - 136°C, depending on the location within the chamber. D ifferences in inle t air temperature s created proportionally smaller differences in air temperature within the dryer. Thus, a 40°C difference in inlet air temperature (between 180°C and 220°C inlet air temperature) led to a ~28°C difference in air temperature within each loc ation in the dryin g chamber. This temperature drop is due mostly to evaporative cooling due to droplet drying, as well as environmental heat loss through the chamber walls . The magnitude of the drop between the inlet and outlet temperatures observed in th is dryer i s simila r 42 to that found in previous studies that compar ed inlet and outlet air temperatures of portable and pilot - scale spray dryer units (LiCari and Potter 1970 a ; Doyle, Meske, and Marth 1985; Miller, Goe pfert, and Amundson 1972; Birchal et al. 2006) . The general trend between chamber locations shows that air temperature is lowest at the top of the drying chamber and increases moving downward in the chamber. This was as expected since the greatest amount of evaporative cooling occ ur s where the nozzle meets the inlet air, near the top of the chamber. Variability in temperature at each location was small, indicating that regions of air temperature are constant . While the drying chamber is the most important area within the spray dryer for temperature profiling, further experimentation could be done to measure air temperature in each relevant location within the dryer (primary/secondary collector, cyclone, exhau st). Table 1 . Average d rying chamber air temperature ( °C ± standard deviation ) measured at 7, 45, and 90 cm from the chamber ceiling (top, middle, bottom , and average of entire chamber, respectively) during normal spray drying oper ation at inlet air temperatures (T inlet ) of 180, 200, and 220°C. T Inlet Top Middle Bottom Average 180 98.7 ± 1.3 A * 105.0 ± 1.5 B 108.3 ± 1.9 C 104.0 ± 4.3 200 114.7 ± 1.1 A 119.6 ± 1.6 B 123.4 ± 1.3 C 119.3 ± 3.8 220 126.3 ± 2.3 A 132.3 ± 1.7 B 136.0 ± 2.1 C 131.6 ± 4.5 *Within a row, means with common sup 0.05). Th ese results show that droplets experience constantly changing air temperature s while the air currents carry droplets within the drying chamber . Because of this, tracking air 43 temperature aroun d a droplet to predict bacterial inactivation over time is difficult without a complex CFD model. The low - temperature treatment was carried out using oven temperatures of 80, 95, and 110°C which were representative of the temperature profile within the dry ing chamber with inlet air at 180°C. Further experiments could repeat the methodologies described previously using oven temperatures in the range of 110 - 136°C to gather data for spray drying with inlet air temperature up to 220°C. 3.4.2. Thin - layer drying droplet inactivation results High - temperature treatment showed significant inactivation of Salmonella over 25 s ( Figure 6 , Table 2 ) . However, there was n o significant difference ( P > 0.05) between inactivation rat e at temperatures of 180, 190, and 200°C with some samples at 15 and 20 s , and all samples at 25 s being below detection limit s ( 3.4 log CFU/g) . Samples were visibly dry after 5 s and were brittle after 10 s regardless of the treatment temperature. This ob s ervation indicates that the falling rate drying period is very short for these droplets, with most of their treatment time spent as a dry particle at equilibrium temperature. 44 Figure 6 . Survival of Salmonella Enteritidis PT30 in soy protein isolate inoculated on nylon mesh disc after low (80 - 110°C, top) and high - temperature (180 - 200°C, bottom) treatment in a convection oven. 0 1 2 3 4 5 6 7 8 9 0 10 20 30 40 50 60 Survivors (Log CFU/g) Time (s) 80°C 95°C 110°C 0 1 2 3 4 5 6 7 8 9 0 10 20 30 40 50 60 Survivors (Log CFU/g) Time (s) 180°C 190°C 200°C 45 Table 2 . D - values (± 95% confidence intervals) for Salmonell a Enteritidis PT3 0 in soy protein isolate inoculated onto nylon mesh discs treated in a convection oven at 80 - 200°C. Air temperature (°C) D - value * (s) 80 17.2 ± 3.1 A 95 13.8 ± 2.8 A 110 8.0 ± 3.2 B 180 4.6 ± 1.3 B 190 4.9 ± 1.6 B 200 5.2 ± 3.4 AB *Within a column, means 0.05). Only one data point was above the limit of detection at 20 s with none found at 25 s. This is due to the extreme conditions causing more rapid inactivatio n than expected, as well as a high limit of detection. Due to the small amount of inoculum used to inoculate each sample, a comparatively high dilution factor was required to produce enough liquid for plating, and thus the limit of detection is quite high using this methodology ( 3. 4 log CFU/g ). This issue could be solved in future experiments by treating multiple inoculated meshes as a single sample to increase the amount of inoculum treated per sample , and thereby decrease the limit of detection. Low - temperature treatment similar ly showed significant bacterial inactivation during 60 s ( Figure 6 , Table 2 ) . While D - values are reported assuming a log - linear inactivation model, the data suggest that there could be a decrease in inactivation rate after 40 s of treatment . This tailing e ffect could be further investigated by extending the treatment time beyond 60 s . While the population decreased below the limit of detection at 110°C after 40 s , survivors were recovered from sample s at 80 and 95°C after 60 s and could potentially persist longer . Similar to the high - 46 temperature treatments, meshes were visibly dry and were brittle after treatment times of 10 - 20 s regardless of treatment temperature. Based on the inactivation data, a ir temperature was a significant factor ( P 0.05) affecting the inactivation rate of Salmonella in SPI solution inoculated on the nylon mesh ( Table 2 ) . The D - values at various air temperatures can be used to represent the inactivation of bacteria in droplets in various temperature regions within a spray dryer, which can be utilized for pred icting the dynamic inactivation rate during spray drying. Regarding source error , v ariability of the data is fairly high due to the very short treatment time s including the time required to remove a samp le from the oven to stop inactivation by chilling the mesh . Small differences (1 - 2 s) in the time taken to remove samples could cause substantial differences in inactivation due to the relatively short treatment time . Ano ther potential source of error usin g this methodology may come from the contact between the inoculated nylon mesh and the metal rack used to hold the mesh inside the oven. Heat transfer between this metal rack and the mesh is different than th at between th e air and mesh , and thus any portio n of the mesh in contact with the metal likely had a different bacterial inactivation rate than intended. While this area was relatively small compared to the surface area of the entire mesh, an improved experimental desi gn could ensure that the inoculated portion of the mesh disc is only in contact with air. Due to the miniscule amount of liquid involved in this experiment, data regarding changes in moisture content data could not be collected. Obtaining accurate measurem ents of such small changes in mass was not possible using the nylon mesh approach, as the changes in mass (< 0.04 g) between a wet and dry sample were too small to accurately measure. This difficulty is similar to the limitations of droplet drying studies using the glass filament method pre viously described 47 in s ection 2.2.2 . Future experiments could involve drying multiple meshes at a time to increase t he combined mass of each sample and make changes in moisture content more measurable. 3.5. Conclusion In this study, air temperature within the pilot - scale spray dryer chamber w as measured to profile the temperature distribution within the dryer . An experimental methodology for measuring the inactivation of Salmonella within drying droplets was developed a nd tested to measure inactivation at varying air temperatures. Consequently, the decimal reduction time and the temperature de pendence for Salmonella were successfully quantified with the simulated spr ay dr ied droplets . 48 4. SIMULATED DROPLET DRYING KINETICS AND APPLICATION OF BACTERIAL INACTIVATION MODELS 4.1. Introduction While both droplet drying kinetics and bacterial inactivation modeling have been researched extensively, very little work has been done on the combination of the two modeling of bacterial ina ctivation occurring within drying droplets . In order to find ou t how best to model such processes, multiple models w ere tested for their fit to the experimental data collected in c hapter 3 . These models var ied in the drying droplet variables (droplet temperature and moisture content) that could impact bacterial inactivation . Ideally, simultaneous inactivation kinetics and drople t drying experimental data could be collected and used to identify the most relevant dr ying kinetics parameters that impact inactivation. However, collection of such data (droplet temperature and moisture content ) for atomized droplets is difficult , and ex perimental efforts to measure such values have not been successful for droplets smaller than ~1 mm. Therefore, drying models that have been previously validated in the literature based on data from these large - scale droplet drying experiments w ere use d to develop a simplified heat - mass transfer model for an ideal droplet representative of th ose created during spray drying. The data generated from this model w ere then combined with the bacterial inactivation data collected in chapter 3 to create an inactivation model that could account for the effect of droplet dryi ng parameters on inactivation rate. 4.2. Objective s The objective of this study was to simulate droplet drying kinetics data using previously validated drying models and use the data to develop a bacterial inactivation mod el that incorporat es the effect of drop let drying parameters on inactivation rate . 