THE UTILIZATION OF CAVITATION FOR THE HOMOGENIZATION OF MILK PRODUCTS By CHING CHEE LOO A THESIS Submitted to the School of Graduate Studies of Michigan State College of Agriculture and Applied Science in partial fulfillment of the requirements for the degree of DOCTOR OF PHILOSOPHY Department of Agricultural Engineering 1952 ProQuest Number: 10008370 All rights reserved INFORMATION TO ALL USERS The quality of this reproduction is dependent upon the quality of the copy submitted. In the unlikely event that the author did not send a complete manuscript and there are missing pages, these will be noted. Also, if material had to be removed, a note will indicate the deletion. uest. ProQuest 10008370 Published by ProQuest LLC (2016). Copyright of the Dissertation is held by the Author. All rights reserved. This work is protected against unauthorized copying under Title 17, United States Code Microform Edition © ProQuest LLC. ProQuest LLC. 789 East Eisenhower Parkway P.O. Box 1346 Ann Arbor, Ml 48106-1346 ACKNOWLEDGMENTS The author is indebted to Professor Arthur W. Farrall, head of the Agricultural Engineering Department, Michigan State College, for his con­ stant concern and advice, and for his. bestowment of the Graduate Research Assistantship which enabled the author to complete this work, Dr. Walter M. Carleton, associate professor of the De­ partment of Agricultural Engineering, for his helpful counsel, interest, and encouragement during the entire course of the experiment, as well as reading and offering criticisms on the manuscript of this thesis, Dr. G. Malcolm Trout, professor of the Department of Dairy, Michigan State College, for his inestimable suggestions, constructive criticism, kind permission to use the equipment in the laboratories of the Department of Dairy and assistance in procuring milk and other dairy products for the experiment, Mr. James B. Cawood, mechanical technician of the Research Laboratory, Department of Agricultural Engineering, Michigan State College, for his valuable aid in the construction of equipment used in the experiment, Dr. Jay R. Brunner, assistant professor of the Department of Dairy, Michigan State College, for his unselfish help in performing part of the tests of the samples, 304389 iii Mr. Arthur V. Arm!tage, superintendent of the Michigan State College Creamery, and his staff for their cooperative­ ness that enabled the expeditious progress of the work, Vickers Incorporated, for their donation of the swashplate pump without which this investigation would have been many times more difficult, and Mrs. Jean Bowen, for her many corrections in the manu­ script and her expert typing of this thesis. Ching Chee Loo candidate for the degree of Doctor of Philosophy Final examination, March 4, 1952, 10:00 A. M., Agricultural Engineering Conference Room Dissertation: The Utilization of Cavitation for the Homo­ genization of Milk Products Outline of Studies Major subject: Agricultural Engineering Minor subjects: Mathematics, Mechanical Engineering, Chemi cal Engineering Biographical Items Born, September 29* 1923* Canton, China Undergraduate Studies, Henry Lester Institute of Technical Education, Shanghai, 1940-43, St. John's University, Shang hai, 1944-46 Graduate Studies, Colorado A & M College, 1947-48, Ohio State University, 1948-49, Michigan State College, 1950-52 Experience: Superintendent, Cathay Dairy Farm, Shanghai, 1943-47* Graduate Assistant, Ohio State Uni­ versity, 1948-49* Graduate Research Assistant Michigan State College, 1950-52 Member of Gamma Sigma Delta, Associate Member of the American Society of Agricultural Engineers THE UTILIZATION OP CAVITATION FOR THE HOMOGENIZATION OF MILK PRODUCTS By Ching Chee Loo AN ABSTRACT Submitted to the School of Graduate Studies of Michigan State College of Agriculture and Applied Science in partial fulfillment of the requirements for the degree of DOCTOR OF PHILOSOPHY Department of Agricultural Engineering Year Approved -i 1952 , 0117 ///■ vi CHING CHEE LOO ABSTRACT The phenomenon of cavitation* which is the rapid forma­ tion and collapse of cavities in a liquid* has been known to have a serious damaging effect in hydraulic equipment and it is also believed by many authors to be capable of producing emulsion. It was the aim of this work to examine critically the role of cavitation in homogenization of milk products and to determine the possibility of more effective utilization of cavitation in homogenization. By inserting a steel cylinder between the first-stage and second-stage homogenizer blocks it was possible to obtain samples of milk which had not gone through the second-stage valve and yet would show the influence of the backing up of pressure by the second-stage valve on the homogenization efficiency of the first-stage valve. It was found that back pressures lower than atmospheric or higher than 500 psi re­ duced the homogenization efficiency. Two bleeding valves* which resembled the regular homo­ genizer valve but had tiny bleeding holes at various locations were used to show pressure variation and the progress of homo­ genization inside the valve clearance. Results showed that a big dip in pressure to almost atmospheric occured near the inner edge of the valve and homogenization was practically completed right beyond this location. The dip In pressure was believed to be an indication of the occurence of cavita­ tion. ABSTRACT CHING CHEE LOO A homogenizer valve with the valve seat narrowed down to a knife-edge homogenized both milk and concentrated milk sat­ isfactorily at a pump pressure of 800 to 1000 psi and a back pressure of 50 to 150 psi. Ice cream mix was not satisfactorily homogenized at similar pressures unless air at a saturation pressure of 75 psi was introduced into the mix. The air was believed to help overcome the inhibitive effect on cavitation of sugar and gelatin which were present in large quantities in the ice cream mix. A Vickers swash-plate pump was used to give very smooth pressure for these experiments. Several other knife-edged valves were tried in a high capacity triplex type homogenizer, but results were insuffic­ ient for a reliable evaluation of the knife-edged valve when used in that type of homogenizer. TABLE OP CONTENTS Page INTRODUCTION.......................................... 1 REVIEW OP LITERATURE.................................. 5 GENERAL STATEMENT OP PROBLEM.......................... 9 EXPERIMENTAL WORK..................................... 10 Part I Part II Cavitation by Partial Vacuum ........ Purpose............................. 10 Method.................................. 11 Procedure...................... 12 Results............. .............. . 15 Discussion. 15 ............. Influence of Exit SideHydrostatic Pressure on Homogenization Efficiency 15 ............................... 15 Methods andProcedures................... 15 Results................................ 21 Discussion.............................. 25 Purpose Part III 10 "Bleeding Valve"Experiments.............. 26 Purpose................................. 26 Apparatus............................... 26 Procedures.............................. 29 Results................................. 5° Discussion....... ....................... 55 ix Page Part IV Construction of an Experimental Knifeedged Homogenizer Valve.......... Part V 57 Homogenization Characteristics of the Knife-edged Valve with No AirInjection... 45 Procedure for milk 45 • Procedure for concentrated milk........ 44 Procedure for ice cream.mix............ 45 Results of the homogenization of milk using the knife-edgedvalve............. 45 Results of the homogenization of milk using the Manton-Gaulin valve in the Vickers pump set-up.................... 52 Results of the homogenization of con­ centrated milk using the knife-edged valve.......... 55 Results of the homogenization of ice cream mix using theknife-edged valve... Discussion................. ............. Part VI 57 Homogenization Characteristics of the Knife-edged Valve with AirInjection Purpose ............... 60 60 Procedure........... ................... 60 Results 62 .......................... Conclusion.......... .......... Part VII 55 66 Durability Test of the Knife-edged Homogenizer Valve......................... 68 X Page Purpose Procedure .......................... ........ 68 68 Result.................... 69 Conclusion................ 70 Part VIII Trial of the Knife-edged Valve in a High Capacity Triplex Homogenizer............. 71 Purpose................................. 71 Procedure............................... 72 Results................................. 73 Conclusions............................. 73 CONCLUSIONS........................................... 75 APPENDICES APPENDIX I The Design of the Vacuum Homogenization Valve .......................... 76 APPENDIX II The Calibration of the Capacity Regu­ lation Valve of the Rotary Pump Used in the Experiment of Vacuum Homogen­ ization..................... 80 APPENDIX I H A Mathematical Study of the Magnitude of the Force Necessary to Break a Fat Globule................................. 84 APPENDIX IV A Mathematical Study of the Size of Cavity Which is Capable of Breaking a Fat Globule on Its Collapse.......... APPENDIX V Determining the Representativeness of the Milk Collected in the Steel Cylinder 87 xi Page Inserted between the First- and the Second-stage Valve Blocks of a MantonGaulin Laboratory Homogenizer........ APPENDIX VI 91 Some Peculiarities in the Pressure Adjustment of the Single-Piston Twostage Laboratory Model Homogenizer.... APPENDIX VII 95 Statistical Analysis of the Results Obtained from the Experiments of Applying Pressure to the Exit Side of a Homogenizer Valve in a MantonGaulin Single-piston Homogenizer 99 APPENDIX VIII Statistical Analysis of the Results Obtained from the Bleeding Valve Experiments........... ......... ...... APPENDIX IX 102 Composition of the Plain Ice Cream Mix and Chocolate Ice Cream Mix % Used in the Experiments.............. APPENDIX X 109 Statistical Analysis of Twelve Runs of Homogenization of Milk Using Knifeedged Valves of Four Different Diameters............................. APPENDIX XI 110 A Comparison of the U.S.P.H.S. Method and Farrall's Method of Judging the Degree of Homogenization of Milk............................... APPENDIX XII Statistical Analysis of the Results 117 xii Page of Homogenizing Milk with Air In­ jectionUsing the Knife-edged Valve... 122 APPENDIX XIII Statistical Analysis of the Results of Homogenizing Ice Cream Mix with Air Injection Using the Knife-edged Valve................................. APPENDIX XIV 124 Statistical Analysis of the Results of Homogenizing Concentrated Milk with Air Injection Using the Knifeedged Valve....................... BIBLIOGRAPHY.......................................... 129 131 LIST OP FIGURES Figure 1. Page Diagram showing the experimental set-up for sucking milk through a special valve of curved cross-section........................... 2. 12 Arrangement for applying vacuum to the exit side of a homogenizer valve and for collecting 16 milk samples................... 3. Disc inserted between the first-stage valve block and the second-stage valve block for taking milk samples between the two valves 4. 17 Inserting a steel cylinder between the firststage and the second-stage of a homogenizer.... 5. Enlarged views of the "bleeding valve" 6. Cut-away view of the valve block of a Manton- 19 27 Gaulin homogenizer showing the bleeding valve in position.................................... 7. 28 Variation of the hydrostatic pressure along the clearance of a homogenizer valve 32 8. Knife-edged homogenizer valve 40 9. Cavity collapse pressure control valve for use ............ in connection with the knife-edged homogenizer valve......... 40 xiv Figure 10. Page Assembled view of the experimental homogenizer using a Vickers pump............................. 11. 4l Operation chart of the knife-edged valve for 0 to 500 psi second-stage pressure with no air injection. .......................... 12. 48 Operation chart of the knife-edged valve for 0 to 150 psi second-stage pressure with no air injection......................... 13 . Cross-sectional views of knife-edged homo­ genizer valves of three different diameters designed to fit into a Cherry-Burrell 500gallons -per-hour homogenizer.................. 50 LIST OF FIGURES IN APPENDICES Figure AI Page Cross-sectional view of the experimental vacuum homogenization valve.................... A2 79 Calibration chart of the capacity regulation valve of the rotary pump used to produce vacuum for the vacuum homogenization valve A3 8l Pipe line connection of the vacuum homo­ genization valve, the regulation valve, and the rotary pump................................ A4 Views of the regulation valve showing the slot cut to increase its sensitivity....... A5 Two plates separated by a drop of liquid....... A6 A liquid sphere breaking into halves along a meridian plane............................... A7 8l 82 84 85 Hypothetical process of breaking a liquid sphere by reducing the equatorial diameter to zero........................................ A8 ........................... A9 ................................................. 85 86 86 A10 Hypothetical process of shearing a liquid sphere....... All Degrees of homogenization of successive quarts of milk discharged from the Manton-Gaulin labatory homogenizer with a steel cylinder inserted 86 xvi Figure Page between the first-stage and the second-stage blocks.............. .......................... A12 92 Farrall's index versus U.S.P.H.S. index of the degrees of homogenization of eleven samples of milk............... .......... . 118 LIST OF TABLES TABLE I Page THE DEGREE OF HOMOGENIZATION OF MILK (EXPRESSED IN U.S.P.H.S. INDEX) TREATED BY SUCTION THROUGH A SPECIAL VALVE OF CURVED CROSS-SECTION.......... II 13 DEGREE OF HOMOGENIZATION (EXPRESSED AS U.S.P.H. S. INDEX) AS INFLUENCED BY APPLYING VACUUM TO THE EXIT SIDE OF A HOMOGENIZER VALVE............. III 22 DEGREE OF HOMOGENIZATION OF MILK (EXPRESSED AS U.S.P.H.S. INDEX) AS INFLUENCED BY APPLYING PRES­ SURE TO THE EXIT SIDE OF THE HOMOGENIZER VALVE............................................. IV 23 DEGREE OF HOMOGENIZATION OF MILK (EXPRESSED AS U.S.P.H.S. INDEX) AS INFLUENCED BY APPLYING PRESSURE TO THE EXIT SIDE OF THE HOMOGENIZER VALVE............................................. V 24 HEIGHTS OF WATER JETS ISSUING FROM THE PLASTIC TUBINGS OF THE BLEEDING VALVES IN INCHES OR FEET AS INDICATED................................ VI 31 DEGREE OF HOMOGENIZATION (EXPRESSED IN FARRALL1S INDEX) OF MILK TAKEN AT DIFFERENT LOCATIONS OF A FOUR-HOLE BLEEDING VALVE...,.................... VII 33 DEGREE OF HOMOGENIZATION (EXPRESSED IN FARRALL’S INDEX) OF MILK TAKEN AT DIFFERENT LOCATIONS OF AN EIGHT-HOLE BLEEDING VALVE..................... 34 xviii TABLE Page VIII U.S.P.H.S. INDICES OF FOUR RUNS OF HOMOGEN­ IZATION OF MILK USING A KNIFE-EDGED VALVE....... IX 47 U.S.P.H.S. INDICES OF TWELVE RUNS OF HOMOGEN­ IZATION OF MILK USING FOUR KNIFE-EDGED VALVES OF FOUR DIFFERENT DIAMETERS...................... X 49 EFFECTS OF HOMOGENIZATION BY MEANS OF THE KNIFE-EDGED VALVE AND THE MANTON-GAULIN VALVE ON THE PROTEIN STABILITY AND CURD TENSION OF MILK........................... XI DEGREE OF HOMOGENIZATION OF MILK HOMOGENIZED BY THE MANTON-GAULIN VALVE IN THE VICKERS PUMP SET-UP..................................... XII 53 EFFECTS OF HOMOGENIZATION BY MEANS OF THE KNIFEEDGED VALVE AND THE MANTON-GAULIN VALVE ON THE PROTEIN STABILITY, CURD TENSION AND FAT GLOBULE SIZE OF CONCENTRATED MILK.............. 54 XIII EFFECTS OF HOMOGENIZATION BY MEANS OF THE KNIFEEDGED VALVE AND THE CHERRY-BURRELL VALVE ON THE VISCOSITY AND FAT GLOBULE SIZE OF ICE CREAM MIXES........................................... XIV EFFECTS OF ADDING AIR TO MILK ON HOMOGENIZATION EFFICIENCY...................................... XV 63 EFFECTS OF ADDING AIR TO ICE CREAM MIX ON HOMOGENIZATION EFFICIENCY ANDVISCOSITY......... XVI 56 64 EFFECTS OF ADDING AIR TO CONCENTRATED MILK ON HOMOGENIZATION EFFICIENCY................... 66 xix TABLE XVII Page DURABILITY OF THE KNIFE-EDGED HOMOGENIZER VALVE............................................ 69 XVIII PERFORMANCE OF KNIFE-EDGED VALVE IN A 500GALLONS-PER-HOUR TRIPLEX HOMOGENIZER............. 73 LIST OP TABLES IN APPENDICES TABLE AI Page THE CAPACITY OF THE ROTARY PUMP AT VARIOUS DEGREES OF VACUUM AND SETTINGS OF THE 85 REGULATION VALVE................................. All DEGREES OF HOMOGENIZATION OF SUCCESSIVE QUARTS OF MILK DISCHARGED FROM A MANTON-GAULIN LAB­ ORATORY MODEL CGB 25 GPH HOMOGENIZER WITH A STEEL CYLINDER INSERTED BETWEEN THE FIRSTAND THE SECOND-STAGE VALVE BLOCKS............... AIII 91 PRESSURE READINGS INDICATED BY A SINGLE PRES­ SURE GAGE OF A TWO-STAGE SINGLE-PISTON HOMO­ GENIZER WHEN THE VALVES WERE ADJUSTED IN THE CONVENTIONAL WAY................................. AIV CAPACITY OF THE TWO-STAGE SINGLE-PISTON LABORATORY HOMOGENIZER AT VARIOUS PRESSURES AV 9^ 95 BEHAVIOR OF THE READINGS OF TWO PRESSURE GAGES OF A TWO-STAGE SINGLE-PISTON HOMO­ GENIZER - 1 ...................................... AVI 95 BEHAVIOR OF THE READINGS OF TWO PRESSURE GAGES OF A TWO-STAGE SINGLE-PISTON HOMO­ GENIZER - II ..................................... AVII 96 BEHAVIOR OF THE READINGS OF A SINGLE PRESSURE GAGE OF A TWO-STAGE TRIPLEX HOMOGENIZER......... 97 xxi TABLE Page AVIII EFFECT OF THE APPLICATION OF PRESSURE ON THE EXIT SIDE OF A HOMOGENIZER VALVE ON HOMOGEN­ IZATION EFFICIENCY - 1 ......................... AIX 99 ANALYSIS OF VARIANCE OF THE EXPERIMENT OF APPLYING PRESSURE TO THE EXIT SIDE OF A HOMO­ GENIZER VALVE WHILE THE PRESSURE DIFFERENCE ACROSS IT WAS KEPT AX CONSTANT.................. 100 EFFECT OF THE APPLICATION OF PRESSURE ON THE EXIT SIDE*OF HOMOGENIZER VALVE ON HOMOGEN­ IZATION EFFICIENCY AXI - II...................... 101 ANALYSIS OF VARIANCE OF THE EXPERIMENT OF APPLYING PRESSURE TO THE EXIT SIDE OF HOMO­ GENIZER VALVE WHILE ITS SETTING WAS KEPT CONSTANT AXII ................................. 102 DEGREES OF HOMOGENIZATION (IN TERMS OF FARRALL1S INDEX) OF MILK AT FOUR DIFFERENT LOCATIONS IN THE HOMOGENIZER VALVE........... AXIII ANALYSIS OF VARIANCE OF THE BLEEDING VALVE EXPERIMENT USING A FOUR-HOLE VALVE........... AXIV 105 104 DEGREES OF HOMOGENIZATION (IN TERMS OF FARRALLfS INDEX) OF MILK AT EIGHT DIFFER­ ENT LOCATIONS IN THE HOMOGENIZER VALVE....... AXV ANALYSIS OF VARIANCE OF THE BLEEDING VALVE EXPERIMENT USING AN EIGHT-HOLE VALVE......... AXVI 106 U.S.P.H.S. INDICES OF HOMOGENIZATION OBTAINED BY USING FOUR SIZES OF KNIFE-EDGED VALVES, 107 xxii TABLE Page THREE FIRST-STAGE PRESSURES, AND FOUR SECOND-STAGE PRESSURES....................... AXVII 110 TWO 2-WAY TABLES, SUMMARY OF TWELVE RUNS OF HOMOGENIZATION OF MILK USING KNIFE-EDGED VALVES....................................... AXVIII Ill ANALYSIS OF VARIANCE OF THE TWELVE RUNS OF HOMOGENIZATION OF MILK USING KNIFE-EDGED VALVES OF FOUR DIFFERENT DIAMETERS........... - 115 AXIX THE DEGREE OF HOMOGENIZATION OF ELEVEN SAMPLES OF MILK MEASURED BY THE U.S.P.H.S. AND FARRALL'S METHODS........................ AXX REGRESSION OF THE U.S.P.H.S. INDEX ON FARRALL’S INDEX OF HOMOGENIZATION........... AXXI 119 EFFECT OF ADDING AIR TO MILK ON HOMOGENIZA­ TION EFFICIENCY.............................. AXXII 117 122 ANALYSIS OF VARIANCE OF THE EFFECT OF ADDING AIR TO MILK ON HOMOGENIZATION EFFICIENCY.................................... AXXIII EFFECT OF ADDING AIR TO ICE CREAM MIX ON HOMOGENIZATION EFFICIENCY................... AXXIV 125 124 THREE TWO-WAY TABLES OF THE EFFECT OF ADD­ ING AIR TO ICE CREAM MIX ON HOMOGENIZATION EFFICIENCY................................... AXXV 125 ANALYSIS OF VARIANCE OF THE EFFECT OF ADD­ ING AIR TO ICE CREAM MIX ON HOMOGENIZATION EFFICIENCY................................... 127 xxlll TABLE AXXVT Page EFFECT OF ADDING AIR TO CONCENTRATED MILK ON HOMOGENIZATION EFFICIENCY................ AXXVII 129 ANALYSIS OF VARIANCE OF THE EFFECT OF ADDING AIR TO CONCENTRATED MILK ON HOMOGENIZATION EFFICIENCY.................... 150 INTRODUCTION Homogenization has been having a widening application in the milk industry since its invention half a century ago. During this half century most of the research work in homo­ genization has been centered around its physical and chemical effects on the quality of the product. Very little work has been done concerning the physical process of homogenization. Several theories, without substantial experimental support, have been advanced to explain the mechanism of homogenization. Among them the more popular ones are shearing, grinding, ex­ ploding, and impinging. A new theory was proposed by Loo, Slatter, and Powell in 194-9 (16). They obtained experimental evidence showing that homogenization of milk products was partially due to a physical phenomenon known as cavitation. Cavitation, the rapid formation and subsequent collapse of bubbles in a liquid, has been known for some time as the cause of certain kinds of damage in ship propellers and other hy­ draulic equipment. It also has been believed to have an important role in the production of emulsion by ultrasonic means. The action of cavitation is very much the same as water hammer. The magnitude of its hammering force was estimated by Bottomley (5) at 120 tons per square inch. Therefore, - 2 cavitation may be likened to the action of numerous minute yet powerful immaginary hammers in the liquid. In view of the fact that homogenizers designed on the conventional theories spend a great portion of the power supplied in over coming friction it appears worthwhile to investigate the possibility of easier homogenization by better utilization of cavitation. 3 - - REVIEW OP LITERATURE Publications concerning homogenization of milk pro­ ducts have been plentiful. Perhaps the most voluminous and comprehensive bibliography ever published on homogen­ ization is the one prepared by Trout (24). However, the amount of literature concerning the physical process of homogenization has been very small, and a great portion of it was only speculative. A paper suggesting cavitation as a factor of homogen­ ization was published by Loo, Slatter and Powell (16). Wenrich (27) in discussing the mechanism of homogenization postulated that there should be partial vacuum at the homogenizer valve. His postulation seems to be consistent with the cavitation theory of Loo, Slatter, and Powell, because under usual conditions a partial vacuum is a necessary con­ dition of cavitation. A considerable amount of literature on cavitation as related to emulsion formation was reviewed by Loo (15). The usual concept of cavitation procedure is that, when the hydrostatic pressure drops to vapor pressure, there will appear in a liquid, vapor cavities which will collapse instantaneously when the vapor is forced to condense by rising hydrostatic pressure (l4) (21) (26 ). A theory quite different from the usual concept and which had been overlooked until lately is that formulated - 4 by Van Iterson (25) in 1936. He suggested that cavitation erosion was due to the collapse of minute air bubbles in water in a state of air supersaturation. A dynamical aspect of the problem was examined with the aid of a micro­ scope. It was found that for water saturated with air at atmospheric pressure, the bubbles originated within the boundary layer at points where the absolute pressure was about half an atmosphere in the case of clean water: bubble then had an initial diameter of 0.6 microns. the The estimated life history of such a bubble was extremely short in terms of space and time. He concluded that surface tension might exert an appreciable influence on cavitation. Van Iterson's theory was examined by Bottomley (5) both theoretically and experimentally and was found to be more acceptable than the conventional theory of vapor condensa­ tion as the cause of bubble collapse. Bottomley was able to arrive at, by means of thermodynamical calculations, two equilibrium states of air in water that may exist under the same set of conditions. One of the equilibrium states would be one in which there were no air bubbles and the air pressure in the liquid was that of air saturation pressure. The other equilibrium state would be one where there were a definite number of bubbles formed with a definite radius and the gas pressure was capillary pressure which was higher than sat­ uration pressure. There could