49 4.3. Materials and Methods 4.3.1. Droplet drying modeling methods The CDC model described in Eq. ( 1 ( 3 ) was used for modeling droplet drying due to its relative simplicity com pared to other models as well as its use in previous droplet drying modeling studies , where it was found to fit experimental data well. The standard CDC model was utilized in this approach as opposed to the modified CDC model. This model was chosen because the modified CDC model was shown to have mixed results regarding improvement of droplet drying models , and t herefore the simpler option in the standard CDC model was chosen. Several assumptions were utilized to make the simulated droplet drying model poss ible. The appropriate use and justification for these assumptions from the literature can be found in section 2.2 . First, t he initial droplet moisture content was ass umed to be equal to the critical moisture value at which crust formation begins. Temperature and moisture content profiles within individual droplets were considered to be uniform , and the environmental drying variables (air temperature, relative humidity, wet bulb temperature ) were kept constant. This differs from d roplet drying models that utilize CFD modeling , as the surrounding environment conditions constantly change in models for full - scale spray dryers. However, in a previous study no significant dif ference in drying kinetics was observed based on the use of co nstant or varying dryer conditions , such as air temperature, humidity, and velocity , so this assumption can be used for modeling a simulated drying experiment in an oven (Woo et al. 2008) . Additionally, while heat capacity and heat of vaporization of water within a droplet change with temperature, they were kept constant for this modeling process to simplify the model and because this detail was not noted in previous studies on droplet dryin g models. Finally, the heat transfer coefficient used 50 for the convection oven was taken from a previously published study using the same oven , but a flat plate rather than a n ellipso idal surface for estimation (Garcés - Vega 2017) . Critical moisture conten t was set at the initial moisture content, of 9 kg H 2 O/kg solids for a 10% w/w solids solution of soy protein isolate. Equilibrium moisture content was set at 0.07 kg H 2 O/kg based on the average equilibrium moisture content of soy protein powder dried in t he pilot - scale spray dryer described in chapter 3 . Relative humidity was set to 1%, based on the humidity measurements done in the lab - scale oven experiment in chapter 3 . The density of the feed solut ion was determined and used to calculate both the mass of a droplet as well as the mass of solids within a droplet. Wet bulb temperature within the drying chamber was calculated based o n the air temperature and relative humid ity within the oven using the following equation (Stull 2011) : ( 16 ) where T wb is the wet bulb temperature, T a is the air temperature, and RH is the relative humidity. The remaining parameters used in the droplet drying model are listed in Table 3 . 51 Table 3 . Boundary and initial conditions used in the simulated droplet dryi ng model. Parameter Value Air temperature (°C) 80 - 20 0 Droplet diameter (µm) 1 0 - 320 Critical moisture content (kg H 2 O/kg solids) 9 Equilibrium moisture content (kg H 2 O/kg solids) 0.07 Relative humidity (%) 1 Density of feed solution (kg/m 3 ) 1044 Mass of droplet (kg) * 4.37 10 - 12 Mass of solids in droplet (kg) * 1.97 10 - 13 Heat of vaporization of water (J/kg) * 2.43 10 6 Heat capacity of water (J/kg*K) 4120 Heat transfer coefficient (W/m 2 * K) 104.5 *Value given for a droplet with 16 0 µm diameter Using the parameters described above and Eq. ( 1 ) and ( ( 6 ), the system of ordinary 2018b (MathWorks, Natick, MA) (Appendix A) . This gave simu ltaneous moisture content and temperature data for a simulated droplet under the given conditions. 4.3.2. Bacterial inactivation modeling methods Drying droplet simulations were carried out for each condit ion used in chapter 3 to deter mine survival of Salmonella in a convection oven. Each bacterial survival data point was matched with the temperature and moisture conte nt of a simulated droplet under the same 52 conditions at that time point , which allowed for inactivation model ing as a fun ction of droplet temperature and/or moisture content. The primary model used in this study was the log - linear bacterial survival model ( Eq. ( 17 ). ( 17 ) where N(t) is the bacterial load at time t , N 0 is the initial bacterial load, t is time, and D is decimal reduction time. Multiple secondary models were tested to determine the best - fitting model fo r bacterial inactivation within drying droplets. These models are similar to th e modified MSU model for inactivation of Salmonella during moist - air convection heating , which included a parameter for surface moisture proposed by Jeong et. al (Jeong, M arks, and Orta - Ramirez 2009) . The variables used in these models are droplet temperature , moisture content , and the combina tion of the two ( Eq. ( 18 - ( 20 ) . ( 18 ) ( 19 ) ( 20 ) where D Td , D X , and D Td,X are the decimal reduction time s at droplet temperature T d , moistu re content X , and both droplet temperature T d and moisture content X , respectively. D ref is the decimal reduction time at reference droplet temperature and moisture content, T ref and X ref . z Td and z X are the changes in droplet temperature and moisture co ntent, respectively, required to enact a 1 - log change in decimal reduction time. 53 Reference values for temperature and moisture content ( T ref and X ref ) were set to 77°C and 1 kg H 2 O/kg solids , respectiv ely . Each model was fitted to the experimental data usi ng the (Appendix A) , which generated parameter estimates , parameter uncertainty, and fit statistics for the model. 4.3.3. Model evaluation and selection Before t esting the fit of the models described in Eq. ( 18 - ( 20 ) , the scaled sensitivity coefficients (SSCs) of each model w ere plotted to determine whether the p arameters were able to be estimated separately. Models with SSCs that were large ( maximum SSC > 5 % of the sc ale of the dependent variable) and uncorrelated were deemed acceptable for parameter estimation. In the case of models where the scale of SSCs was to o low to simultaneously estimate parameters, parameters were estimated individually . This was done by setti ng the values of parameters with S SCs deemed too small to a range of fixed values to estimate and determine the other parameter values at the minimum root - mean squared error ( RMSE ) as the best fitting estimates. The predicted inactivation data generated fr om these models were fitted to the experimental inactivation data collected in chapter 3 to determine the fit of each model, and ultimately determine the optimal model for the droplet drying process. Model s were evaluated for th eir fit by calculating the RMSE : ( 21 ) The RMSE is a measure of how well a model predict s the trends present in the observed data , with a low RMSE indicat ing that the model fits the data well. In predictive microbiology, a RMSE of approximately 1 - log CFU/g or less has previously been deemed acceptable when the observed data yields a ~5 - log CFU/g reduction (Farakos et al. 2014; Casulli 2016) . 54 The Akaike Information Criterion (AICc) was used to determine the most likely correct model for the data provided. This criterion is improved by the goodness - of - fit of the model and penalized based on the number of p arameters included in the model, with the lowest score indicating the best model . The AICc for each model was compared and used to determine the most likely correct model for bacterial inactivation during droplet drying. 4.4. Results and Discussion 4.4.1. Droplet dry ing simulation results The standard CDC drying model described by Eq. ( 1 ( 3 ) and the initial conditions described in section 4.3.1 w ere used to simulate the temperature and moistu re content of drying droplets using controlled air temperatures from the thin film inactivation experiment ( Figure 7 ) . This model creates temperature and moisture c ontent curves , which converge at the air temperature and equilibrium moisture content values ( Figure 7 ). Various droplet sizes were simulated to illustrate the distribut ion of droplet sizes created by the atomizer and the effect of droplet size on drying time, but only droplets of 160 µm diameter were used for inactivatio n modeling , as that was the droplet size contained within the thin film in the convection oven drying study. As expected, the time required to reach equilibrium moisture content decrease d as the air temperature increase d and droplet size decrease d . Time f or a 160 µm diameter droplet to reach equilibrium was ~25 and 15 s at air temperatures of 80 and 200°C, respectively. This gives an approximate range for the drying time of a similarly sized droplet in a spray dryer with an inlet air temperature of 200°C , as such a droplet wou ld be very briefly exposed to 200°C air after being atomized, then a range of air temperatures between 80 and 200°C afterwards. 55 Figure 7 . Droplet temperature ( T d ) and moisture content ( X ) of simulated drople ts of diameter 10, 20, 40, 80, 160, and 320 µm at air temperature s of 80°C (top) and 200°C (bottom) using the drying model described in section 4.3.1 . 56 4.4.2. Inactivation modeling Scaled sensitivity coefficient s were pl otted for each model tested for their correlation and scale . While none of the parameters were correlated with one another, the scale of the sensitivity of both z T and z X were too small to be accurately estimated simultaneou sly with the other parameters in all the models tested ( Figure 8 ) . This was due to the rapid drying of the droplets within the thin film layer and comparatively slow rat e of bacterial inactivation , causing the temperature and moisture content of the droplets to r each equilibrium before sufficient levels of inactivation w ere achieved to determine each model sensitivity to the parameters. Therefore, z T and z X were estimated individually by fixing the other parameters in each model, and thus all parameters were suc cessfully estimated for each model being tested ( Table 4 ). Figure 8 . Scaled sensitivity coefficients and predicted log reductions for Eq. ( 17 ) and ( 20 ) us ing an air temperature of 80°C, and droplet diameter of 160 µm after optimizing parameter estimates. 57 Table 4 . Parameter estimates and model evaluation for secondary models of Salmonella inactivation in drying soy protein isolate dr oplets , using T ref = 77°C and X ref = 1 kg H 2 O/kg total . Equation Parameter Estimate * RMSE (log CFU/g) AIC c ( 18 ) D ref (s) 14.7 ± 1.1 0.67 150.5 z T (°C) 174.7 ± 20. 