be no intermediate state and the system would jump from one state into another according - 5 to whether the pressure was tending to rise or fall. He showed that the energy which produced movement in the liquid during collapse was not derived from the hydrostatic pressure but was the surface energy released due to the reduction in the surface area of the bubble less the net energy required to compress the air into solution. Maximum velocity of collapse could be that of sound in water and the instantaneous pressure 120 tons per square inch. Lord Rayleigh (19) derived mathematically an expression of the velocity of the collapse of a vapor cavity. He based his calculation on the assumption that the cavity was round and there was a complete vacuum in the cavity at the moment of its collapse. His expression for the radial velocity of the inrushing liquid was UR = where - ljj feet per second, U r is the radial velocity of the inrushing liquid, feet per second, R0 is the initial radius of the cavity, feet, R is the radius at the moment under consideration, feet, P is the hydrostatic pressure, poundals per square foot, and p is the density of the liquid, pounds per cubic foot. Harvey (13) studied the relation among the hydrostatic pressure, amount of dissolved air, and the destructive effect - 6 on red blood cells by cavitation produced by ultrasonic vibration. He found that "there is a rather well defined pressure at which the time of laking (of the red blood cells) becomes practically infinite, even though there is still air dissolved which cavitates under the reduced pressure." He also found that laking was prevented by a greater amount of dissolved gases, but he was unable to explain the phenomenon. His experiments indicated that "for a given sound density it would appear that the tension of a gas in solution in relation to pressure was the most important factor in determining cavitation of a fluid and consequent destruction of cells suspended in it," and that "with a lower gas tension that corresponds to equilibrium with the gas phase, increasing the hydrostatic pressure will prevent cavitation and laking; the higher the gas tension, the more the hydrostatic pressure must be increased". Rogowski and Sollner (20) found that the emulsions pro­ duced by ultrasonics are different according as a gas is present as a third phase or not and that emulsions containing gas are much easier to produce and much more stable than those which are gas free. Similar results were obtained by Sata (22). Bergmann (2), explaining his production of water benzol emulsion by ultrasonic irradiation gave the supposition that the process was due to "particles of water being flung by the ultrasonic wave into the overlying benzol". - 7 - Freundlich and Sollner (12) studied the liquefaction of thixotropic gels by ultrasonics. They attributed the lique­ faction effect to ’’the formation of cavities and their collapse in the sound beam." They proved their belief by increasing the external pressure on the liquid, thereby preventing cavitation, and liquefaction no longer took place. Bondy and'Sdllner (3) (4) studied the formation of nonmetallic and metallic emulsions by means of quartz piezo ul­ trasonic equipment and found that cavitation was necessary in the production of non-metallic emulsions, whereas cavi­ tation was of no importance in the production of metallic emulsions. They controlled the cavitation phenomenon by either applying high pressure to the system or experimenting in vacuo. Pease and Blink (l8) made the distinction between cavi­ tation arising from pre-existing gas nuclei and that appearing in gas-free water. They called the former false cavitation and the latter true cavitation. more difficult to produce. The true cavitation was much They also found that substances having polar groups included in the molecule and also sub­ stantial non-polar chains in the molecule offered a' large degree of "protection" from cavitation (gelatin, egg albumen, sodium stearate, sulfonated soap, 1-leucine, glycerine, glycerol, n-butyl alcohol, etc..) Burger and Sollner (6) studied the action of ultrasonic waves in suspensions and found that it could cause coagulation and orientation of the dispersed phase. - 8 - Harvey (13) also observed the flocculation of coal and other particles by ultrasonics. He explained, "the coal particles stick and are forced by radiation pressure into a clump." - 9 - GENERAL STATEMENT OF PROBLEM The problem was to seek the conditions which would allow the most efficient homogenization in the light of cavitation effect and to design the necessary mechanical device that can be readily adapted to dairy plant operation. The methods of producing cavitation may be divided into two groups, namely, 1. methods employing sonic or ultrasonic vibration, and 2. methods in which the shape of the flow passage is designed to cause a sufficient fluctuation in hydrostatic pressure. On account of the facilities and of the time available the methods of the second group were preferred for the inves­ tigation. Since the mechanism of cavitation was not exactly known the whole investigation was more or less of an exploratory nature. It was very hard to set up a definite schedule before­ hand, because many unexpected factors and conditions would arise. However, the problem could be generally divided into three phases: a critical examination of the theory of cavi­ tation as a factor of homogenization, the design of a device for producing cavitation in milk or other milk products, and a study of the homogenization characteristics of this device. - 10 - / EXPERIMENTAL WORK Part I Cavitation by Partial Vacuum Purpose From the analysis of the flow through a pressure homogenlzer it could be seen that the pump pressure has two distinct hydraulical effects on the flow at the vena contracta at the homogenizer valve. One is a tendency to raise the pressure head there, the other is a tendency to raise the velocity head there. The reduction of the pressure at the vena contracta, which is the condition necessary for the occurence of cavitation, depends on the increase of velocity. Therefore, the two effects produced by the pump pressure are in reality opposing to each other so far as the production of cavitation is concerned. This is evident from the equation for the pressure at the vena contracta derived by Loo (15) for a Cherry-Burrell 125 viscolizer. That equation when written in word form is as follows: (pressure at vena contracta) = (pump pressure) - (velocity head at vena contracts) x (density of the liquid) Both of the two terms on the right hand side of the equation increase as the valve is being closed. To bring about a suf­ ficient drop of pressure at the vena contracta the valve clearance has to be very small. pump pressure to a high value. This in turn backs up the Since a conventional homogenizer - 11 valve Is built primarily to create shearing and impingement, the resistance to the flow of liquid is very great and a con­ siderable portion of the energy put into the milk is consumed in overcoming the resistance. If cavitation is a factor which alone can produce homogenization, then such resistance does not appear necessary. If suction is used to draw the milk through the valve, then in the above equation the term of pump pressure will be replaced by atmospheric pressure plus the hydrostatic pressure due to the depth of the liquid. This new term is far smaller than the normal homogenization pressure. Therefore, the velocity necessary to bring down the pressure at vena contracta would become much smaller. However, the pressure which is acting on the collapsing cavities will be greatly reduced. According to the vapor condensation theory of cavitation this reduction in pressure would seem unfavorable to the strength of collapse of a bubble. But according to the theory of Van Iterson the re­ duction in pressure in a supersaturated air bubble does not seem to affect the amount of surface energy released and the force of collapse, unless the trigger action of releasing .the surface energy is governed by the magnitude as well as the variation of the pressure. Method A special homogenizer valve of curved cross-section (see Appendix I for its design and Appendix II for its capacity regulation) was connected to the suction side of a pump. - 12 Milk was sucked through it at different degrees of vacuum. Samples of milk were collected and tested according to the definition of homogenized milk set by the United States Public Health Service (U.S.P.H.S.). A diagram showing the set-up is presented in Figure 1. to H g. m a n o m e te r re< o u f/e f r o ta r y pomp Fig. 1 Diagram showing the experimental set-up for sucking milk through a special valve of curved cross-section. Procedure The milk used was regular pasteurized milk from the Michigan State College Creamery. The fat test was 3.1$. The milk was placed into the supply tank of the set-up after it was warmed up to l60°F. The pump was started and the homogen­ izer valve was adjusted to give various degree of vacuum. The milk was collected for later determination of U.S.P.H.S. index of homogenization. - 13 Results Very little homogenizing effect was obtained by the afore described method and procedure as Is obvious from the experimental data presented in Table I. TABLE I THE DEGREE OF HOMOGENIZATION OF MILK (EXPRESSED IN U.S.P.H.S. INDEX) TREATED BY SUCTION THROUGH A SPECIAL VALVE OF CURVED CROSS-SECTION Sample Temp, F. Vacuum In. Hg. •ffflt. t-.pg-h a-Pf-.P-p Aft hnnr»g top bottom U.S.P.H.S. index Rotary pump 1 160 17 12.4 2.85 77 2 160 18 14.8 2.55 82.8 Manton-Gaulin Homo. Pump 5 150 20 1/2 11.2 2.6 76.8 4 160 12 10.0 2.8 72.0 5 160 16-1/2 9.8 2.65 75 6 160 14 10.8 2.85 75.5 7 160 19-1/2 10.4 2.6 75.0 8 160 10 10.6 2.7 74.5 - Discussion The vapor pressure of milk at l60°F. is approximately 5 psi (pounds per square inch). This means that if the suction is below 5 psi the vapor bubbles will not collapse. In this - 14 trial practically all the vacuums used were above 10 inches mercury (or less than 5 psi). Foaming due to air leakage at the pump shaft was another handicap. The milk was bipassed back into the supply tank before a steady vacuum was obtained and the milk became heavily laden with air bubbles which would interfere with cavitation procedure. The failure to obtain homogenization effect by sucking the milk through a constriction was not sufficient to rule out the possibility of producing homogenizing cavitation by suction. However, the investigation in this direction was given up at this point, because it might require an unpre­ dictable amount of fundamental research into the mechanism of cavitation which would be in the province of physics rather than agricultural engineering. - 15 Part II Influence of Exit Side Hydrostatic Pressure on Homogenization Efficiency Purpose Since the collapse of a bubble is a pressure effect no matter which of the cavitation theories is correct a study of the relation between the hydrostatic pressure of the exit side of a conventional homogenizer valve and the efficiency of homogenization should be a valuable means of ascertaining further whether cavitation is a responsible factor of homo­ genization. However, it must be understood that the pressure of the exit side of a homogenizer valve is not the same as the pressure around the collapsing bubbles. The latter can­ not be measured very easily in a conventional homogenizer valve. Methods and Procedures 1. Discharging milk into a vacuum from a homogenizer A set-up as shown diagrammatically in Figure 2 was used. To start, a vacuum was first created by running the vacuum pump with valves V4 and VI closed and V2 and V3 opened. When a desired vacuum was reached V4 was opened and the homogenizer started immediately. The homogenizer pressure was adjusted to the desired magnitude as quickly as possible. closed, milk came into trap A only. When stable conditions were obtained VI was opened and V2 and V3 closed. then came into collector A. Since VI is The milk When collector A became filled the rubber hose between V4 and VI was pulled away from VI and inserted into collector B. So the milk in collector A was - 16 - homogenized with vacuum on the exit side and the milk in collector B was homogenized with atmospheric pressure on the exit side, all other conditions being the same for both. Both samples were tested for the degree of homogenization by the U.S.P.H.S. method. . f r o m supply tank V4VZ Collector A col lector B ' tra p A Fig. 2 Arrangement for applying vacuum to the exit side of homogenizer valve and for collecting milk samples. 