2 ( 19 ) D ref (s) 13.1 ± 1.6 1.01 209.4 z X (kg H 2 O/kg solids) 22.0 ± 24.5 ( 20 ) D ref (s) 14.8 ± 1.1 0.66 148.4 z T (°C) 170.9 ± 20.1 z X (kg H 2 O/kg solids) 17.3 ± 15.5 * Error represented as 95% confidence interva l for the parameter estimate. Parameter estimates for both z T and z X in all evaluated models were large compared to the range of droplet temperatures and moisture contents observed in the drying droplet simulations. This could indicate that Salmonella is not very sensitive to changing temperatures or moisture levels . Another possib le explanation is that the expected decrease in thermal resistance of Salmonella due to increasing droplet temperatures is effectively negated by the increased resistance due to decreasing moisture content. This would explain the general linearity of the inactivation data even unde r dynamic temperature and moisture conditions for treatment times from 0 - 60 s ( Figure 9 ) . However, based on trends toward negat ive residuals in the middle treatment tim es (15 - 40 s) and positive residuals at the end of treatment (50 - 60 s) illustrated by Figure 10 , it appears that the model could be further improved . This is especially visible in the observe d inactivation values at 80, 95, and 110°C, where the inactivation rate appears to decrease towards the end of treatment. This trend could be due to a crust formation effect that 58 occurs when droplets reach the ir cr itical moisture content, which may decreas e bacterial inactivation in the falling rate drying period. While the CDC droplet drying model in Eq. ( 1 ( 3 ) takes this into account using the dimensionless moisture content parameter f , a n additional crust formation parameter could be added to the inactivation model in Eq. ( 20 ) to further emphasize the importance of crust formation on inactivation rate. 59 Figure 9 . Measured bacterial inactivation, model pred iction, and 95% confidence and prediction intervals using Eq. (20) (markers, solid lines, dashed lines, and dotted lines, respectively) for inactivation of Salmonella in a 160 µm diameter soy protein droplet dur ing drying at various temperatures (80 - 200°C) 60 Figure 10 . Residual analysis for observed versus predicted survival of Salmonella in a 160 µm diameter soy protein droplet during drying at various temperatures (80 - 200° C) using Eq. (20) . T he most likely correct model for Salm onella inactivation in drying droplets of a soy protein isolate solution was E q. ( 20 ) based on its low AIC C value . This model performed slightly better than Eq. ( 18 ) even with the penalty to AIC c due to the addition of parameter z X . However, the large uncertainty associated with z X in Eq. ( 19 - ( 20 ) indicates that it is likely not a strong predictor of inactivation rate , and perhaps the use of other parameter s related to droplet dryin g properties could improve the model further. Parameters that account for properties such as drying 61 rate , heating rate , and crust formation could better illustrate the factors that are important related to bacterial inactivation i n drying droplets and lead to a better fitting model . 4.5. Conclusion Drying droplet properties ( droplet temperature, moisture content, and drying rate ) were simulated using the standard CDC model and conditions measured from the convection oven in chapter 3 . This was done as such data was not able to be collected experimentally . These simulated drying kinetics data w ere then paired with the bacterial survival data collected from chapter 3 to develop models that consider the effects of such kinetics on bacterial inactivati on during drying. Secondary models involving the parameters droplet temperature and moisture content were fitted to the inactivation data and evaluated for their goodness - of - fit. The optima l model was determined to be a model that considers both droplet te mperature and moisture content. This model can be validated using survival data collected from pilot - scale spray drying of inoculated feeds. 62 5. PILOT - SCALE VALIDATION OF COMBINED SPRAY DRYING AND BACTERIAL INACTIVATION MODELS 5.1. Introduction Modeling and simulation work are important in understanding the factors and mechanisms that impact bacterial inactivation during droplet drying . However, the models need to be validated with a larger - scale o peration with the same complexities as an industrial - scale sys tem. For this validation , experiment s w ere carried out with a solution of soy protein isolate inoculated with Salmonella Enteritidis PT30 , Salmonella spp. being a pathogen of concern in spray dr ying, and Enterococcus faecium , a commonly used non - pathogenic surrogate for Salmonella in low - moisture foods. This inoculated solution was then dried in a pilot - scale spray dryer using a range of common inlet air conditions for such products. Samples from various locations within the dryer were evaluated for the sur vival of these bacteria in order to provide an understanding of bacterial survival within the entire system, including the powdered product. These results can then be used to provide a mathemati cal and biol ogical tool to predict contamination risks within spray drying systems. 5.2. Objective s This study was conducted to validate the previous simulation and modeling work by testing the survival of both Salmonella and Enterococcus faecium in a pilot - sca le spray dryer. 5.3. Materials and Methods 5.3.1. Materials and properties Experiments were carried out using the same FT80 Tall Form Spray Drier (Armfield Inc., Clarksburg, NJ) and operating conditions described in section 3.3.1 . Spraying Systems Co. provided data for a similar nozzle used under similar conditions to those in this thesis (DeMaria 63 2019) . According to the data provided, atomization of a 15% w/w suspension of HPMC - based OPADRY ® YS - 1 - 7003 (Colorcon, Harleysville, PA) at a feed rate of 10 mL/min and atomizing air pressure of 0.8 bar (14.5 psi) would yield a n average droplet diameter of ~50 - 55 µm. While neither of these droplet size estimations completely reflect those used in th is experiment , they are the best estimations that can be obtained without collecting our own data for the system being used. For the purposes of this thesis, t he data pr ovided for atomization of the OPADRY ® solution were used to represent the droplet size created by the atomizer in the experiment, as it most closely fit the atomization and feed conditions used, and was closer to previous experimental data and es timations as opposed to the data for atomization of water (Zbicinski, Strumillo, and Delag 2002; Mezhericher, Levy, and Borde 2015) . 5.3.2. I nactivation study methods Salmonella Enteritidis Phage Type 30 and Enterococcus faecium NR R L B - 2354 were subjected to two 24h/37°C transfers in tryptic soy broth (TSB) to achieve a highly concentrated inoculum (~10 9 CFU/mL). A 10% w/w SPI slurry was created by adding 450 mL of water to 50 g of unflavored soy protein isolate (NOW Foods, Blooming d ale, IL) and blending in a laboratory blender ( Waring, Torrington, CT) for 5 min . The slurry was then stirred at 2 00 RPM on a stir plate for 24 h to fully hydrate the protein and obtain a more homogenous mixture. On the day of testing, 6 mL of inoculated T SB was pipetted into the slurry and stirred at 2 00 RPM for 5 min to blend (~10 7 CFU/mL). Th e inoculated slurry was stirred at 200 RPM when pump ed into the nozzle to prevent phase separation. To prepare the spray dryer for each experiment, the air heater a nd inlet/exhaust fans were set to the operative conditions for approximately 20 min to allow the dryer conditions (inlet air temperature, air pressure, humidity) to reach steady state without air or liquid input from the 64 nozzle. Once steady state was reach ed, compressed air was supplied to the nozzle , and the peristaltic pump began supply ing liquid feed. The dryer was then allowed to run until all of the liquid feed solution was dried (~ 1 hr fo r 500 mL ) , stopping as needed to clea r any clogs in the nozzle o r feed line. After running the liquid solution, the spray dryer was shut down for disassembly, sample collection , and cleaning . Samples were taken from the following locations : feed solution (control), nozzle shield, top, middle, and bottom of the drying c hamber walls (7, 45, and 90 cm from the drying chamber ceiling, respectively) , primary and secondary collectors, cyclone, and exhaust pipe ( Figure 11 ). These locations were chosen based on varying air temperatures, humidity, and pa rticle residence times. The control sample consisted of 5 mL of the inoculated liquid feed , which was reserved to deter mine the starting bacterial concentrati on in the feed solution . Samples from the primary (1 - 5 g) and secondary collectors (15 - 25 g) consi sted of the powder accumulated within . All other sampling locations had their surfaces swabbed using Sterile Dry Sponge Probes (Nasco, Fort Atkinson, WI) wetted with 20 mL of BPW . Swabbing was done in a 10x10 cm area where a semi - flat surface was available (top, middle, and bottom of the drying chamber), and around the perimeter of the sampling location where the diameter of the piping was too small for this type of swabbing (nozzle shield, cyclone, and exhaust pipe). 65 Figure 11 . Diagram of the sampling locations within the FT80 Tall Form Spray Dryer used in the pilot - scale validation study. Control samples were serially diluted with 0.1% BPW and plated on the appropriate media for the microorganism being identified . Powder sample s were diluted 1:10 by mass with BPW , stomached twice for 90 s each , serially diluted with BPW , and plated on the a ppropriate media. Swab samples were similarly stomached twice for 90 s , serially diluted with BPW, and plated on the appropriate media. The m edia used for plating these samples was dependent on the microorganism being recovered . For E. faecium, the medium used was Tryptic Soy Agar (Difco) supplemented with yeast extract (0.6%) (Difco), ferric citrate (0.05%) (Sigma Aldrich, St. Louis, MO), and esculin hydrate (0.025%) (Acros Organics, Morris, NJ) , also known as eTSA (Isenberg, Goldberg, and Sampson 1970) . For S almonella , the medi um used was mTSA. Both media are nonselective and 66 diffe rential . The plates were incubated for 48 h at 37 °C after which all black colonies on mTSA and eTSA were counted as Salmonella or E. faecium , respectively. Only those c ounts between 25 and 250 colonies per plate were used (Food and Drug Administration 1998) . 5.3.3. Spray dryer operational safet y To contain any airborne bacteria inside the B iosafe ty L evel 2 P ilot P lant facility at Michigan State University , the spray dryer used in this study was placed inside a portable clean room structure ( McMaster - Carr, Aurora, OH ) with heavy vinyl plastic curtains surrounding each side. These curtains were tape d to the laboratory walls to form a seal from the rest of the labo ratory. This portable clean room was equipped with a HEPA air filter followed by a n exhaust fan blowing outwards. Thus, a negative air pressure was maintained inside the room to prevent airb orne particles from escaping , while also filtering potentially dan gerous microorganisms before the fan expelled air in to the rest of the lab. The spray dryer exhaust pipe was positioned directly under this ceiling fan such that all air exiting the dryer wa s exhausted into the fan. A n inline HEPA box filter (HVACQuick, Me dford, OR) was installed onto the end of the exhaust pipe to filter microorganisms from the air exiting the dryer. According to recommendation s from MSU EHS ( Environmental Health and Safety, Michigan State University) , p ersonal protective equipment was wor n while inside the clean room. This included N95 respirators (3M, St. Paul, MN), disposable Tyvek coveralls with a hood and booties (DuPont, Midland, MI), and double layered nitrile gloves s ealed to coveralls with duct tape , and a face shield. Once drying of the inoculated feed began, no entry or exit from the clean room was allowed until cleaning was completed to prevent contamination of the general lab space. 67 To ensure that this containment system was working properly, each experimental spray drying run included environmental sampling both inside and outside the clean room. Plates of the appropriate media for the microorganism being tested were opened and placed on the ground in multiple loc ations within the clean room and in the general laboratory area for the entirety of the spray dryer operation to determine if any bacteria were escaping the room. Similarly, each inner wall in the clean room was swabbed in a 10x10 cm area after completion of spray drying and plated on the appropriate m edia to determine whether any bacteria had escaped the dryer and attached to the walls. 5.4. Results and Discussion 5.4.1. General properties The average initial concentrations of E. faecium and Salmonella in the inoculat ed soy protein solution were 9.73 ± 0.18 and 8. 86 ± 0.18 CFU/g solids ( with 95% confidence level ) , respectively. The moisture content of the spray dried soy protein powder was measured at each inlet air temperature and averaged 0.07 kg H 2 O/kg solids , which was used for all droplet drying modeling as the equilibrium moisture content of dried particles. No counts of Salmonella were found on environmental samples, indicating that the containment system worked properly. 5.4.2. Effect of sampling location Population s o f E. fa ecium in the soy powder product (primary and secondary collectors) w ere significantly reduced ( P < 0.05) for all inlet air temperatures ( Table 5 ) . No significant difference ( 0.05) was found in the surviva l of E. faecium or SE PT30 between the se two sampling locations. There are two main differences between the powders in these locations: particle size and residence time. Although the particle size o f the dried powder was not measured, the particles sampled from the secondary collector were much finer than the particles 68 in the primary collector ( Figure 12 and Figure 13 ), which is consistent with the literature regarding dryers with multiple collectors (Masters 1972; Djamarani and Clark 1997) . While particles in the secondary c ollector are smaller and therefore require less drying time to reach a dry state, they also must travel a greater distance to reach the collector than the larger particles in the primary collector. No studies have measured the difference in residence times between particles in the primary v ersus secondary collectors. Therefor e, the effect of the differen ce in residence time between the particles was not considered for the two sampling locations having similar bacterial surviva l. 69 Table 5 . Inactivation of E. faecium and Salmonella ( ± 95% confidence interval ) in soy protein isolate powder sampled from the primary and secondary collectors after spray drying at various inlet air temperatures. Initial concentrations of E. faecium and Salmon ella in the inoculated soy protein solution with 95% c onfidence interval were 9.73 ± 0.18 and 8.86 ± 0.18 CFU/g solids . Bacterial inactivation ( Log CFU/g solids ) * E. faecium SE PT30 Location 180°C 200°C 220°C 180°C 200°C Primary collector 2.83 ± 0.43 AB ** 2.51 ± 0.32 A 2.52 ± 0.43 A 3.64 ± 0.48 B 2.40 ± 1.77 A B *** Secondary collector 2.33 ± 0.09 A 2.33 ± 0.32 A 2.38 ± 0.59 A 4.11 ± 0.37 B 4.15 ± 0.38 B * Values given as mean bacterial inactivation ± 95% confidence interval (3 replications, except where noted ). ** Means sharing a common symbol (A, B , C ***Two replications due to missed dilutions . 70 Figure 12 . Typical appearance of fine soy protein powder accumulated in the secondary c olle ctor after spray drying. Figure 13 . Typical appearance of accumulated coarse soy protein powder in the primary collector after spray drying. 71 No significant difference was found in the survival of E. faecium or SE PT30 in the po wder deposits of the top, middle, and bottom of the drying chamber ( Table 6 ). Although air temperature differed in each region ( Table 1 ) , the se difference s between the air te mperature profile s were considered insufficient to significantly affect bacterial inactivation in the wall deposits. Also, d eposition rate was likely not a factor in any differences in survival in wall deposits , as the amount of powder buildup was fairly c onsistent throughout the drying chamber ( Figure 14 ). Figure 14 . Top - down view of the spray drying chamber with deposited soy protein powder after spray drying . 72 Table 6 . Population of E. faecium and Salmonella ( ± 95% confidence interval ) in soy protein isolate powder swab samples from the nozzle shield, drying chamber, cyclone, and exhaust pipe after spray dr ying at various inlet air temperatures. Population ( Log CFU/cm 2 ) * E. f aecium SE PT30 Location 180°C 200°C 220°C 180°C 200°C Nozzle 1.19 ± 0.05 A ** < limit*** < limit < limit < limit Chamber top 2.72 ± 1.19 AB** 2.41 ± 0.56 AB 2.11 ± 1.16 AB 2.59 < limit Chamber middle 3.07 ± 0.36 AB 2.73 ± 0.52 AB 1.68 ± 1.82 A < limit < l imit Chamber bottom 3.50 ± 0.12 AB 2.56 ± 0.58 AB 2.19 ± 1.66 AB 2.09 < limit Cyclone 3.99 ± 0.34 B 3.32 ± 0.06 AB 1.96 ± 0.58 AB < limit < limit Exhaust < limit < limit < limit < limit < limit * Values given as mean bacterial concentration ± 95% confiden ce interval *** All collected samples were below the limit of detection (0.8 CFU/cm 2 ) . 73 Results from t hese sampling locations are difficult to fully interpret, however, due to the varyi ng residence times for the deposits and their extended exposure to high temperature s . Powder that adheres to the dryer walls early during a drying run will be exposed to the drying conditions for most of the run time (~50 min), while powder that adheres at the end will be minimally treated. As such, the layers of particles that exist within the deposited powder likely experienced different exposure s to the treatment and there fore varied bacterial survival. Thus, surface swab bing yields a composite sample ha ving the higher concentration in the top - most, minimally treated powder. This variation within the deposit could be further investigated by drying a much larger amount of fe ed in order to build a thick er layer of powder on the dryer walls, and sampling lay ers from different depths to see if position within the built - up powder influences bacterial survival . While some samples taken from the cyclone, exhaust, and nozzle areas had E. faecium and SE PT30 concentrations below the detection limit (0.8 log CFU/cm 2 ), each location had samples with at least one surviving colony forming unit (Food and Drug Administration 1998) . This limit of detection was determined based on a minimum count of 25 colonies from a swab of the cylindrical sampling areas of the cyclone, exhaust, and nozzle. The conditions in these areas make survival and recovery of bacteria difficult (high temperature air in the nozzle area, low powder deposit ion in the cyclone and exhaust pipe), but E. faecium still survived and was recoverable by swab ( Figure 15 and Figure 16 ) . This means that E. faecium was survived to some extent at all sampling locations. W hile previous studies have reported surviv al of Salmonella, E. coli, and Listeria monocytogenes in spray dr ied milk, these results show that E. faecium is capable of surviving at multiple location s within a dryer, not just in the final powder 74 product (LiCari and Potter 1970 a ; Miller, Goepfert, and Amundson 1972; Doyle, Meske, and Marth 1985) . Figure 15 . Nozzle shield with deposited soy protein powder after sp ray drying. Figure 16 . Cyclone connecting pipe with deposited soy protein powder after spray drying. It is impractical to compare survival in the se spray dryer deposits to that of the inoculated feed solution or the powder sampled from the collectors due to the difference in sampling 75 methods, and thereby units of concentration (CFU/g solids versus CFU/cm 2 ) for each location. Therefore , results for these swab samples were not report ed in log reductions. 5.4.3. Effect of inlet air temperature Inlet air temperature was a significant factor ( P < 0.05) in survival of E. faecium in the middle region of the drying chamber and the cyclone, but nowhere else in the process. For SE PT30, inlet air te mperature was not a significant survival factor ( P < 0.05) in any sampling loca tion. It is possible that higher inlet air temperatures could have a more substantial impact on bacterial inactivation, but such temperatures could have adverse effects on powde r quality or drying efficiency as they are out of the range of recommended dryi ng temperatures for many spray dried products (Armfield Engineering Teaching Equipment 2013; Masters 1972) . This finding conflicts with the results found in chapter 3 , where air temperature in the convect ion oven had a significant effect on the inactivation rate for Salmonella in drop lets of soy protein isolate solution . This could be due to the difference in air temperatures surrounding the droplets in the convection oven study, air temperature was kept constant in a range from 80 to 200°C. However, in this study the air temperature surrounding droplets varied during the process of droplet drying, with average drying chamber temperatures of 104 to 132°C using inlet air temperatures of 180 to 220°C. C onsi dering the large value for z T estimated for Eq. ( ( 20 ) (170.9°C), the differences in air temperatures within the drying chamber at the inlet air temperatures tested were likely insufficient to yield significant diffe rences in inactiva tion during drying of droplets in this process. 5.4.4. Comparison of survival between organisms S urvival of SE PT30 in the soy protein powder sampled from the primary/secondary collectors was significantly lower ( P < 0.05) than that of E. faeciu m during spray drying ( Table 76 5 ) . Similarly, while E. faecium survivors were found at all surface swab sampling locations and inlet air temperatures , SE PT30 decreased below the detection limits (0.8 CFU/cm 2 ) in most samples at inle t temperatures of 180 and 200°C ( Table 6 ). Surrogate organisms for process validation are generally preferred to ha ve greater thermal resistance than the selected pathogen of concern in order to create a conservative predictor of p athogen inactivation. Therefore, this observation indicates that E. faecium has potential for usage as a surrogate organism for SE PT30 in s oy protein powder during spray drying. The use of this surrogate should be further validated under a greater variety of processing conditions such as inlet air temperature, feed rate, atomization pressure, and feed material before it is used as a reliable surrogate for various spray drying processes. 