2. Discharging milk into a pressure chamber The space between the first- and the second-stage valves of a two-stage single-piston homogenizer was used as a pressure chamber in the first trials. The second-stage valve was used to back up the pressure at various levels on the exit side of the first-stage valve. A sampling disc of the construction shown in Figure 3 was inserted between the first-stage and the second-stage blocks. It was hoped that milk samples so bled from the disc would show only the homogenization effect - 17 - Pig. 3 Disc inserted between the first-stage valve block and the second-stage valve block for taking milk samples between the two valves. of the first-stage valve as influenced by the backing-up of pressure by the second-stage valve. However, it was found that the little bleeding hole on the disc had appreciable homogenizing effect. Another set-up as shown in Figure 4 was designed to pro­ vide a pressure chamber sufficiently large to catch a quart of milk sample. A medical oxygen cylinder was inserted be­ tween the first- and the second-stage blocks. Pressure in the cylinder was regulated by means of the second-stage valve. Referring to Figure 4 the tube conveying milk into the cylinder extended to the bottom of the cylinder so as to assure a con­ tinuous displacement of the content. A screen baffle was mounted at the opening of the tube so as to reduce turbulence. It was determined that representative samples could be obtained by such an arrangement after at least two quarts of milk were passed through the homogenizer after steady conditions were obtained. (See Appendix V) The particular single-piston homogenizer showed a peculiar behavior with regards to its pressure regulation. In the preliminary runs the first and the second-stage pressures were adjusted in the following - conventional manner: 18 - With the first-stage valve open the second-stage valve was adjusted until the pump pressure gage indicated the desired second-stage pressure, then the firststage valve was turned in until the pump pressure gage showed the sum of the desired first- and second-stage pressures. However, it was noticed that the pump pressure gage did not fall to the desired first-stage pressure when the secondstage valve was released, being considerably higher. A second pressure gage was added in between the two valves so that the second-stage pressure could be measured independently and that the real pressure difference across the first-stage valve could be determined. The peculiar behavior became more obvious after the second pressure gage was added. (See Appendix VI.) This peculiarity might be an indication that there was some form of energy loss at the first-stage valve dependent on the second-stage pressure or that the first-stage valve opening was affected to some extent by the second-stage pressure. So two methods of manipulation of the first-stage valve were tried for the purpose of leaving cavitation as the only variable at the first-stage valve. The first method was to assume that the size of the valve opening could be kept constant by using constant pressure difference across the valve. The second method was to assume that the size of the valve opening could be kept constant by using the same valve hand-wheel position. Under the first method the valves were adjusted to give constant pressure - 19 - P © a P O ©P © p O © © eo ra © i© p © o C QW P IOP P ©P mo© © o Pi*i o» <© o o © ©P P xlP P P © © ©•© p OP © c« © ? © m Pti c l ©^ p P © — © © © © w * n3 © a •iH —I© t>-> t>»© o p © Crf) © M p o ra o IP P O t S J © © © © •H r —I © p © © © p © © © © © © BOP o m m S o © © P P P BO © © P P © P P <© P o •H © © ra BO © © © ISJ P © © © BO § o © m« © © BO © P P p p' — O -© P © ra o cn P - 20 difference across the first-stage valve for several different second-stage pressures (chamber pressures). Under the second method the first-stage valve was regulated first and let set at that position for all the various second-stage pressures (chamber pressures). .To obtain milk samples the homogenizer was stopped after three quarts of milk had passed through it under stable con­ ditions and without releasing either of the valves. The milk left in the steel cylinder was supposed to show only the effects of the first-stage valve as influenced by the backing up of the pressure by the second-stage valve. It was then emptied into a quart bottle to be tested for U.S.P.H.S. homo­ genization index. With the first-stage valve remaining in the same position and the steel cylinder removed the homo­ genizer was started again. Milk now discharged from the first- stage valve into free atmosphere and was collected into another quart bottle to be tested for U.S.P.H.S. homogenization index. This index served as the control. Three levels of chamber pressure were used, namely, 500 psi, 1000 psi, and 1500 psi. The corresponding pump pressures under the first method of first-stage valve manipulation (con­ stant pressure difference) were 3000 psi, 3500 psi, and 4000 psi. Under the second method (constant valve handwheel position) the corresponding pump pressures were 2650 psi, 2750 psi, and 2900 psi. - 21 Results 1. Discharging milk into a vacuum from a homogenizer The results presented in Table II show that in all the nineteen comparisons the homogenization efficiency was lowered by applying vacuum to the discharge side of a homogenizer. Practically all the control samples were up to the U.S.P.H.S. requirements for homogenized milk while eleven out of the nineteen collected in vacuum had indices above the U.S.P.H.S. upper limit of 10. - 22 - - in IS ts• -=t IS-• co • • VO rH • • • • • • 0 50 £ X G 0 0 eg G d si G o 50| vH ra G • •rH ■3 •H co• d G o G f t 24 td • rH > G o • o S• • rH H rH VO rH m OJ -=t OJ CVJ CM CM CM O CM -=J" CO vo IS- CO VO CO VO CO CO in CM CM o O rH rH IS- rH i— i • CM rH rH rH CO IS- -3- * I>- 0 ft •H • £ o -P « CO 0 • ft G G fc> o •rl pq G • O 50 cd ffi >= PH EH • .P •• is- d > o G O -P co * o id­-o_a] in CM S rH ft rH Cti 50 9 9 Eh VO o CO rH H H S > x0 d G CO •H • H «5 CO o > W G p o G G t • • CM • CM • Pl,Ov- • • o 0 •<1-11—1 i=> o p j CO 50 G •H X G 0 d G G 0 •h d 0 50 G ed ,G o ra £ • |3 d co d G o 0) • G K X cd • i — l t> P f t *H 43 • £ o -P P CO *H • f t G IS- in s- CM H in co in VO 00 CM in ts- •3- CM rH rH O H m • • rH • • rH • • • £> O *H SB i> ~ st CM CM CM O CM CO rH i —I i —I in - 23 - 2 . Discharging milk into a pressure chamber from a homogenizer (a) Constant pressure difference across homogenizer valve TABLE III DEGREE OF HOMOGENIZATION OF MILK (EXPRESSED AS U.S.P.H.S. INDEX) AS INFLUENCED BY APPLYING PRESSURE TO THE EXIT SIDE OF THE HOMOGENIZER VALVE The pressure difference across the homogenizer valve was kept constant (Temperature of milk 140 to 145 F.) Homo. pump press. 2500 psi Chamber press. 0 (control) Homo, pump press, on the release of cham­ ber oress. 2500 psi Run 1 3000 psi 3500 psi 4000 psi 500 psi 1000 psi 1500 psi 2850 psi 3200 psi 3600 psi 15.3 l4.8 14.6 12.9 12.3 10.9 11.6 8.75 U.S.P.H.S. Run 2 8.4 Run 3 7.6 13.8 13.1 Mean 8.25 14.0 13.4 indices . ‘ 9.28 Statistical analysis of the results (See Appendix VII for the mathematical procedure): Least significant difference between treatment means at Vfo level = 5.98 Least significant difference between treatment 'means at 5fo level = 3.94 - 24 (b) Constant valve handwheel position TABLE IV DEGREE OP HOMOGENIZATION OP MILK (EXPRESSED AS U.S.P.H.S. INDEX) AS INFLUENCED BY APPLYING PRESSURE TO THE EXIT SIDE OP THE HOMOGENIZER VALVE The homogenizer valve was kept at a constant setting which gave a homogenization pressure of 2500 psi on the release of exit side pressure 2500 2650 2750 2900 Second-stage press, psi 0 500 1000 1500 Run 1 14.4 16.4 20.0 20.4 Run 2 6.7 13.2 17.0 Run 3 12.3 14.5 15.9 24.4 12.2 14.1 23.0 13.13 15.80 21.18 Pump press, psi U.S.P.H.S. indices Run 4 Mean 8.65 10.51 9.63 Statistical analysis of the result (See Appendix VII for the mathematical procedure): Least significant difference between means at Vfo level = 4.27 Least significant difference between means at 3% level s 2.97 Least significant difference between means at 10fo level = 2.41 - 25 Discussion It is very obvious from the experimental results that applying either vacuum or pressure to the exit side of a homogenizer valve will cause some definite influence on the homogenization efficiency. In the case of the particular magnitudes of vacuum and pressure used the homogenization efficiency was lowered. This seems to be consistent with Preundlich and Sollner's experiments (12) in which they pre­ vented ultrasonic cavitational liquefaction of thixotropic gels by increasing the hydrostatic pressure. The results not only serve as an evidence of cavitation being a factor of homogenization but also point to a possible optimum collapse pressure of the cavities for smashing the fat globules in milk. - Part III 26 - "Bleeding Valve*1 Experiments Purpose The purpose of using a "bleeding valve", the description of which will be presented later, was to examine further the role of cavitation in homogenization by investigating the pressure distribution in the valve clearance and also the variation of the degree of homogenization of the milk as it travels through the valve. Apparatus A Manton-Gaulin 125 gallons-per-hour triplex two-stage homogenizer was procured for this experiment. The valves were ground to give good fit and all gaskets and packings were replaced by. new ones. The "bleeding valve" was a valve duplicating the original first-stage valve but with a number of small holes drilled at various radial positions for taking milk samples or measuring the pressures at such locations. Its exact details and method of installation are shown in Figures 5 and 6. Plastic tubings, capable of standing vacuum or mild pressure, were connected to the holes for taking samples and measuring pressures. such valves were used. Two One had eight holes located at equal radial intervals between the inner and outer edges of the valve. The other one had four holes drilled at the following locations: 1. tangential to the inner edge of the valve, 2. two thirds of the hole diameter (about 0.01 inches) from the inner edge, - 27 - Top view Cross-sectional side view Figure 5 Enlarged views of the "bleeding valve". d i o 7005 d *H O P 4-3 «H a m © o ^ Ci, © d Vi O © -X rH O © o > rH X> &D d © -H > •© -H © XJ i— I © © ® > rH O -P X © X! © rH P XI P X! ra t>> © V £ © a i •H -p d d © O PiD •H O X> o & o tO Xj © d d -H d rH tsD d •H © P«4O - 29 - 3 . five sixths of the hole diameter from the inner edge, and 4. one diameter of the hole from the inner edge. Procedure (a) Measuring the pressure at the holes of the bleeding valve: It would have been very desirable if tlie absolute values of the pressures at the holes could have been measured. Because of the alignment of the valves strong tubings that could stand pressure could not be used to connect the holes to a pressure measuring device. On the other hand plastic tubings had good flexibility but could not stand pressure. Hence, it was decided to measure the pressures by measuring the heights of the water columns ejecting from the ends of the plastic tubings when water was being pumped through the valve. (b) Determining the variation of the degree of homogen­ ization of milk as it travels through the valve: Five gallons of milk were warmed up to 140 F. and pumped through the homogenizer at 2500 psi. Milk coming out from the plastic tubings was collected in test tubes when a reasonable time had elapsed after the homogenizer pressure became steady. Because of the small size of the samples obtained, only microscopic examina­ tions of them were done to judge their degree of homogenization. The microscopic method employed was that devised by Farrall, Walt, and Hansen (ll). Two slides were made from each sample and four readings (five fields for each reading) were taken - 30 from each slide. The results were then analyzed statistically.