5.4.5. Validation of inactivation model Ideally, the data collected in this s tudy can be used as a scale - up validation of the bacterial inactivation model developed in chapter 4 . This can only be completed to a certain extent, however, as much of the information required to conduct a com plete validation is still unknown. For instance, no data for residence time or droplet temperature ha ve been collected for droplets drying in the convection oven used in chapter 3 or the pilot - scale spray dryer used in this study. Therefore, onl y a preliminary validation of the applicability of the bacterial inactivation model described in chapter 4 to a pilot - scale spray drying process can be completed. To complete such a validation, drying droplets were simulated usi ng the CDC model described in chapter 4 . Several assumptions were made to complete this simulation. First, parameters that are unknown about the spray dryer used in this study were assumed to be the same as for the convection ov en used in chapter 3 . It was also assumed that the air temperature within the spray dryer chamber was the average of the measured air temperatures described in 77 Table 1 (104, 119, and 132°C average air te mperature at inlet air temperature of 180, 200, and 220°C, respectively) , as the actual air temperature experienced by a drying droplet during spray drying w as not measured experimentally. The droplet diameter was assumed to be 55 µm, based on the data pro vided in section 5.3.1 . The residence time for the particles accumu lated in the primary and secondary collectors was assumed to be equal to the time required for a simulated droplet under the same conditions to reach the equilib rium moisture content (0.07 kg H 2 O/kg solids). This assumption is required because no data for residence time of particles was collected in this study, so the residence time for this process is unknown. The data for droplet temperature and moisture content w ere entered into Eq. ( 20 ) to obtain predicted Salmonella inactivation data for each condition ( Figure 17 ). The observed data for Salmonella inactivation in particles collected in the primary and secondary collectors was plotted at the estimated residence time with these predicted curves to illustrate the differences between predicted and observed data. 78 Figure 17 . Predicted inactivation of Salmonella in a droplet drying at constan t air temperatures of 104, 119, and 132°C using Eq. ( 20 ) (lines) and observed inactivation (with 95% confidence intervals) of Salmonella in powdered soy protein isolate in the primary / secondary collectors of the pilot scale spray d ryer after drying at inlet air temperatures of 180 and 200°C for their assumed residence times (markers) . Based on the di ffe rences between the predicted lines and the observed data points in Figure 17 , the inactivation model based on experimental data underpredi cts inactivation during pilot - s cale drying. However, this model is based on a small data set and many assumptions. For instance, if , as has been previously theorized , and thus the time required to reach equilibrium moisture content is only 25 percent of residence time , then the assumption for residence time used in this validation is invalid (Mezhericher, Levy, and Borde 2015) . In this case, the residence time for these particles would instead be approximately four times longer than estimated in this validation (~1 minute), which would make the predicted inactivation much closer to the observed experimental data values. 79 5.5. Conclusion In this study, a pilot - scale spray dryer was used to evaluate the survival of Salmonella and E. faecium in soy protein isolate during spray drying using varying inlet air temperatures. Significan t bacterial reduction s were observed in the soy protein powder that accumulated in the primary and secondary collectors as well as that adhering to the inner surfaces of the spray dryer. Inlet air temperatur e had a n insignificant effect on bacterial inacti vation in most sampling locations . Inactivation of Salmonella w as significantly greater than E. faecium in the final powder product, indicating that E. faecium could be used as a conservative surrogate organism under these conditions . However, a more thoro ugh surrogate evaluation should be conducted before E. faecium is used as a surrogate for SE PT30 in spray drying process under all conditions . T he spray dryin g process was not able to eliminate all bacteria present regardless of inlet air temperature, sam pling location, or organism tested. This confirms that the spray drying process can not be a pasteurization step and caution should be taken to prevent contamin ation of spray dryers during food manufacturing. Finally, a preliminary validation of the bacteri al inactivation model developed in chapter 4 showed that given the as sumptions used in the modeling portions of this study, the inactivation model underpredicted inactivation of bacteria during the pilot - scale spray drying proce ss. 80 6. CONCLUSION S 6.1. Overall C onclusions Survival of Salmonella during drying of a thin layer of droplets was observed at various oven air temperatures . Increases in air temperature around the drying droplets resulted in increased reduction of Salmonella , wit h D - values for droplets dried in 80 - 200°C air in the range o f 4.6 - 17.2 s ( T ref = 77°C, X ref = 1 kg H 2 O/kg total) . Additionally, the temperature profile of a pilot - scale spray dryer was measured , and regions of varied temperatures substantially below the in let air temperature were observed. This information indicate d that spray drying would be un likely to decrease Salmonella more than 2 - 3 log reductions of Salmonella based on the D - values observed and the short residence times of droplets within spray dryers . Th ese bacterial inactivation data w ere then paired with a droplet drying model to evaluate the effects of droplet temperature and moisture content on inactivation rate. Droplet temperature and moisture content were projected for a simulated drying drople t using conditions replicating those used in the thin - layer droplet bacterial survival study. Three secondary models for bacterial inactivation rate were fitted to th ose inactivation data, and the most likely correct model was determined to be one that con siders both droplet temperature and moisture content . A pilot - scale spray dryer was used to determine the survival of Salmonella and the potential surrogate organism E. faecium during spray drying of soy protein isolate at various inlet air temperatures. I nlet air temperature was not a significant factor in t he survival of either organism, and while bacterial survival within soy protein powder varied between sampling locations, surviving bacteria w ere found in all locations of the dryer. E. faecium was foun d to have significantly greater survival than Salmonel la in the spray dried soy protein powder, indicating that it could potentially be used as a viable surrogate organism for the spray drying process. 81 Finally, when th ese bacterial survival data w ere used to validate the model of bacterial inactivation during droplet drying , the model underpredicted inactivation during the spray drying process. 6.2. Commercialization P otential The work completed in this thesis could be helpful in several ways for food manufactur ers that utilize spray drying in their processes . It c onfirms previous results regarding bacteria l surviv al during spray drying of various food products , and indicates that those results apply to soy protein isolate as well . Manufacturers may use this info rmation to understand that spray drying can be useful to enact some bacterial inactivation in the case of a contaminated product, such as accidentally under - pasteurized or environmentally contaminated feed material . This information could also be used to i dentify better cleaning protocols , by changing the frequency of cleaning and targeting of specific areas of high contamination risk. Finally, the pilot - scale study can be used to inform operating conditions that aim to ensure product quality while also max imizing microbial safety . 6.3. Future W ork 6.3.1. Experimen tal work There are many opportunities for improvement and future work involving the thin film droplet drying method. First, an apparatus that is capable of measuring the temperature and moisture content of dro plets during the drying process simultaneously with bacterial inactivation data would be highly valuable for the validation of the work presented in this thesis. Additionally, further experiments could use a variety of treatment conditions to test their ef fect on drying kinetics and bacterial survival, including process humidity, air velocity, feed material, 82 and solids content of liquid feed. This would expand the applicability of these lab - scale results to a wider variety of pilot and industrial - scale spra y drying processes. Given the inability to simu ltaneously estimate the param e ters z T and z X , future experiments using the thin - film droplet drying method could be modified. The experiment could be run at lower temperatures for longer times in order to leng then the period during which the effect of temp erature and moisture content could be modeled more effectively. This could include drying temperatures that are below those relevant to actual spray drying processes (<80°C) , but would extend the inactivation and drying curves created over a much longer ti me. This would be useful by collecting more useable data to be used for estimat ing both D and z - values, which could then be applied to faster drying conditions. The pilot - scale spray drying conditions could be expanded upon similar ly to the thin - film droplet drying experiment. Numerous processing conditions and feed properties could be tested for their effect on bacterial survival, such as drying chamber pressure, feed rate, atomization pressure, feed material, and solids content of f eed. Along with bacterial survival data, quality of the powders produced during the spray drying process could be tested to determine the processing conditions that produce acceptable products. In addition to bacterial inactivation, there is potential for bacterial growth to occur within spray dryers. If insufficient drying conditions lead to accumulation of feed material with sufficiently high moisture content on the inner surfaces of the dryer, any surviving bacterial population co uld grow. To test this e xperimentally, powdered foods such as soy protein isolate could be inoculated with bacteria and kept at a certain a w and temperature in a humidity - controlled environment. Samples of this powder could be taken over time to determine if such conditions were sufficient to allow for bacterial growth. A model of bacterial growth as affected 83 by environmental temperature and moisture content could be created based on the collected data. Such a model could be used to inform the use of variou s cleaning methods to in troduce less water into the system, as well as setting up minimum standards for powder moisture content and temperature conditions to prevent bacterial growth during operation . 