# Results (a) Measurement of pressures at the holes of the bleeding valve. There was a sharp reduction in the height of the water jet at about 0.015 inches to 0.03 inches from the inner edge of the bleeding valve. It then rose to a new height at about 0.045 inches from the inner edge and then tapered off to al­ most no water issuing at the outermost hole. The results shown in Table V are plotted in Figure 7. (b) Results of microscopic examination of milk samples taken from the bleeding holes of the bleeding valves. Statistical analysis of the results showed that the milk samples from the three innermost holes were highly different from the milk sample taken at the homogenizer outlet. Milk samples from the other eleven holes were insignificantly different from the milk sample taken at the homogenizer outlet. - 31 ■or trH + + + + + + + H]J- H]d- H |d r -l|jt in rH H|d CO rH H |jt h | jJ CVJ a) + H |jt H|d- H|d h |j* + Hid* Hjd- H|d- H|d HlOJ H|N H|(\l h |oj CO I CVJ h |c\ i s rH CVJ rH P Eh C O 0 & Ch 1 CO CO* H C3 tr­ P P |x| H io H|d- in Xf -=t CO © O CO P O s PS P p p H sa = rH h |o j P x x CVI CO xj- CO CO CO cti S EH O P H e H |d- rH CO > 0 O » rH 0 H ^S 1 xf CO o m -H= = = CVJ CO CO x — i —i o o o o o o m i —i rH in h h|c\i P |<\i rH - I CO I cvj co O O O O O in Pt 0 C Q •H 0 o I > m U rH Cm cd > • (S 0 O p *H O O 0o faOH 0 H O S O w 03 fta fi 0 *H 3u w ft a a CVJ CVJ - 32 42 40 38 Figure 7 Variation of the hydroistatio pressure along the clearance of a homogenizer valve. The chart was constructed with the assumption that pressure was proportional to the height of the water Jet issuing from a bleeding hole in the valve. 36 34 32 30 pump pressure * 2500 psi 28 26 24 pump pressure » 2000 psi 22 20 -pump pressure = 1500 psi 18 16 14 pump pressure * 1000 psi 12 10 8 pump pressure * 500 psi 6 outer edge of valve 4 2 0 i 0.04 0.08 0.12 0.16 0.20 Distance from the inner edge of the valve, in. - 33 - 1 . 4-hole bleeding valve TABLE VI DEGREE OP HOMOGENIZATION (EXPRESSED IN FARRALL1S INDEX) OP MILK TAKEN AT DIFFERENT LOCATIONS OF A 4-HOLE BLEEDING VALVE Distance from inner edge of valve homo. outlet 0 .008" 0 .010" 0.013" 77.8 42.4 29.2 8.0 5.2 Slides 94.6 23.8 97.4 2.6 7.8 Series I 78.4 26.4 32.4 2.6 10.6 67.6 34.2 15.6 5.2 5.2 57.4 7.8 57.8 5.2 5.2 Slides 86.2 32.6 34.4 5.2 13.6 Series II 61.4 26.2 44.4 2.6 15.6 45.2 15.6 24.4 10.8 13.0 71.07 26.12 41.95 Ylean 0 .016" 9.52 5.27 Least Significant difference between means at 5% level - 14.70 Least significant difference between means at 1% level = 19.80 The mathematical operations of the statistical analysis are contained in Appendix VIII - 34 - +> o 00 00 on oo vo 00 co rH s t VO rH on oo rH I—I in VO rH on rH VO rH on on CO on rH CVJ vo co vo st in in oo •P co » CO H ■—i On cvj vo in on CO st CO sj- st- o on oo on co co • H CVJ rH H CO CO Sj- • rH on on on rH on • on CO CO rH CO on rH st vo obtained from rH 00 St in oo co rH was 00 00 t-— co in on CVJ vo CVJ • CO rH VO cvj on rH S t • VO cvj vo on CVJ rH VO S t ♦ was negative., no sample rH vo hole oo oo at this ■ri- CO rH ♦ rH ON on on pressure VO CVJ The DEGREE OF HOMOGENIZATION (EXPRESSED IN FARRALL’S INDEX) OF MILK TAKEN AT DIFFERENT LOCATIONS OF AN 8-HOLE BLEEDING VALVE this on CO CO hole. s 5> - P © rH •H © r-i l> t> - P > O rH O © © © © +3 O N O C )*H H O +3 © © O O © © © © © O 60 © © 0 •H © O 1*4 W O .© +3 ,© ro © © 60 o valve plug i C3 (D CtO § 0 .© © 00 *© © 1 © u «H hzzm ^zzzzzzzzz 3 © 03 p* •-4 © © S" OO © •H © Jh N Fig. 10 Assembled views of the experimental homogenizer Vickers pump. ($) Side view. (b) Front view. using - 41 - - 43 Part V Homogenization Characteristics of the Knife-edged Valve with No Air Injection The knife-edged valve was tried on milk, concentrated milk and ice cream mix without any addition of air to the product. The procedure of the experiment and the method of judging the degree of homogenization were not all the same # for the three products. Hence, they are described separately below. Procedure for milk A total of sixteen runs using milk were carried out at various levels of first-stage pressure (pump pressure) and second-stage pressure (collapse pressure or exit side pressure). The first four runs had second-stage pressures varying from 0 to 500 psi. They yielded evidence that there was an optimum second-stage pressure somewhere around 100 psi. So the following twelve runs were concentrated around this optimum region. Also, in these twelve runs, valves of four different diameters were tried to study the effect of valve diameter on homogenization efficiency. The samples were tested for U.S.P. H.S. homogenization index and the results were analyzed sta­ tistically. One sample of milk homogenized with the knife- edged valve at 1000 psi first-stage pressure and 100 psi second-stage pressure was tested for protein stability and curd tension. The results were then compared with those of unhomogenized milk and milk homogenized with the Manton-Gaulin laboratory homogenizer at 2500 psi. - 44 Two methods of determining protein stability were used. One was the heat stability test according to Cole and Tarassuk's method (7). The other was the alcohol test, that is, noting the strength of alcohol solution (percent of 95$ alcohol) needed to cause flaking of the milk (5 ml. milk to 10 ml. alcohol solution). Curd tension was tested according to the method adopted by the American Dairy Science Asso­ ciation in 19^1. The tester was of the Submarine Signal Company design. For the purpose of comparison, the original Manton-Gaulin valve was used in the Vickers pump set-up to homogenize milk at 1000 psi pump pressure, and several different second-stage pressures. The samples of milk so homogenized were tested for U.S.P.H.S. index. Procedure for concentrated milk The concentrated milk was prepared by mixing proper amounts of 30$ cream and water into 3-ta-l condensed skim milk to a composition of 7 .9$ fat and 20 .6$ milk solids-notfat. Part of the concentrated milk was homogenized by means of the Manton-Gaulin laboratory homogenizer at 2500 psi. The rest of it was homogenized by means of the knife-edged valve in the experimental homogenizer using 1000 psi first-stage pressure and 100 psi second-stage pressure. Samples from both machines and a sample of unhomogenized concentrated milk were tested for Farrall’s index, protein stability and-curd tension. Protein stability was tested according to the method of Cole - 45 and Tarassuk (7 ) and also according to the alcohol method as described previously for milk. The curd tension test was done for both concentrated milk and diluted concentrated milk (one part concentrated milk to one part water). Procedure for ice cream mix Two runs of plain ice cream mix and one run of chocolate ice cream mix of usual composition (see Appendix IX) were carried out using various combinations of first-stage pressure and second-stage pressure. The ice cream mix to be used in the experiment was taken from the College Creamery ice cream pasteurizer just before it was to be homogenized. A sample of the same batch of ice cream mix homogenized by the College Creamery was used as a control. All the samples were tested and compared for viscosity with a Brookfield viscosimeter and for fat globule size in terms of Farrall’s index. Results of the homogenization of milk using the knife-edged valve a. Runs 1 to 4. The pressures used were as follows. Runs 1 and 3, first-stage 900 psi second-stage 0 to 500 psi. Runs 2 and 4, first-stage 1400 psi second-stage 0 to 500 psi. The results are tabulated in Table VIII, From these results an operation chart of the knife-edged valve was constructed as shown in Figure 11. The operation chart shows clearly that the degree of homogenization increased rapidly (lowering - 46 of* U.S.P.H.S. index) as the second-stage pressure was in­ creased to around 100 psi. Further increase in second-stage pressure produced no significant change in degree of homo­ genization when first-stage pressure was 1400 psi, but defin­ itely reduced the degree of homogenization (rising of U.S.P. H.S. index) when the first-stage pressure was 900 psi. b. Runs 5 to 16. The U.S.P.H.S. indices obtained by using knife-edged valves of four different diameters, three different first-stage pressures and four different second-stage pressures are tab­ ulated in Table IX and plotted in Figure 12. It was noted that the index obtained for the three-six­ teenths valve at P2 = 800 psi and Pg = 50 psi and the index for the one-half inch valve at P^ = 600 psi and = 50 psi seemed to be erroneous, being outstandingly too high. This would be especially obvious if the results of the twelve runs were plotted and compared. So in the statistical analysis the two values were replaced by values obtained by the method of estimating missing values In a randomized block experiment (2) (23 ). The other two missing values, represented by asterisks in the table, were estimated in like manner. The total degrees of freedom and degrees of freedom for error were correspondingly reduced by four. Before applying the formulas for estimating missing values, the experimental data were divided into three two-way tables, one for each firststage pressure. Then the formula for one missing value or - 47 TABLE VIII U.S.P.H.S. INDICES OP POUR RUNS OP HOMOGENIZATION OP MILK USING A KNIPE-EDGED VALVE Run No. 1 2 3 4 1st.-stage Press.,psi 2nd.-stage Press.,psi U.S.P.H.S. Index 900 0 20.4 900 50 10.5 900 100 8.1 900 300 15.2 900 500 26.1 1400 0 12.6 1400 50 . 4.1 1400 100 4.1 1400 300 6.7 1400 500 4.8 900 0 17.5 900 50 8.0 900 100 10.2 900 300 13.1 900 500 25.6 1400 50 i4oo 100 4.5 1400 300 3.1 i4oo 500 7.2 5.12 * 48 <* 30 25 20 15 U.S.P.H.S. index of homogenization 1st.-stage press.s 900 psi. 10 1st.-stage press.® 1400 psi. 5 0 0 100 200 300 400 500 Second-stage pressure 1 psi Figure 11 Operation chart of the knifeedged valve for 0 to 500 psi second-stage pressure with no air injection. - 49 TABLE IX U.S.P.H.S. INDICES OP TWELVE RUNS O F 'HOMOGENIZATION OP MILK USING POUR KNIFE-EDGED VALVES OF POUR DIFFERENT DIAMETERS Valve Dia. dj inches 3/16 1/4 3/8 1/2 2nd.-stage Press ., Pp 50 psi 100 psi 150 psi First-stage Press. psi 0 psi 600 39.8 32.2 34.2 * 800 12.7 19.4 8.0 10.9 1000 18.1 9.2 8.5 6.7 600 39.5 28.3 27.0 33.3 800 16.1 8.7 11.4 12.8 1000 17.2 11.4 9.2 6.7 600 35.0 29.2 28.3 29.2 800 15.2 12.0 11.0 11.5 1000 16.9 9.2 5.4 5.9 600 36.5 45.0' 35.2 43.3 800 18.5 13.9 14.9 14.5 1000 16.4 10.3 8.0 * *Samples were not obtained because of running out of milk during the experiment. 40 50 - d=3/l6n , p^*600 psi 35 dsl/4", p-L-600 psi 30 25 ■ 20 U.S.P.H.S, index of homogenization d=3/8”, Pls600 psi , P ^ B O O psi 15 , pi“800 psi d=3/8" , p^=800 psi "> Pi*S00 psi 10 , Pj_=1000 psi -a=i/2" , pj_=1000 psi 'y ds3/l6", px-1000 psi X a=3/8", pi=1000 psi 0 0 50 100 Second-stage pressure, psi 150 Figure 12 Operation chart of the knifeedged valve for 0 to 150 psi second-stage pressure with no air injection. - 51 two missing values was applied accordingly. Hence, the follow­ ing values were obtained. For = 600 psi, Pq = 150 psi, and d = 3/ 16" the estimated index was 38 .1 . For Pj = 800 psi, ?2 = 50 psi, and d = 3/16" the estimated index was 9 .0 . For Pj = 600 psi, ?2 - 50 psi, and d = 1/2" the estimated index was 34.4. For P^ = 1000 psi, ?2 ~ 150 psi, and d = 1/2" the estimated index was 6 .3 . A statistical analysis, of which the mathematical oper­ ations are presented in Appendix X, showed that there was sig­ nificant difference at Vfo level between the half inch valve and the other valves, and between zero second-stage pressure and the other second-stage pressures. The results of protein stability tests and curd tension test of milks homogenized by the knife-edged valve and by the Manton-Gaulin homogenizer are presented in Table X. They show that the knife-edged valve at 1000 psi first-stage pres­ sure and 100 psi second-stage pressure produced practically the same effects on the protein stability and curd tension as the Manton-Gaulin homogenizer at 2500 psi operation pressure. - 52 - TABLE X EFFECTS OF HOMOGENIZATION BY MEANS OF THE KNIFEEDGED VALVE AND THE MANTON-GAULIN VALVE O N ’ THE PROTEIN STABILITY AND CURD TENSION OF MILK Heat stability test Control (Unhomo, milk) Milk Homo, by Manton-Gaulin Valve1 Milk Homo, by Knife-edged Valve2 No coagulation after 80 min. Curdled at 69 min. Set at 69 min. Set at 80 min. 90^ 00 85^ Curd tension 26 gm. 14 gm. 14 gm. in Alcohol test 1. The homogenization pressure was 2500 psi. 2. The homogenization pressures were 1000 psi pump pressure and 100 psi second-stage pressure. Results of the homogenization of milk using the Manton-Gaulin valve in the Vickers pump set-up As stated previously the Manton-Gaulin valve was used in the Vickers pump set-up at the same pressures as the knifeedged valve for the purpose of comparison. The results of the test showed that none of the samples of milk homogenized by the Manton-Gaulin valve in the Vickers pump set-up were up to the U.S.P.H.S. requirements for homogenized milk. All of them had a sticky cream layer of various thicknesses after 48 hours standing in a cooler. - 55 TABLE XI DEGREE OF HOMOGENIZATION OF MILK HOMOGENIZED BY THE MANTON-GAULIN VALVE IN THE VICKERS PUMP SET-UP Pump pressure, psi 1000 1000 1000 1000 0 50 100 150 Run 1 41.5 55.0 57.0 45.0 Run 2 22.5 55.8 29.2 27.4 Run 5 26.8 24.2 24.8 50.0 Second-stage pressure, psi Results of the homogenization of concentrated milk using the knife-edged valve The results of protein stability test, curd tension test, and microscopic examination of the unhomogenized concentrated milk and homogenized concentrated milk from both Manton-Gaulin laboratory homogenizer and the knife-edged valve homogenizer are tabulated in Table XII. Both the heat stability test and alcohol test revealed practically no difference among the three samples. The curd tension test of diluted concentrated milk showed about the same reduction in curd tension in the homogenized samples, but the curd tension test of undiluted concentrated milk failed to show any significant differences among the three samples. The microscopic examination showed a somewhat better fat globule size reduction In the sample - 54 - homogenized by the knife-edged valve homogenizer at 1000 psi pump pressure and 100 psi second-stage pressure than in the sample homogenized by the Manton-Gaulin laboratory homogenizer at 2500 psi pump pressure. TABLE XII EFFECTS OF HOMOGENIZATION BY MEANS OF THE KNIFEEDGED VALVE AND THE MANTON-GAULIN VALVE ON THE PROTEIN STABILITY, CURD TENSION AND FAT GLOBULE SIZE OF CONCENTRATED MILK Control (Unhomo. conc. milk) Conc. Milk Homo. by Man­ ton-Gaulin Valve 1 Conc. Milk Homo. by Knife-edged Valve^ Curdled at 6 min. Set at 7 min. Curdled at 6 min. Set at 7 min. 6 min. Alcohol test 10% 10% 10% Curd tension (sample undiluted) 58 gm. 57 gm. 58 gm. Curd tension (sample diluted) 21 gm. 11 gm. 9 gm. Farrall1s Index 66l 72.5 Heat stability test Curdled at Set at 7 min. 45.9 1. The homogenization pressure was 2500 psi. 2. The homogenization pressures were 1000 psi first-stage and 100 psi second-stage. - 55 Results of the homogenization of ice cream mixes using the knife-edged valve Results of two runs using plain ice cream mix and one run using chocolate ice cream mix are shown in Table XIII. They show that the knife-edged valve homogenizer operating at pump pressures from 700 to 1400 psi and second-stage pressure from 50 to 200 psi definitely did not homogenize so well as the Cherry-Burrell Superhomo operating at 2500 psi pump pressure and 800 second-stage pressure, though viscosity of the samples seemed to be in favor of the knife-edged valve. Clumping of fat globules was observed in some of the samples from both machines, but no definite trend was discerned. - 56 TABLE XIII EFFECTS OF HOMOGENIZATION BY MEANS OF THE KNIFEEDGED VALVE AND THE CHERRY-BURRELL VALVE ON THE VISCOSITY AND FAT GLOBULE SIZE OF ICE CREAM MIXES Ice Cream mix Homogen­ izer Plain Knifeedged valve • CherryBurrell Superhomo. Knifeedged valve Plain CherryBurrell Superhomo. Knifeedged valve Chocolate Homogenization Pressures, psi 1st. 2nd. stage stage 700 700 850 850 1000 1000 50 100 Absolute Farrall's viscosity, index centipoise 14.6 14.7 19.4 190.2 100 19.0 50 350.5 342.5 437.3 100 20.7 19.3 515.0 2500 800 23.0 31 .1* 800 800 1000 1000 1200 1200 20.8 20.8 108.2* 1400 1400 100 200 100 200 100 200 100 200 2500 800 500 500 700 700 1400 50 21.5 21.2 24.3 94.9* 97.7 125.5 96.6 66.2* 24.6 70.6 132.5 79.0 26.6 16.2 50 76.2 100 68.0 86.0 423.2 389.4 50 100 100 22.6 23.6 77.0 66.0 Cherry172.4 600 1500 Burrell Superhomo. *Sample showed clumping of fat globules. 272.8 472.5 153.4 63.8* - 57 Discussion The experiments of the knife-edged valve with no air in­ jection revealed that, in the case of milk, there was an opti­ mum second-stage pressure around 50 to 150 psi. Milk could be satisfactorily homogenized at 1000 psi pump pressure and 50 to 150 psi second-stage pressure. A satisfactory expla­ nation of the phenomenon of optimum second-stage pressure is that the optimum pressure is just high enough that on the one hand it intensifies the striking effect of the collapsing cavities and yet on the other hand it does not cause any unfavorable effect on the generation of cavities. From the analysis of the effect of valve diameter on the efficiency of homogenization the valve diameter did not seem to be very critical within certain limits. If this is true, three possible advantages might be derived, namely, 1. flexibility in the capacity of a valve, 2. "finger-tip" manipulation of the homogenizer valve, and 5. less mechanical abrasion due to grits present in the flow. The first advantage is obvious. The second advantage is due to the fact that the pressure force on a smaller valve plug requires smaller effort to turn the valve handwheel. It is common experience that quite an effort Is needed to turn the valve handwheel to get the pressure up to 2000 psi in a conventional homogenizer. The third advantage is possible, because a smaller diameter would require a bigger valve clear­ ance, and a bigger valve clearance would allow grits to go through with less abrasive effect. - 58 The operation chart probably can be applied to the con­ ventional poppet type homogenizer valves too. However, be­ cause of the constant high collapse pressure due to wide valve surface the operation region will be limited to an area somewhere away on the right side of the optimum region on the operation chart. The protein stability of the concentrated milk was very low as the curdling time was only six minutes at 120°C. Since all the three samples, one unhomogenized and two homogenized, showed practically the same stability it is quite likely that the lowering of stability of the proteins in concentrated milk was chiefly caused by treatments other than homogenization. With a conventional homogenizer, the pressure used to homogenize ice cream mix generally is lower than that used to homogenize milk. With the knife-edged valve homogenizer, it was found that ice cream mixes could not be homogenized satis­ factorily at pressures equal to or even 400 pounds higher than that which yielded satisfactory homogenization of milk. A possible reason why the cavitation homogenizer valve (knifeedged valve), when compared to the shearing' homogenizer valve (poppet-type valve), did not homogenize ice cream mixes so easily as it did milk was that the ice cream mixes contained large quantities of sugar and some amount of gelatin. Sugar and gelatin consist in their chemical structures of many polar groups (molecular groups and double and triple bonds that show a strong attraction for water). Such polar groups were found - 59 to hinder cavitation by Pease and Blinks (18). Therefore, the experiment of using a knife-edged valve to homogenize ice cream mix yielded two significant points. First, it showed that, unaerated ice cream mix (later tests were made with aerated mix) is more easily homogenized than milk in the case of the poppet type valve, but the reverse is true in the case of the knife-edged valve. Second, based on Pease and Blinks*s observation, the key to successful homo­ genization of Ice cream mixes may lie in determining how to overcome the interference of polar groups of sugar and gelatin. - 60 Part VI Homogenization Characteristics of Knife-edged Valve with Air Injection Purpose From the literature reviewed it appeared that dissolved gases had a very significant place in the phenomenon of cavi­ tation. According to Harvey (13 ), Rogowski and Sollner (20), Pease and Blinks (18 ), and Sata (22) the dissolved gases had direct relation to the ease of producing cavitation. Accord­ ing to Van Iterson (25 ) and Bottomley (5 ) the amount of dissolved gases would determine how low a hydrostatic pressure would he needed to produce destructive cavitation. In ordinary milk products such as milk and Ice cream mixes which are in constant contact with air the amount of dissolved air should he quite close to saturation under atmospheric pressure. By means of the experimental homo­ genizer It was possible to add a controlled amount of air Into the milk product just before it was to go through the homogenizer valve. Hence it was possible to investigate the effect of varying the amount of dissolved air on the efficiency of homogenization. Procedure The only part of the procedure that needs description is the procedure of regulating the amount of gases in the milk product, the rest of the procedure being the same as described in Part V. - 61 In the following description of the procedure P ^ Pa, and P2 are used to represent the desired pump pressure, air sat-* % uration pressure and second-stage pressure respectively. air vent was first closed and the machine started. The After the first-stage valve was adjusted to obtain P^ on the pump pressure gage and the second-stage valve was adjusted to obtain Pa on the second-stage pressure gage, the air vent valve was opened up gradually until a distinct rattling noise could be heard. At the same time the pointer of the first-stage gage began to show erratic vibration. Then the vent valve was turned back just far enough to reduce the rattling noise to a smooth hissing noise and the gage pointers just ceased erratic vibra­ tion. The second-stage valve was then tightened to get P2 on the second-stage gage. The procedure of obtaining P^, Pa, and ?2 was then completed. After a reasonable time had elapsed a sample could be collected at the outlet of the homogenizer. Since it was found that optimum second-stage pressure existed around 100 psi, the values of P2 used In the present series of experiments were up to only 200 psi. Pa, the air saturation pressure or the pressure at which the air would come out from solution to form cavities, was necessarily smaller than P2 in order that the cavities would collapse. Also since it was found that, without adding air, a pump pressure of 800 psi would homogenize milk just up to the limit of the U.S.P.H.S. requirement, effects in either direction should be more easily detected if this pump pressure was used. - 62 So five of the seven runs using milk were carried out using 800 psi pump pressure. In the remaining two runs the pump pressures were 1000 psi and 600 psi respectively. In the case of ice cream mix, there were three runs using 1000 psi pump pressure and three other runs using 800 psi pump pressure. Only plain ice cream mix was used. In the case of concentrated milk the air saturation press­ ures used ranged from below atmospheric to 75 psi. Samples with air saturation pressure below atmospheric were used for the purpose of imitating the conditions of concentrated milk in actual production process in which the concentrated milk receives deaerating effect In the vacuum pan and is not appreciably exposed to atmospheric air before going into the homogenizer. Partially deaerated milk was obtained by spray­ ing the concentrated milk at 145° P. Into a container at 17 to 18 inches vacuum. It was reheated to l40° F. and trans­ ferred to the supply tank of the homogenizer with care not to incorporate air Into it. Resuits (a) Milk. The degrees of homogenization of milks homogenized by means of the knife-edged valve with air injection are shown in Table XIV. Run 1 shows a very noticeable