6.3.2. M odeling improvements The models provided in this thesi s could be further impro ved in several ways. First, with more data collection and model complexity , certain assumptions could be eliminated. For example, by collecting droplet moisture content and temperature data in real - time with inactivation data, the u se of simulated droplet drying data could be validated. This would involve some new droplet drying experimental apparatus, as previous studies have not been able to observe the drying properties of to - scale droplets created by spray dryer atomizers . Second , assumptions such as th e exclusion of an initial drying phase or temperature and moisture content homogeneity within a droplet could be eliminated with more data on the drying kinetics of the specific product being tested, as well as more complex models t hat can account for prof iles of droplet properties. Additional droplet drying kinetics models (REA, deterministic) could be used and compared to the CDC model to see which is the best fit for the given droplet drying data. Similarly, additional secondary m odels that include param eters such as drying rate and heating rate of droplets could be tested for their potential improvement of inactivation modeling. Finally, the fit of the log - linear primary model could be compared with that of the Weibull primary mod el, which is another pri mary inactivation model commonly used in predictive microbiology. The next step in the application of both bacterial inactivation and droplet drying models is their use in CFD modeling. Once bacterial and droplet properties is under stood at the single droplet scale , those models can be coupled with the air flow data from a simulated spray dryer 84 using CFD software. As mentioned in section s 2.1 and 2.2 of this thesis, a substantial amount of research has already been completed on the use of CFD to track properties of the spray drying pr ocess. These CFD models can incorporate the bacterial inactivation models develop ed in this thesis to create a holis tic process model of spray drying encompassing bacterial survival throughout the system. Such a model could utilize the data collected in ch apter 5 of this thesis for validation. 85 APPENDI X 86 MATLAB Code for Droplet Drying Simulation and Inactivation Modeling %% Drying Droplet Properties and Inactivation Kinetics Modeling %% Housekeeping clear %clear all variables close all hidden %clear figures format compact clc %% Initial variables Xinit = 9; %Dry basis Tinit = 20+273; %Room temperature [K] X_T_init = [Xinit; Tinit]; %for droplet drying kinetics forward problem % Ta = [80 95 110 180 190 200]; %Use these temperatures for convection oven drying droplet simulation. Ta = [104 119.3 131.6]; %Use these temperatures for pilot scale spray dryer validation. % Ta = [80 2 00]; %Use these temperatures for plotting droplet drying at 80 and 200C. Ta = Ta+273; %Convert to Kelvin % D = [160]; %Use for convection oven parameter estimation. D = [55]; %Use for pilot scale spray dryer validation % D = [10 20 40 80 160 320]; %Use for distribution of simulated droplet sizes. D = D.*10^( - 6); %Convert to um tfinal = 60; %All experiments/simulations go to 60 seconds. inac_data = xlsread( 'mesh_inactivation_data.xlsx' , 'Log Reductions' ); %Rea d in inactivation data from mesh experiment globa l sim_data x_all sim_data = inac_data; %Will include simulated droplet data along with experimental inactivation data y80 = inac_data(1:18,3); y95 = inac_data(19:35,3); y110 = inac_data(36:46,3); %Makes plot ting easier y180 = inac_data(47:57,3); y190 = inac_data(58:67,3); y200 = inac_data(68:73,3); %% FORWARD PROBLEM: Generate droplet drying data, plot SSC's fnameFOR=@Dro pletForward; %% Compile Td, X, dX/dt data for each droplet simulation into x_all xs=linsp ace(0,tfinal,601)'; %xs are the times for SSCs to make a smooth curve. ns=length(xs); %length of xs for plotting ypredInit=fnameFOR(X_T_init,xs,Ta(1),D(1)); %Simulate drying properties only at one specified Ta and D xs=[xs ypredInit(1:ns) ypredInit(ns+1:2*n s) ypredInit(2*ns+1:3*ns)]; %Add those drying properties for this one case to xs. x_all = xs(:,1); %x_all will c ontain all simulated droplet properties. for i=1:length(Ta) for j = 1:length(D) ypredInit=fnameFOR(X_T_init,xs,Ta(i),D(j)); DryingCond(:,6*(i - 1)+j) = [Ta(i); D(j);zeros(length(xs(:,1)) - 2,1)]; %Need to fix if change Temp x_all = [x_all xs(:,1) DryingCond(:,6*(i - 1)+j)]; %Add time column between each condition x_all = [x_all ypredInit(1:ns) ypredInit(ns+1:2*ns) ypr edInit(2*ns+1:3*ns)]; for k=1:length(inac_data) if sim_data(k,1) == (Ta(i) - 273) %Copies T,X,d X/dt data for that time interval for that droplet into the sim_data matrix sim_data(k,4) = ypredInit(10*(sim_data(k,2))+1); sim_data(k,5) = ypredInit(10*(sim_data(k,2))+1+ns); sim_data(k,6) = ypredInit(10*(sim_ data(k,2))+1+2*ns); end end end end x_all(:,1) = []; %x_all contains all temp and MC data for droplets dried, separated b y a column containing time data between temperatures. %Column1 = time, column2 = X, column3 = Td, column4 = dX/dt, and so on. xobs = [sim_data(:,2) sim_data(:,4) sim_data(:,5) sim_data(:,6)]; %Contains time, X, Td, and dX/dt x80 = xobs(1:18,1); x95 = xobs( 19:35,1); x110 = xobs(36:46,1); x180 = xobs(47:57,1); x190 = xobs(58:67,1); x200 = xobs(68:73,1); % Times f or each temperature data set. yobs = sim_data(:,3); %Contains observed log reduction data %% Plot Td and X for droplets at Ta = 80C, 200C 87 %If plotti ng for 80C and 200C at Droplet diameter 10,20,40,80,160,320um, %then use the following settings for Ta and D in "Initial Variables" section. %Ta = [80 200]; %D = [10 20 40 80 160 320]; % cmap = ['r' 'm' 'y' 'g' 'c' 'b']'; % for i=1:length(Ta) % figure % hold on % set(gca, 'fontsize',14,'fontweight','bold'); % PlotTitle = ['Simulated drying d roplet, Ta = ',num2str(Ta(i)),'K']; % title(PlotTitle) % xlabel('Time (s)') % yyaxis left % ylabel('Droplet temperature (K)'); % yyax is right % ylabel('Moisture Content (kg H2O/kg solids)') % for j=1:length(D) % yyaxis l eft % plot(x_all(:,1),x_all(:,30*(i - 1)+5*j - 1),' - ','color',cmap(j,:),'LineWidth',2) % yyaxis right % plot(x_all(:,1),x_all(:,30*(i - 1)+5*j - 2),' -- ','color',cmap(j,:),'LineWidth',2) % end % legend('Td (D=10um)','Td (D=20um)','Td (D=40um)','Td (D=80um)','Td (D=160um)','Td (D=320um)','X (D=10um)','X (D=20um)','X (D=40um)','X (D=80um)','X (D=160um)','X (D=320um)','Location','Best') % end %% Option to write T/X/dX data to Excel spreadsheet for plotting % filename_out = ' Matlab_created_drying_data2.xlsx'; % excel_data = array2table(x_all); % writetable(excel_data, filename_out); %% PICK SECONDARY MODEL FOR INVERSE PROBLEM HERE %Set up reference values for inverse problem global Tref Xref dXdtref Tref = 350; Xref = 1; %Initial parameter guesses beta0(1)= 12; %Dref beta0(2)= 200; %zT beta0(3)= 5; %zX %Uncomment the line for the model you want to use in the inverse problem. % ---------- -------------------------------------------------------------- % fnameINV=@inv_T; bet a0=[beta0(1) beta0(2)]; p=length(beta0); % fnameINV=@inv_X; beta0=[beta0(1) beta0(3)]; p=length(beta0); fnameINV=@inv_T_X; beta0=[beta0(1) beta0(2) beta0(3)]; p=length(bet a0); %% Scaled sensitivity coefficients before running inverse problem Xp=SSC_V3(beta0,xs,fnameINV); %% Can check correlation between any 2 parameters by dividing and plotting them rat12=Xp(:,1)./Xp(:,2); if p == 3 rat13=Xp(:,1)./Xp(:,3); rat23=X p(:,2)./Xp(:,3); end if p == 4 rat14=Xp(:,1)./Xp(:,4); rat24=Xp(:,2)./Xp(:,4); rat34=Xp(:,3)./Xp(:,4); end %Now plot the ratios between parameter SSC's figure hold on plot(xs(1:ns),rat12, 'r' ) if p == 3 plot(xs(1:ns),rat13, 'g' ) plot(xs(1 :ns),rat23, 'y' ) end if p == 4 plot(xs(1:ns),rat14, 'b' ) plot(xs(1:ns),rat24, 'm' ) plot(xs(1:ns),rat34, 'c' ) end 88 title( 'Checking parameter correlation before running inverse problem' ) %% plot SSC's for Log CFU/g cmap = [ 'r' 'g' 'b' 'c' 'y' 'm' ]'; f igure hold on set(gca, 'fontsi ze' ,14, 'fontweight' , 'bold' ); ypred=fnameINV(beta0,xs); h2(1)=plot(xs(1:ns),ypred(1:ns), ' - ' , 'color' ,cmap(1,:), 'LineWidth' ,2); %plot the predicted C to compare to SSCs for i=1:p h2(i+1) = plot(xs(1:ns),Xp(1:ns,i), ' - ' , 'color' ,cmap(i+1,:), 'LineWidth' ,2); end if p == 2 %Set appropriate # of legend entries based on # of parameters in model legend( 'Log CFU/g' , ' \ beta_1' , ' \ beta_2' ) end if p == 3 legend( 'Log CFU/g' , ' \ beta_1' , ' \ beta_2' , ' \ beta_3' ) end if p == 4 legend( 'Log CFU/g' , ' \ beta_1' , ' \ beta_2' , ' \ beta_3' , ' \ beta_4' ) end xlabel( 'Time (s)' ); ylabel( 'SSC (Log CFU/g)' ); grid on %% INVERSE PROBLEM: Bacterial inactivation parameter estimates %nlinfit returns parameters, residuals, Jacobian (sensitivity coefficient matrix), %co variance matrix, and mean square error. ode45 is solved many times %iteratively % xobs(1,2)=stdC;xobs(1,3)=stdT;%send the y stdev into the function for regression [beta,resids,J,COVB,mse] = nlinfit(xobs,yobs,fnameINV,beta0); mdl = fitnlm(xobs,yobs,fn ame INV,beta0); %Replace nlinfit with fitnlm AICc = mdl.ModelCriterion.AICc rmse=sqrt(mse) %mean square error = SS/(n - p) total for weighted least squares n=length(xobs); nn=n(1); p=length(beta); beta condX=cond(J); %must be < 1 million detXTX=det(J'*J); % must not be near zero, the larger, the better %rmse for each scaled dependent variable rCFU=resids(1:n); rmseCFU=sqrt(rCFU'*rCFU/(n - 1)); %% Model evaluation (R, Parameter CIs, Plot ypred vs yactual, Mean of resids, Residual scatter plot/histogram) %R is th e correlation matrix for the parameters, sigma is the standard error vector [R,sigma]=corrcov(COVB); relerr=sigma'./beta %Confidence intervals for parameters ci=nlparci(beta,resids,J) % %Computed ypredicted & plot vs actual data % y pred=fnameINV(beta,xs); %Mean of the residuals meanr=mean(resids) %Residual scatter plot x3=[xobs; xobs;]; figure hold on h4=plot(x3(1:n), resids(1:n), 'square' , 'Markerfacecolor' , 'b' ); YLine = [0 0]; XLine = [0 max(xobs(:,1))]; plot (XLine, YLine, 'R' ); %plot a straight red line at zero ylabel( 'Observed y/ \ sigma - Predicted y/ \ sigma' , 'fontsize' ,14, 'fontweight' , 'bold' ); xlabel( 'time (min)' , 'fontsize' ,14, 'fontweight' , 'bold' ); %Residual histogram figure h=histogram(resids); hold on set(gca, 'fontsize' ,14, 'fontweight' , 'bold' ); xlabel ( 'Observed y/ \ sigma - Predicted y/ \ sigma' , 'fontsize' ,16, 'fontweight' , 'bold' ) ylabel( 'Frequency' , 'fontsize' ,16, 'fontweight' , 'bold' ) %% (1) Estimate parameters separately (Using model w/ zT) fnameINV=@inv_Tp_wF; %Inverse problem w/ temperature fixed paramete r and forward problem included. 