undesirable effect of the large amount of air and some slight improvement at medium amount of air. Run 2, consisting of three repli­ cations, was analyzed statistically (See Appendix XII). The - 63 analysis showed no significant difference among the effects of various amounts of air (from 0 to 25 psi). Runs 3 and 4 did not seem to show any significant difference either. TABLE XIV EFFECTS OF ADDING AIR TO MILK ON HOMOGENIZATION EFFICIENCY (U.S.P.H.S. indices of milk homogenized by the knife-edged valve at l40°F.) Run No. 1 Homo. Pump Pres. psi 2nd. stage Pres. psi 6oo 600 600 100 200 800 2 8oo 800 300 50 50 50 0 26.0 27.3 4i.o 200 18.7 23.0 22.3 33.3 51.3 10.2 11.5 12.3 11.9 11.4 10.9 11.9 9.8 11.7 7.8 12.5 l4.i 3 800 100 200 13.5 18.7 4 1000 100 9.9 800 Air Saturation Pressure3 psi 10 20 50 25 75 150 12.5 15.2 13.1 16.3 18.0 18.4 9.2 10.9 9.9 (b) Ice cream mix. Results of the homogenization of ice cream mix using the knife-edged valve with air injection are presented in Table XV. rH CO in • • • CO o o \ h -ft- on rH rH in m oo • • • coco m OHO PH rH rH VOft* • • • O r f rH o ft- ftrH • 0 ft > • O O O 0 • ♦ • f t OJ O CO O OJ OJ rH in o O # • # O O H 0J CM OJ o o o * * • OHO O rH 0J 0J o o in • • • O i—1rH CM CM CM « 0 TO P H OJ rH OH • t • phco o m vo co rH rH OH O CO • • * co f t - n O OH CM • • • cm vo in in ph ph CM VO CM OH • * * o vo vo oh in vo s 0 p x 9 9 Eh > _ Q S W O K ft H O o ft Eh H o ft h H ft < ft o ft H ft ft ft O H EH < to ft M O ft ft CO 03 EH O ft ft ft ft 0 TO 0 0 O N •H -H TO P P 0 •H faO O m e - o H ft rH 0 (*! p *H P E 0 pH ' " phoo oh rH OH • • 0 ft > P P OJ ft • ir u n o 0 « • • f t VO OJ OJ O OJ OJ OJ in t n o t ♦ * ft- PH OH 0J CM rH in in in * • < rH OHO CM H CM O O Q • • * OHO-OH i—I CM i—I Superhomo < M ft o 0 -P ra 0 •H O 0 P. > •H rH -P 0J P > 0 o to 0 P 50 •H TO 0 f>s 1 -P 0 •H Qh W *H o p o J3 0 •H 0 > ft •P TO P J>» 0 ,h •=? 1—1 ( —• I PH IPM 0 to P H t-CMCO • • • rH 00 VO o \ co in rH PH-ft OJ • • * co tp-rn rH OHLfH H r-Hft- IP« « • rH in in PH CM in o r i • • * V O O ^f PH CM 0J «\ in tpCM rH ft-ft II • 0 ft > • o L fu n 0 « • • f t P-OHpn O 0J OJ OJ O O O • • • in t- M 0J CM CM o o o • • • rH PH PH VO CM CM o o in • • * 0J CM rH in cm oj OJ rH rH o in • • • t —rH IPt - f t " -ft vo in vo • • • 0J CMO CM in PH • * * PHtP- KH ip -in ph rH o o in in t— o o in L ftt- o o in m ip - o o o o o o OJ OJ CM o o o o o o rH rH I—1 o o o o o o OJ OJ CM i—i 0 to p H • • • ohoj tpph rH ov CM OJ • • 0 •H P -P 0 0 o o in •H 0 P f t m t •H ft ft ft * CD rH CO 0 H • • 0 •H O O O o Qj g g 0 0 O O O o H P f t CO 00 CO f t PH CL, sample was homogenized by Cherry-Burrell psi second-stage pressure. S ft O Eh H X W t3 o S o CO ph O o o o o o o coooco o o o o o o o o o rH rH rH o o o o o o o o o r iH H P -P ft O O ^Control and 500 1 o s O '—' § 0 ft o •HO o <+h in O i—1 pump IP- rH m • « • ft- vo co ftM ftb rH rH at 2500 psi 0 50 H 10 0 P TO 0 P P> rH < pressure - 64 - - 65 The statistical analysis (Appendix XIII) showed an im­ provement of homogenization efficiency at 1% level of sig­ nificance when the air saturation pressure was 75 psi. Also there was a difference at 5% level of significance between 75 psi and 50 psi saturation pressures. The use of 50 psi air saturation pressure was insignificantly different from adding no air. No significant difference was observed be­ tween the two second-stage pressures. The average indices of samples homogenized at 1000-75-100 psi (pump pressure-air saturation pressure-second-stage pressure)5 1000-50-200 psi and 1000-75-200 were comparable to the average index of a sample homogenized by a CherryBurrell Superhomo at 2500 psi pump pressure and 500 secondstage pressure. The viscosities of the knife-edged valve samples were all appreciably lower than the Cherry-Burrell sample. (c) Concentrated milk. Results of homogenizing concentrated milk at various con­ centrations of dissolved gases using the knife-edged valve are presented in Table XVI. A statistical analysis of the results (see Appendix XIV) revealed that the deaerated samples were less homogenized than all the others at a significance level of lfo. All the samples with air injection were insignificantly different from each other. Only 20 and 75 psi air saturation pressures produced improvement over atmospheric saturation pressure at a significance level of 5 TABLE XVI EFFECTS OF ADDING AIR TO CONCENTRATED MILK ON HOMOGENIZATION EFFICIENCY (Farrall's indices of concentrated milk homogenized by the knife-edged valve at a homogenizer pump pressure of 900 psi and second-stage pressure of 100 psi at a temperature of l40° F.) Deaerated sample Air Saturation Pressure , psi Atmos. 20 10 50 25 Replica­ tion I 188.0 166.8 127.8 114.4 63.1 66.3 43.1 53.9 64.0 40.6 Replica­ tion II 213.0 91.4 102.7 125.3 124.0 117.9 85.9 172.2 75 92.6 79.6 64.4 133.5 93.5 65.0 117.0 91.0 65.5 99.6 Conclusion The fact that adding a certain amount of air into ice cream mix raised the homogenization efficiency to satisfactory value was a likely indication that air helped overcome the previously postulated inhibitive effect of sugar and gelatin on cavitation in ice cream mix. However, In the case of milk the addition of a similar amount of air did not yield any significant effect on the efficiency of homogenization. A larger amount of air only reduced the homogenization efficiency, This might mean that the natural amount of dissolved gases in milk is not insufficient as far as the production of cavitation is concerned and that the addition of air to milk only tends to cushion the hammering effect of collapsing cavities. - 67 The fact that deaerated concentrated milk was much harder to homogenize not only is a confirming evidence of the role of cavitation in homogenization hut also may have importance in the actual production of evaporated milk. It seems that allow­ ing milk to take up a sufficient amount of air when going from the vacuum pan to the homogenizer will insure good homogeniza­ tion of the product. However, amounts more than saturation at atmospheric condition does not seem necessary. It was believed that more uniform results could be obtained by using a more sensitive device for controlling the amount of dissolved air in the experiments. It was quite likely that much of the variation due to error came from the lack of pre­ cision in controlling the air. There was considerable variation among runs when homo­ genizing ice cream mix. One possible reason was that oiling- off of the fat In the supply tank was rather heavy. The mix in the supply tank could be agitated only mildly because too strong agitation might incorporate air bubbles into the mix and hence would ruin the purpose of the experiment. - 68 Part VII Durability Test of the Knife-edged Homogenizer Valve Purpose Since the knife-edged homogenizer valve was designed to produce cavitation which is very damaging, it was necessary to determine how well the valve could stand cavitation action under continuous operation conditions. It was not expected that the knife-edged valve might be made to last as long as the conventional poppet type stellite valve. However, it was hoped that it might be made into an item which might be very inexpensively replaced as soon as it began to show re­ duction in its efficiency. Procedure A study of the durability of the knife-edged valve under continuous cavitation action was carried out in the following manner. The valve used had a seat similar to the one shown in Figure 9, but its plug was a polished flat disc instead of a cone.. While such a construction was not expected to be different in effectiveness its polished surface would allow cavitation to produce clear markings of erosion. The material used for making the valve was brass, which was very soft. An emulsion of mineral oil (SAE No. 50 motor oil) and water in a volumetric ratio of 1:4 with 10 grams of Ivory soap to a gallon of mixture was run through the homogenizer and recir­ culated, The machine was stopped, cleansed and used to homo­ genize a gallon of milk in the usual manner at certain time intervals. The degrees of homogenization of the milk samples - 69 served as an indication of the efficiency of the valve. Pressures were maintained at 1000 psi pump pressure and 100 psi second-stage pressure throughout the experiment. Temper­ ature of the emulsion varied from 120 to 150° F. with l4o° being most common. A stream of tap water washing down the outside of the return tube of the homogenizer helped dissipate the heat added into the recirculating emulsion by the pump. The capacity of the pump was checked occasionally. Result The result of the durability test of the knife-edged valve shown in Table XVII shows that there was practically no reduction in efficiency of the valve during the entire five hours operation. There were faint radial erosion mark­ ings on the valve plug. TABLE XVII DURABILITY OF THE KNIFE-EDGED HOMOGENIZER VALVE (U.S.P.H.S. indices of samples taken at various time intervals during five hours operation) Time, Minute U.S.P.H.S. index 0 5.05 50 6.72 60 6.90 120 4.50 180 5.00 500 6.20 - 70 Conclusion Though the durability test was not carried out long enough to determine actually how long the useful life of the knifeedged valve would be, the ability of the brass knife-edged valve to maintain high efficiency during the test period of five hours was a good basis on which to predict a useful life of, say, 100 hours if the valve were made of harder material such as stainless steel. A valve stamped out from stainless steel sheet like the one shown in Figure 15a could be cheaply made for frequent replacement. - 71 Part VIII Trial of the Knife-edged Valve in High Capacity Triplex Homogenizer Purpose Since the knife-edged valve homogenized milk very sat­ isfactorily at 1000 psi pump pressure and 100 psi secondstage pressure in a small experimental homogenizer it was desired to determine whether the same principle could he readily applied to high capacity commercial homogenizers. Though it was found that in the experimental homogenizer the size of the valve did not seem to be critical, it must be realized that the flow rate per inch of valve diameter in the experimental homogenizer was very small, being about 65 gallons per hour per inch diameter. If this ratio were adopted in designing a knife-edged valve for a commercial homogenizer of 500-gallons-per-hour capacity, a diameter of about seven and a half inches would be necessary. undoubtedly impractical. Such a size would be In order to make a knife-edged valve that could be readily fit into an ordinary commercial homogenizer a high flow rate per inch diameter would have to be used. Also commercial homogenizers are, almost as a rule, of the triplex type. A triplex pump exhibits some degree of pressure fluctuation believed to be bigger than that of the swash-plate pump of the experimental homogenizer. Differences like these might affect the performance of a knife-edged valve in a commercial homogenizer. - 72 Procedure The commercial homogenizer used was a Cherry-Burrell 500gallons -per-hour triplex type which was used daily by the Michigan State College Creamery to homogenize fluid milk. It was thoroughly overhauled to operate satisfactorily before three knife-edged valves of different sizes were tried in it. Since it was a single-stage machine a needle valve similar to the ball valve shown in Figure A1 was added to the outlet of the homogenizer to control the pressure at the exit side of the knife-edged valve. A sanitary pressure gage that read up to 200 psi was inserted between the original homogenizer out­ let and the second-stage valve (the needle valve). As a measure against air leak along the supply line the supply tank was elevated about one foot above the homogenizer inlet and a paper gasket was inserted in each pipe joint. The machine was tempered with hot water before the milk at 140° F. was pumped through it at 1000 psi pump pressure and 100 psi second-stage pressure. was used for the trial of one valve. About 10 gallons of milk A quart of milk near the end of the 10 gallons was collected for the determination of U.S.P.H.S. index. This index was compared with that of a sample taken from the creamery production line in the same day. The three knife-edged valves are shown in Figure 15. Though they differed in construction, they all had the same basic feature - a sharp edge against a smooth surface. CJ •d O Jh © ■P CD & •COH •O (D > H CO CO 2 -P CD t* f-t co iH JQ © © +3 © © H TO © O ©t © © H O 00 r to ^1 © © +3 © £ © •H 'd r-t © P> © Figure 13 Cross-sectional views of knife-edged homogenizer valves of three different diameters designed to fit into a Cherry-Burrell 500-gallons-per-hour homogenizer. Scale, full size. - 7sa - - 73 Results Results of using knife-edged valves of three different diameters In a 500-gallons-per-hour triplex homogenizer are presented in Table XVIII. TABLE XVIII PERFORMANCE OF KNIFE-EDGED VALVE IN A 500GALLONS-PER-HOUR TRIPLEX HOMOGENIZER Valve Diameter, inch Pump Pre s ., psi 2nd.