89 beta0fixed=beta0(1); betas(1)=beta0(1); xobs_all = [sim_data; ones(length(x_all(:,1)) - length(xobs(:,1)),6)]; xobs_all = [x_all xobs_all]; yobs_all = [yobs(:, 1); zeros(length(x_all(:,1)) - length(yobs(:,1)),1)]; ind = 1; modnum =1; betaopt=[]; %Once the parameter has been optimized, set zT_fixed so it does not loop. %Then parameter CI's can be estimated. for zT_fixed=174.7:0.5:174.7 %Try z_T at range of values to estimate Dref, test RMSE of model. Have now minimized to 174.7, so dont need to loop anymore. [beta,resids,J,COVB,mse] = nlinfit(xobs,yobs,@(beta,t)fnameINV(beta,t,zT_fixed), betas); rmse=sqrt(mse); rmsep(ind)=rmse; zT_fixedp(ind)=zT_fixed; Drefp(ind) = beta; betas=beta; ind=ind+1; end % Plot t he RMSE curve for each fixed parameter value to find optimum Dref: % figure % hold on % plot(zT_fixedp,rmsep,'r - ') % set(gca, 'fontsize',14,'fontweight','bold'); % xlabel('zT') % ylabel('RMSE (log CFU/g)') % Optimum values: [rmse_opt(modnum) ind_opt]=min(r msep); Dref_opt(modnum) = Drefp(ind_opt); zT_opt(modnum) = zT_fixedp(ind_opt); ci_Dref(modnum,:) = nlparci(beta,resids,J); %Now swap Dref in as fixed variable to get estimate of z T error Dref_fixed = Dref_opt(modnum); betas = zT_opt(modnum); fnameINV=@inv_ Tp_Dfixed; [beta,resids,J,COVB,mse] = nlinfit(xobs,yobs,@(beta,t)fnameINV(beta,t,Dref_fixed), betas); ci_zT(modnum,:) = nlparci(beta,resids,J); %Use model w/o fixed parameters to get AIC: fnameINV=@inv_T_simple; betaopt = [Dref_opt(modnum) zT_opt(modnum)]; mdl1 = fitnlm(xobs,yobs,fnameINV,betaopt); %Replace nlinfit with fitnlm AICc1 = mdl1.ModelCriterion.AICc %% (2) Estimate parameters separately (Using model w/ zX) fnameINV=@inv_X p_wF; beta0fixed=beta0(1); betas(1)=beta0(1); xobs_all = [sim_data; ones(leng th(x_all(:,1)) - length(xobs(:,1)),6)]; xobs_all = [x_all xobs_all]; yobs_all = [yobs(:,1); zeros(length(x_all(:,1)) - length(yobs(:,1)),1)]; ind = 1; modnum=2; betaopt=[]; for zX_fixed=22:0.1:22 %test RMSE of model. Have now minimized to 22.0, so dont need to loop anymore. [beta,resids,J,COVB,mse] = nlinfit(xobs,yobs,@(beta,t)fnameINV(beta,t,zX_fixed), betas); rmse=sqrt(mse); rmsep(ind)=rmse; zX_fixedp(ind)=zX_f ixed; Drefp(ind) = beta; betas=beta; ind=ind+1; end % Plot the RMSE curv e for each fixed parameter value to find optimum Dref: % figure % hold on % plot(zX_fixedp,rmsep,'r - ') % set(gca, 'fontsize',14,'fontweight','bold'); % xlabel('zX') % ylabe l('RMSE (log CFU/g)') % Optimum values: 90 [rmse_opt(modnum) ind_opt]=min(rmsep); Dref_ opt(modnum) = Drefp(ind_opt); zX_opt(modnum) = zX_fixedp(ind_opt); ci_Dref(modnum,:) = nlparci(beta,resids,J); %Now swap Dref in as fixed variable to get estimate of zX err or Dref_fixed = Dref_opt(modnum); betas = zX_opt(modnum); fnameINV=@inv_Xp_Dfixed; [ beta,resids,J,COVB,mse] = nlinfit(xobs,yobs,@(beta,t)fnameINV(beta,t,Dref_fixed), betas); ci_zX(modnum,:) = nlparci(beta,resids,J); %Use model w/o fixed parameters to get AIC: fnameINV=@inv_X_simple; betaopt = [Dref_opt(modnum) zX_opt(modnum)]; mdl2 = fitn lm(xobs,yobs,fnameINV,betaopt); %Replace nlinfit with fitnlm AICc2 = mdl2.ModelCriterion.AICc %% (3) Estimate parameters separately (Using model w/ zT & zX) fnameINV=@inv_T_Xp_wF; beta0fixed=beta0(1); betas(1)=beta0(1); xobs_all = [sim_data; ones(length(x_ all(:,1)) - length(xobs(:,1)),6)]; xobs_all = [x_all xobs_all]; yobs_all = [yobs(:,1); zeros(length(x_all(:,1)) - length(yobs(:,1)),1)]; i=1; j=1; ind=1; mod num=3; betaopt=[]; for zT_fixed=170.9:0.1:170.9 %test RMSE of model. for zX_fixed=17.3:0.1:17.3 % Has been optimized to 17.3 [beta,resids,J,COVB,mse] = nlinfit(xobs,yobs,@(beta,t)fnameINV(beta,t,zT_fixed,zX_fixed), betas); rmse=sqrt(ms e); rmsep(ind)=rmse; zX_fixedp(ind)=zX_fixed; zT_fixedp(ind)=zT_fixed; Drefp(ind) = beta; betas=beta; j=j+1; ind=ind+1; end i=i+1; end % Plot the RMSE curve for each fixed parameter value to find optimum Dref: % figure % hold on % plot3(zT_fixedp,zX_fixedp,rmsep) % set(gca, 'fontsize',14,'fontw eight','bold'); % xlabel('zT') % ylabel('zX') % zlabel('RMSE (log CFU/g)') %Optimum values: [rmse_opt(modnum) ind_opt]=min(rmsep); Dref_opt(modnum) = Dr efp(ind_opt); zT_opt(modnum) = zT_fixedp(ind_opt); zX_opt(modnum) = zX_fixedp(ind_opt); ci_Dref(modnum,: ) = nlparci(beta,resids,J); %Now swap Dref in as fixed variable to get estimate of zX error Dref_fixed = Dref_opt(modnum); betas = [zT_opt(modnum) zX_op t(modnum)]; fnameINV=@inv_T_Xp_Dfixed; [beta,resids,J,COVB,mse] = nlinfit(xobs,yobs,@(beta,t)fnameINV(be ta,t,Dref_fixed), betas); ci_mod3 = nlparci(beta,resids,J); %Use model w/o fixed parameters to get AIC: fnameINV=@inv_T_X_simple; betaopt = [Dref_opt(modnum) zT_opt(modnum) zX_opt(modnum)]; mdl3 = fitnlm(xobs,yobs,fnameINV,betaopt); %Replace nlinfit with f itnlm AICc3 = mdl3.ModelCriterion.AICc %Compile CI's and calculate +/ - for each ci_zt(2,:) = [0 0]; ci_z T(3,:) = ci_mod3(1,:); 91 ci_zX(3,:) = ci_mod3(2,:); ci95Dref = [(Dref_opt(1) - ci_Dref(1,1)) (Dref_opt(2) - ci_Dref(2,1)) (Dref_opt(3) - ci_Dref(3,1))]; ci95zT = [(zT_opt(1) - ci_zT(1,1)) (zT_opt(2) - ci_zT(2,1)) (zT_opt(3) - ci_zT(3,1))]; ci95zX = [(zX_opt(1) - ci_zX(1,1 )) (zX_opt(2) - ci_zX(2,1)) (zX_opt(3) - ci_zX(3,1))]; %% Plot yobs vs ypred for best AIC model (with CI and PI), all data together %Best AIC model is mod el 3, parameters are Dref, zT, and zX fnameINV = @inv_T_X_simple; [beta,resids,J,COVB,mse] = nlinfit(xob s,yobs,fnameINV,betaopt); ci_dummy=nlparci(beta, resids, J); [ypred, delta] = nlpredci(fnameINV,xobs,betaopt,resids,J,0.05, 'on' , 'curve' ); %confidence ba nd for regression line [ypred, deltaob] =nlpredci(fnameINV,xobs,betaopt,resids,J,0.05, 'on' , 'observation' ); %prediction band for individual points CBu = ypred+delta; CBl = ypred - delta; PBu = ypred+deltaob; PBl = ypred - deltaob; % Plot all temperatures togethe r: figure hold on set(gca, 'fontsize' ,14, 'fontweight' , 'bold' ); cmap = [ 'r' 'g' 'b' 'c' 'y' 'm' 'k' ]'; xlabel( 'Time (s)' ) ylabel( 'Log reductions (Log CFU/g)' ) %First, plot observed data as points. plot(x80,y80, 'or' ) plot(x95,y95, 'om' ) plot(x110,y110, 'oy' ) plot(x180,y180, 'og' ) plot(x190,y190, 'oc' ) plot(x200,y200, 'ob' ) %Now plot predicted data as lines. plot(x80,ypred(1:18), ' - r' ) plot(x95,ypred(19:35), ' - m' ) plot(x110,ypred(36:46), ' - y' ) plot(x180,ypred(47:57), ' - g' ) plot(x190,ypred(58:67), 'c' ) plot(x200,ypred( 68:73), 'b' ) %Plot each temperature individually as subplots: figure %80C subplot(3,2,1); h old on set(gca, 'fontsize' ,12, 'fontweight' , 'bold' ); xlabel( 'Time (s)' ) ylabel( 'Log reductions (log CFU/g)' ) axis([0 60 - 8 4]) title([ '80' char(176) 'C' ]) plot(x80,y 80, 'ok' ) plot(x80,ypred(1:18), ' - k' ) plot(x80,CBu(1:18), ' -- k' ) plot(x80,CBl(1:18), ' -- k' ) plot(x80,PBu(1:18), ':k' ) plot(x80,PBl(1:18), ':k' ) %95C subplot(3,2,2); hold on set(gca, 'fontsize' ,12, 'fontweight' , 'bold' ); xlabel( 'Time (s)' ) ylabel( 'Log reductions (l og CFU/g)' ) axis([0 60 - 8 4]) title([ '95' char(176) 'C' ]) plot (x95,y95, 'ok' ) plot(x95,ypred(19:35), ' - k' ) plot(x95,CBu(19:35), ' -- k' ) plot(x95,CBl(19:35), ' -- k' ) plot(x95,PBu(19:35), ':k' ) plot(x95,PBl(19:35), ':k' ) 92 %110C subplot(3,2,3); hold on set(gca, 'fonts ize' ,12, 'fontweight' , 'bold' ); xlabel( 'Time (s)' ) ylabel( 'Log reductions (log CFU/g)' ) axis([0 60 - 8 4]) title([ '110' char(176) 'C' ]) plot(x110,y110, 'ok' ) plot(x110,ypred(36:46), ' - k' ) plot(x110,CBu(36:46), ' -- k' ) plot(x110,CBl(36:46), ' -- k' ) plot(x110,PBu(36: 46), ':k' ) plot(x110,PBl(36:46), ':k' ) %180C subplot(3,2,4); hold on set(gca, 'fontsize' ,12, 'fontweight' , 'bold' ); xlabel( 'Time (s)' ) ylabel( 'Log reductions (log CFU/g)' ) axis([0 60 - 8 4]) title([ '180' char(176) 'C' ]) plot(x180,y180, 'ok' ) plot(x180,ypred(47:5 7), ' - k' ) plot(x180,CBu(47:57), ' -- k' ) plot(x180,CBl(47:57), ' -- k' ) plot(x180,PBu(47:57), ':k' ) plot(x180,PBl(47:57), ':k' ) %190C subplot(3,2,5); hold on set(gca, 'fontsize' ,12, 'fontweight' , 'bold' ); xlabel( 'Time (s)' ) ylabel( 'Log reductions (log CFU/g)' ) axis([ 0 60 - 8 4]) title([ '190' char(176) 'C' ]) plot(x190,y190, 'ok' ) plot(x190,ypred(58:67), ' - k' ) plot(x190,CBu(58:67), ' -- k' ) plot(x190,CBl(58:67), ' -- k' ) plot(x190,PBu(58:67), ':k' ) plot(x190,PBl(58:67), ':k' ) %200C subplot(3,2,6); ho ld on set(gca, 'fontsize' ,12, 'f ontweight' , 'bold' ); xlabel( 'Time (s)' ) ylabel( 'Log reductions (log CFU/g)' ) axis([0 60 - 8 4]) title([ '200' char(176) 'C' ]) plot(x200,y200, 'ok' ) plot(x200,ypred(68:73), ' - k' ) plot(x200,CBu(68:73), ' -- k' ) plot(x200,CBl(68:73), ' -- k' ) plot(x200,PBu(68:73), ':k' ) plot(x200,PBl(68:73), ':k' ) %% Run SSC's again using optimized parameters fnameINV = @inv_T_X; modnum = 3; p=3; beta = [Dref_opt(modnum) zT_opt(modnum) zX_opt(modnum)]; Xp=SSC_V3(beta,xs,fnameINV); %can check correlation between any 2 betas by dividing an d plotting them rat12=Xp(:,1)./Xp(:,2); if p == 3 rat13=Xp(:,1)./Xp(:,3); rat23=Xp(:,2)./Xp(:,3); end if p == 4 rat14=Xp(:,1)./Xp(:,4); 93 rat24=Xp(:,2)./Xp(:,4); rat34=Xp(:,3)./Xp(:,4); end figure hold on plot(xs(1:ns),rat12, 'r' ) if p == 3 plot(xs(1:ns),rat13, 'g' ) plot(xs(1:ns),rat23, 'y' ) end if p == 4 plot(xs(1:ns),rat14, 'b' ) plot(xs(1:ns) ,rat24, 'm' ) plot(xs(1:ns),rat34, 'c' ) end title( 'Checking parameter correlation after running inverse problem' ) %% plot X' for Log CF U/g %plot for C cmap = [ 'r' 'g' 'b' 'c' 'y' 'm' 'k' ]'; figure hold on set(gca, 'fontsize' ,14, 'fontweight' , 'bold' ); %plot C vs t to know the total span ypred=fnameINV(beta,xs); zeroline = zeros(length(xs(:,1)),1); plot(xs(1:ns),zeroline(:), 'color' , 'k' , 'Li neWidth' ,1.5, 'HandleVisibility' , 'off' ) h2(1)=plot(xs(1:ns),ypred(1:ns), ' - ' , 'color' ,cmap(1,:), 'LineWidth' ,2); %plot the predicted C to compare to SSCs for i=1:p h2(i+1) = plot(xs(1:ns),Xp(1:ns,i), ' - ' , 'color' ,cmap(i+1,:), 'LineWidth' ,2); end if p == 2 %Se t appropriate # of legend entries based on # of parameters in model legend( 'Log reduction (Log CFU/g)' , 'D _ref' , 'z_T' , 'Location' , 'Best' ) end if p == 3 legend( 'Log reduction (Log CFU/g)' , 'D_r_e_f' , 'z_T' , 'z_X' , 'Location' , 'Best' ) end if p == 4 lege nd( 'Log reduction (Log CFU/g)' , 'D_ref' , 'z_T' , 'z_X' , ' \ beta_4' , 'Location' , 'Best' ) end xlabel( 'Time (s)' ); ylabel( 'Scaled sensitivity coefficient (Log CFU/g)' ); grid off %% Model validation %To use: Change Ta and D in Initial variables section to the average drying %chamber temperatures and 55um. Click run (you will get errors early, that is OK). %Then run this section. global Tref Xref dXdtref Tref = 350; Xref = 1; dXdtref = - 1; %Plot predicted lines at validation temperatures: beta_val = [14.8 170.9 17.3] y_ val = inv_T_X_val(beta_val, x_all); y_val(:,4:6)=[]; figure hold on set(gca, 'fontsize' ,14, 'fontweight' , 'bold' ); xlabel( 'Time (s)' ) ylabel( 'Log reductions (Log CFU/g)' ) plot(xs(:,1),y_val(:,1), ' - b' , 'LineWidth' ,2) plot(xs(:,1),y_val(:,2), ' - g' , 'LineWidth' ,2) plot(xs(:,1),y_val(:,3), ' - r' , 'LineWidth' ,2) %Plot pilot - scale spray dryer data: res_time(1 ) = 17.2; res_time(2) = 15.2; res_time(3) = 14.8; data_val = [ - 3.64 0.48; - 4.11 0.52; - 2.40 1.77; - 4.15 0.38]; errorbar(res_time(1),data_val(1,1),data_val(1,2), 'bo' ) errorbar(res_time(1),data_val(2,1),data_val(2,2), 'bs' ) errorbar(res_time(2),data_val(3,1), data_val(3,2), 'go' ) errorbar(res_time(2),data_val(4,1),data_val(4,2), 'gs' ) 94 legend( 'T_a_v_g=104C' , 'T_a_v_g=119C' , 'T_a_v_g=132C' , 'Primary, T_i_n_l_e_t=180C' , 'Seconda ry, T_i_n_l_e_t=180C' , 'Primary, T_i_n_l_e_t=200C' , 'Secondary, T_i_n_l_e_t=200C' ) %% Forward problem functions function Xp=SSC_V3(beta,x,yfunc) %Computes scaled sensitivity coefficients =Xp, nxp matrix %% X' = scaled sensitivity coefficients using forward - difference % This is a forward problem with known approximate parameters d=0.001; ypred=yfunc(beta,x); for i = 1:length(beta) %scaled sens coeff for forward problem betain = beta; %reset beta betain(i) = beta(i)*(1+d); yhat{i} = yfunc(betain,x); SSC{i} = (yhat{i} - ypred)/d; %scaled sens coeff for ith parameter Xp(:,i)=SSC{i}; %extract from cell array to 2D array end end function y = DropletForward(beta,t,Ta,D) %t column 1 are the times %y1 is X, y2 is Td, y3 is dX/dt %Parameters from our drying experiment: Xcr = 9; %Cr itical moisture content, dry basis [kg H2O/kg solids] 10% solids w/w Ta_C = Ta - 273; %Air temp [C] r = D/2; %Average droplet radius [m] A = 4*pi()*r^2; %Average droplet surface area [m^2] V = 4/3 *pi()*r^3; %Average droplet volume [m^3] n = 1; %Modified CDC model parameter that allows a convex drying rate rather than linear rho_feed = 1044; %Density of feed, measured for 10% w/w SPI mix [kg/m^3] rho_H2O = 997; %Density of water [kg/m^3] md = rho_fe ed*V; ms = md - rho_H2O*V; Xeq = 0.07; %Equilibriu m moisture content, dry basis, measured for powder after drying at 180C inlet air temp [kg H2O/kg solids] RH = 0.01; %Relative humidity [fraction] h_heat = 104.5 ; %Heat transfer coefficient [W/m^2*K] Twb = 2 73+Ta_C*atan(0.151977*(RH+8.313659)^(1/2))+atan( Ta_C+RH) - atan(RH - 1.676331)+0.00391838*(RH)^(3/2)*atan(0.023101*RH) - 4.686035; %Wet bulb temp [K], from Stull 2011 Hvap = - 2430*10^3; %Heat of vaporization of water cp = 4120; %Specific heat of water [J/kg*K] %Generate droplet drying data now: tspan=t(:,1); %we want y at every t [t,y]=ode45(@droplet,tspan,beta); function dy = droplet(t,y) %Computes dT/dt and dX/dt at each time point f = @(X)((X - Xeq)/(Xcr - Xeq))^n; dy(1)= f(y(1))*(A*h_heat/ms/ Hvap)*(Ta - Twb); dy(2)= (h_heat*A*(Ta - y(2 )) - Hvap*ms*dy(1))/(md*cp); dy=dy'; end y1=y(:,1); y2=y(:,2); %predicted values (y1=X, y2=Td) for i=1:(length(t) - 1) %Calculates drying rate as X(t+1) - X(t) for each time point y3(i)=y1(i+1) - y1(i); %y3=dX/dt end y3(length(t)) = 0; %Final timepoint drying rate is 0 y3=y3'; y=[y1;y2;y3]; %put the y's into a column and return the values end %% Inactivation model functions %Barebones models: function y = inv_T(beta,t) global Tref sim_data x_all; time = t(:,1); X = t(:,2); Td = t(:,3); delta = 1/10; % Each time step is 1/10 of a second, using xs=linspace(0,60,601); for i=1:length(time) DV(i) = beta(1).*(10.^((Tref - Td(i))./beta(2))); y(i) = - 1.*delta.*trapz(1./DV); end 95 y=y'; end function y = inv_X(beta,t) global Xref sim_data x_all; time = t(:,1); X = t(:,2); Td = t(:,3); delta = 1/10; % Each time step is 1/10 of a second, using xs=linspace(0,60,601); for i=1:length(time) DV(i) = beta(1).*(10.^((Xref - X(i))./beta(2))); y(i) = - 1.*delta.*trapz(1./DV); end y=y'; end function y = inv_T_X(beta,t) global Tref Xref sim_data x_all; time = t(:,1); X = t(:,2); Td = t(:,3); delta = 1/10; % Each time step is 1/10 of a second, using xs=linspace(0,60,601); for i=1:length(time) DV(i) = beta(1).*(10.^((Tref - Td(i))./beta(2))+((Xref - X(i))./beta(3))); y(i) = - 1.*delta.*trapz(1./DV); end y=y'; end %Functions for Dref estimation using f ixed other parameters: function y = inv_Tp_wF(beta,t,zT_fixed) global T ref sim_data x_all; %Now calculate smooth inactivation curve for simulated droplet xobs = t; y_all = zeros(601,6); delta = 1/10; % Each time step is 1/10 of a second , using xs=linspace(0,60,601); for i=1:length(x_all(1,:))/5 %Each Ta ge ts a loop for j=1:length(x_all(:,1)) %Each timestep within x_all DV(j,i) = beta(1).*(10.^((Tref - x_all(j,5*(i - 1)+4))./zT_fixed)); %Calculate D - value at each condi tion y_all(j,i) = - 1.*delta.*trapz(1./DV(1:j,i)); %Integrate all D - values up to that timepoint to get total inactivation end end %Now need to assign the correct y_all to yobs as yobs for i=1:length(xobs(:,1)) %For each obser ved data point for j = 1:length(x_all(1,:))/5 %Loop through all simulated air temperatures to check for a match if sim_data(i,1)+273 == x_all(1,5*(j - 1)+2) obsTime = sim_data(i,2); obsTimeIndex = obsTime*10+1; y(i)=y_all(obsTimeIndex,j); end end end y=y'; end function y = inv_Xp_wF(beta,t,zX_fixed) global Xref sim_data x_all; %Calculate smooth inactivation curve for simulated droplet xobs = t; y_all = zero s(601,6); delta = 1/10; % Each time step is 1/10 of a second, using xs=linspace(0,60,601); for i=1:length(x_all(1,:))/5 %Each Ta gets a loop for j=1:length(x_all(:,1)) %Each timestep within x_all DV(j,i) = beta(1).*(10.^((Xref - x _all(j,5*(i - 1)+3))./zX_fixed)); y_all(j,i) = - 1.*delta.*trapz(1./DV(1:j,i)); end end %Now need to assign the correct y_all to yobs as yobs for i=1:length(xobs(:,1)) %For each obser ved data point for j = 1:length(x_al l(1,:))/5 %Loop through all simulated air temperatures to check for a match 96 if sim_data(i,1)+273 == x_all(1,5*(j - 1)+2) obsTime = sim_data(i,2); obsTimeIndex = obsTime*10+1; y(i)=y_all(obsTimeIndex,j); end end end y=y'; end function y = inv_T_Xp_wF(beta,t,zT_fixed, zX_fixed) global Tref Xref sim_data x_all; %Calculate smooth inactivation curve for simulated droplet xobs = t; y_all = zeros(601,6); delta = 1/10; % Each time step is 1/10 of a second, using xs=linspace(0,60,601); for i=1:length(x_all(1,:))/5 %Each Ta gets a loop for j=1:length(x_all(:,1)) % Each timestep within x_all DV(j,i) = beta(1).*(10.^(((Tref - x_all(j,5*(i - 1)+4))./zT_fix ed)+((Xref - x_all(j,5*(i - 1)+3))./zX_fixed))); y_all(j,i) = - 1.*delta.*trapz(1./DV(1:j,i)); end end %Now need to assign the correct y_all to yobs as yobs for i=1:length(xobs(:,1)) %For each observed data point for j = 1:length(x_all(1,:))/5 %Loop through all simulated air temperatures to check for a match if sim_data(i,1)+273 == x_all(1,5*(j - 1)+2) obsTime = sim_data(i,2); obsTimeIndex = obsTime*10+1; y(i)=y_all(obsTim eIndex,j); end end end y=y'; end %Functions for parameter (zT and zX) estimate error using fixed Dref: function y = inv_Tp_Dfixed(beta,t,Dref_fixed) global Tref Xref sim_data x_all; %Now calculate smooth inactivation cu rve for simulated droplet xobs = t; y_all = zeros(601,6); delta = 1/10; % Each time step is 1/10 of a second, using xs=linspace(0,60,601); for i=1:length(x_all(1,:))/5 %Each Ta gets a loop for j=1:length(x_all(:,1)) %Each timestep w ithin x_all DV(j,i) = Dref_fixed.*(10.^((Tref - x_all(j,5*(i - 1)+4))./beta(1))); y_all(j,i) = - 1.*delta.*tr apz(1./DV(1:j,i)); end end %Now need to assign the correct y_all to yobs as yobs for i=1:length(xobs(:,1)) % For each observed data point for j = 1:length(x_all(1,:))/5 %Loop through all simulated air temperatures to check for a match if sim_data(i,1)+273 == x_all(1,5*(j - 1)+2) obsTime = sim_data(i,2); obsTimeIndex = obsTime*10+1; y(i)=y_all(obsTimeIndex,j); end end end y=y'; end function y = inv_Xp_Dfixed(beta,t,Dref_fixed) global Tref Xref sim_data x_all; %Calculate smooth inactivation curve for simulated droplet x obs = t; y_all = zeros(601,6); delta = 1/10; % Each time step is 1/10 of a second, using xs=linspace(0,60 ,601); for i=1:length(x_all(1,:))/5 %Each Ta gets a loop for j=1:length(x_all(:,1)) %Each timestep within x_all DV(j,i) = Dref_fixed.*(10.^((Xref - x_all(j,5*(i - 1)+3))./beta(1))); 97 y_all(j,i) = - 1.*delta.*trapz(1./DV(1:j,i) ); end end %Now need to assign the correct y_all to yobs as yobs for i=1:length(xobs(:,1)) %For each observed data point for j = 1:length(x_all(1,:))/5 %Loop through all simulated air temperatures to check for a match if sim_data(i,1)+273 == x_all(1,5*(j - 1)+2) obsTime = sim_data(i,2); obsTimeIndex = obsTime*10+1; y( i)=y_all(obsTimeIndex,j); end end end y=y'; end function y = inv_T_Xp_Dfixed(beta,t,Dref_fixed) global Tref Xref sim_data x_all; %Calculate smooth inactivation curve for simulated droplet xobs = t; y_all = zeros(6 01,6); delta = 1/10; % Each time step is 1/10 of a second, using xs=linspace(0,60,601); for i=1:length(x_all(1,:))/5 %Each Ta gets a loop for j=1:length(x_all(:,1)) %Each timestep within x_all DV(j,i) = Dref_fixed.*(10.^(((Tref - x_all(j,5*(i - 1)+4))./beta(1))+((Xref - x_all(j,5*(i - 1)+3))./beta(2)))); y_all(j,i) = - 1.*delta.*trapz(1./DV(1:j,i)); end end %Now need to assign the correct y_all to yobs as yobs for i=1:length(xobs(:,1)) %For each observed da ta point for j = 1:length(x_all(1,:))/5 %Loop through all sim ulated air temperatures to check for a match if sim_data(i,1)+273 == x_all(1,5*(j - 1)+2) obsTime = sim_data(i,2); obsTimeIndex = obsTime*10+1; y(i)=y_all(obsTimeIndex,j); end end en d y=y'; end %Functions for getting AIC values: function y = inv_T_simple(beta,t) global Tref Xref sim_data x_all; %Now calculate smooth inactivation curve for simulated drop let xobs = t; y_all = zeros(601,6); delta = 1/10; % Each time step is 1/10 of a second, using xs=linspace(0,60,601); for i=1:length(x_all(1,:))/5 %Each Ta gets a loop for j=1:length(x_all(:,1)) %Each timestep within x_all DV(j,i) = beta(1).*(10.^((Tref - x_all(j,5*(i - 1) +4))./beta(2))); y_all(j,i) = - 1.*delta.*trapz(1./DV(1:j,i)); end end %Now need to assign the correct y_all to yobs as yobs for i=1:length(xobs(:,1)) %For each observed data po int for j = 1:length(x_all(1,:))/5 %Loop through all simulated air temperatures to check for a match if sim_data(i,1)+273 == x_all(1,5*(j - 1)+2) obsTime = sim_data(i,2); obsTimeIndex = obsTime*10+1; y(i)=y_all(o bsTimeIndex,j); end end end y=y'; end function y = inv_X_simple(beta,t) global Tref Xref sim_data x_all; 98 %Calculate smooth inactivation curve for simulated droplet xobs = t; y_all = zeros(601,6); delta = 1/10; % Each time step is 1/10 of a second, using xs=linspace(0,60,601); for i=1:length(x_all(1,:))/5 %Each Ta gets a loop for j=1:length(x_all(:,1)) %Each timestep within x_all DV(j,i) = beta(1).*(10.^((Xref - x_all(j,5*(i - 1)+3))./beta(2))); y_all(j,i) = - 1.*delta.*trapz(1./DV(1:j,i)); end end %Now need to assign the correct y_all to yobs as yobs for i=1:length(xobs(:,1)) %For each observ ed data point for j = 1:length(x_all(1,:))/5 %Lo op through all simulated air temperatures to check for a match if sim_data(i,1)+273 == x_all(1,5*(j - 1)+2) obsTime = sim_data(i,2); obsTimeIndex = obsTime*10+1; y(i)=y_all(obsTimeIndex,j); end end end y=y'; end function y = inv_T_X_simple(beta,t) global Tref Xref sim_data x_all; %Calculate smooth inactivation curve for simulated droplet xobs = t; y_all = zeros(601,6); delta = 1/10; % Each time step is 1/10 of a second, using xs=linspace(0,60,601); for i=1:length(x_all(1,:))/5 %Each Ta gets a loop for j=1:length(x_all(:,1)) %Each timestep within x_all DV(j,i) = beta(1).*(10.^(((Tref - x_all(j,5*(i - 1)+4))./beta(2))+((Xref - x_all(j,5*(i - 1)+3)) ./beta(3)))); y_all(j,i) = - 1.*delta.*trapz(1./DV(1:j,i)); end end %Now need to assign the correct y_all to yobs as yobs f or i=1:length(xobs(:,1)) %For each observed data point for j = 1:length(x_all(1,:))/5 %Loop through all simulated air temperatures to check for a match if sim_data(i,1)+273 == x_all(1,5*(j - 1)+2) obsTime = sim_data(i,2); obsTimeIndex = obsTime*10+1; y(i)=y_all(obsTimeIndex,j); end end end y=y'; end %Function for validation function y = inv_T_X_val(beta,t) global Tref Xref sim_data x_all; %Calculate smooth inactivation curve for simulated droplet xobs = t; y_all = zeros(601,6); delta = 1/10; % Each time step is 1/10 of a second, using xs=linspace(0,60,601); for i=1:length(x_all(1,:))/5 %Each Ta gets a loop for j=1:length(x_all(:,1)) %Each timestep within x_all DV(j,i) = beta(1).*(10.^(((Tref - x_all(j,5*(i - 1)+4))./beta(2))+((Xre f - x_all(j,5*(i - 1)+3))./beta(3)))); y_all(j,i) = - 1.*delta.*trapz(1./DV(1:j,i)); end end y=y_all; end 99 REFERENCES 100 REFERENCES Adhikari, B, T Howes, BR Bhandari, and V Troung. 2003. 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