-stage Pres., psi U.S.P.H.S. Index U.S.P.H.S. Index of Control Sample* 5/8 1000 100 19.4 8.9 5/4 1000 100 12.6 9.2 1 1000 100 16.2 9.5 *Control sample was homogenized by the regular CherryBurrell valve at 2000 psi pump pressure. In all the three trials the knife-edged valve working at 1000 psi pump pressure and 100 psi second-stage pressure did not homogenize as well as the original valve working at 2000 psi pump pressure. There was no definite indication of the re­ lation between the valve diameter and the efficiency of a knife-edged valve. Conclusions More trials designed for a good analysis of variance would be needed for a reliable evaluation of the knife-edged valve when used in a commercial homogenizer. From the meager experimental data, the following conclusion might be drawn - 74 with reservation. There were several possible reasons why the result of using the knife-edged valve in a commercial homogenizer was not satisfactory. The lack of a definite relationship be­ tween the efficiency and the diameter might mean that physical factors other than valve diameter were responsible. These physical factors might include the shape and the workmanship of the valve, and the pressure fluctuation that existed. Fluctuation in pressure, especially the second-stage pressure, would have a pronounced influence on the efficiency as could be observed in the operation chart of a knife-edged valve (Figure 12). Poor workmanship might cause uneven fluid speed distribution around the valve and hence uneven cavitation effect. With regards to the shapes of the valves, though they all had a sharp edge against a smooth surface, there was the difference of the angle between one side of the edge and the surface. As can be seen in Figure 13, the angles on the approaching sides were 90°, 45°, and 60° in the and 1" valves respectively. 3/8", 5/4" The corresponding angle in the knife-edged valve used in the experimental homogenizer was 60°. Another possible source of error might have been the amount of milk used in each trial run. The amount of ten gallons for one run might have been insufficient. One and two-tenths minutes was all the time that was required to pump the ten gallons through. Allowing time for the adjustment of the press­ ures, there might be only twenty seconds or so left. CONCLUSIONS Among the various experimental results the more signif­ icant ones are those concerning the location of the homogen­ izing region in a poppet type homogenizer valve, the in­ fluence of back pressure in both the poppet type and the knife-edged valves, and the effects of dissolved gases on the homogenization efficiency. They established very well the place of cavitation in homogenization of milk products and were made use of in the' design and operation of the knifeedged homogenizer valve which showed a very satisfactory per­ formance in the experimental set-up. This investigation of cavitation in homogenization was, however, by no means exhaustive. An investigation, relative to cavitation, of other eminent factors such as the temper­ ature and the composition of the product being homogenized, and the shape of the constriction of the valve might yield information for even more effective and wiser utilization of cavitation for the purpose of homogenization. Some physical and chemical changes associated with homogenization such as the clumping of the fat globules after they have been broken up, the development of anti-oxidation effect, the occasionally observed pasty appearance of homogenized ice cream mix, etc., might have their explanation In cavitation. With due effort the adaption of the principle of cavitation homogenization to commercial operation should be possible. APPENDIX I Design of the Vacuum Homogenization Valve The vacuum homogenization valve used in Part 1 of the • experimental work was designed to provide a smooth constric­ tion which would cause the hydrostatic pressure to drop to about 5 psl when the milk was being sucked through at the rate of 25 gallons per hour. The procedure of the design was in four steps: to find the velocity of the flow at the valve needed for the pressure drop, to find the corresponding valve clearance, to determine the specification of the valve spring, and to design the accessory parts for housing the valve in a 1§ inch sanitary pipe cross. a. To find the velocity of the flow at the valve that would reduce the hydrostatic pressure to the vapor pressure of milk The experimental set-up for vacuum homogenization is diagrammatically shown below. - 77 supply tank I J homo. 1 valve Px= 14.7 psl. P2= ^.8 psl. VX= V2= ? 0 pump l r P1= pressure at the supply tank = atmospheric pressure, approximately = 14.7 psl. P2= vapor pressure of milk at homogenization temperature l6o°P, = vapor pressure of water at l60°P., approximately = 4.8 psl. density of milk = 66 lbs./cu. ft. Applying Bernoulli's equation to the supply tank and the homogenizer valve, pl 4*. V? = * m 2g M 14.7 x 144 66 Solving for V2 , 2 ^ + 2g + 0 = 4.8 x 144 ^ V§ 66 2g V2 = 37.6 fps. b. To find the valve clearance Assuming a pump capacity of 25 gallons per hour, or 0.00093 cubic feet per second. A = cross-sectional area of the flow at the valve = Q/V2 = 0.00093/37*6 = 0.0000247 sq. ft. = 0.00356 sq. in. - 78 Assuming a 3/8 in. effective diameter of the valve,, valve clearance = 0 .00356/ff x 0.375 = 0.00302 in. c. Design of the valve spring Assuming that the valve should open when the pressure in the valve chamber drops down to 10 psi and that during oper­ ation the pressure in the valve chamber is around 5 psi, then the change of load on the spring = (l0-5 )(g )2 J = 0.55 lbs. valve clearance ~ 0.00302 in. therefore, spring rate = 0 .55/ 0.003 = 183 lbs./in. Let G = torsional modulus of elasticity = 11,500,000 psi D = diameter of the spring = 9/l 8 in. n = number of coils in the spring 6 = d = diameter of the wire of the spring Then 183 - 11,500,000 d V 8 x 6 x Solving, d = 1/8 in., approximately. Hence, the specification of the spring should be as follows: wire size = 1/8 in. dia. spring diameter = 9/l 6 in. no. of coils = 6 pitch = 3/16 in. connection for vacuum gaga regular milk pipe cross outlet guide steel ball curved seat inlet Figure A1 Cross-sectional view of the ex­ perimental vacuum homogenization valve. - 80 - APPENDIX II The Calibration of the Capacity Regulation Valve of the Rotary Pump Used In the Experiment of Vacuum Homogenization Since the rotary pump available for the experiment of vacuum homogenization had a capacity of 375 gal. per hour, a by-pass valve was used to cut down the capacity to the de­ sired value, namely 25 gallons per hour. shown in Figure A3. valve. The arrangement is The by-pass valve was a 1 inch sanitary Marks were stamped on the valve as shown for grad­ uation purpose. for the purpose. But the valve was found to be insensitive A thin slot was cut on the valve plug as shown in Figure a4 to allow more precise control. The valve was set at different positions and the time required to pump one gallon of water at various degrees of vacuum was noted. The capacity corresponding to different valve settings was calculated and plotted to construct a calibration chart for the capacity regulation valve. However, the reliability of the results was rather doubtful, because the pump was leaking at the shafts. 60 72 40 90 120 180 360 10 0 2 1 4 5 3 6 Regulation valve setting 7 Rate of discharge, gallons/hour discharging - 81 - 8 Fig, A2 Calibration chart of the capacity regulation valve of the rotary p.ump used to produce vacuum for the vacuum homogenization valve. to Hcf. tnano'riefet regvlaiiom x/al^e inlet Fig. A3 Pipe line connection of the vacuum homogenization valve, the regulation valve, and the rotary pump. - 82 - Top view ^slot out to increase ^ sensitivity Cross-sectional side view Cross-sectional view at A-A of the valve plug Fig. A4 Views of the regulation valve showing the slot cut to increase its sensity. - 83 TABLE A I THE CAPACITY OP THE ROTARY PUMP AT VARIOUS DEGREES OP VACUUM AND SETTINGS.OP THE REGULATION VALVE Reg. valve setting Vacuum in. Hg. Amount of water delivered, gal. Time, sec. Capacity gal./hr. 0 20 1 12 300 1 20 1 15 240 2 20 1 17 212 3 19 1 14 257 3 20 1 32 112 4 l8 1 15 240 4 19 1 22 164 5 18 1 15 240 5 19 1 23 156 6 17 1 14 257 7 18 1 52 69 7 17 1 27 133 7 l6 1 17 212 8 17 1 35 102 - 84 APPENDIX III A Mathematical Study of the Magnitude of the Force Necessary to Break a Fat Globule Though the exact manner in which a fat globule is broken up in the process of homogenization is uncertain, the force necessary to break a fat globule into two halves may be cal­ culated hypothetically by assuming that the globule is broken in one of the three possible ways, namely, breaking into two halves along a meridian plane, by gradual narrowing down at the middle (i.e. gradual reduction in equatorial diameter), or by shearing along a meridian plane. The effects of the enveloping serum, the electrostatic charges, and the elasticity of the liquid fat are neglected in the following calculations. 1. Breaking open along a meridian plane The force may be calculated from the equation for force between two plates separated by a thin layer of a liquid fat, which is p = 2AS(C-S|-?- - + BS sine dynes (17) F n where 0 = angle of contact d = distance between the two plates R = radius of curvature of the meniscus F A = area of each plate S = surface tension B » circumference of the plate. Fig. A5 Two plates separated by a drop of liquid. - 85 If w© have two imaginary parallel planes very close together at a meridian plane of a fat globule, we have 0 = 90° r = -r = -(radius of the fat globule) c A = v r2 B = 2 nr Then, F = 2nr2S(g.°.s 90° d + or F = 2 vr2s( 0 + _L) + or F * 3TrS dynes 1) + 2nr s sln g0o 2r 2irS Fig. A6 A liquid sphere breaking into halves along a meridian plane. 2. Breaking a fat globule by reducing the equatorial diameter to zero oso-oo Fig. AT Hypothetical process of breaking a liquid sphere by reducing the equatorial diameter to zero. Since a sphere has the minimum surface area with respect to volume, any deformation must be accompanied by an Increase in surface area. If the elasticity of the liquid is neglected, the work necessary to deform the globule equals the correspond­ ing increase in surface energy. Let W be the work necessary to deform a sphere of fat into two halves. Then - 86 ¥ = increase in surface energy s 2Sfr(2r]_)2 - S?r(2r)2 ergs where r = radius of the original globule rx= radius of the resultant half-volume globules = Therefore, W = 2S?t(2 } Ji r )2 - (if r Sn(2r)2 = 1.04 Sifr2 ergs Assuming that this work is done by a force travelling all across the diameter of the globule, as shown in Figure a8 , then F = 1.04 S*rr2/2r * 0.52 Snr dynes Fig. a 8 If the distance travelled by the force is r as shown in Fig. A9 then F = 1.04 S^r2/r = 1.04 Svr dynes Fig. A9 / I \ 3. Breaking a fat globule by shearing O o Fig. A10 Hypothe­ tical process of shearing a liquid sphere. Since the fat is assumed to have no shearing elasticity the work done in shearing should be the same as that calculated for breaking by reducing the equatorial diameter to zero. F = 0.52 S^r dynes Hence, - 87 APPENDIX IV A Mathematical Study of the Size of the Cavity Which is Capable of Breaking a Fat Globule on its Collapse Since the force necessary to break a fat globule into two halves has been found hypothetically in Appendix III the size of the cavity necessary to produce such a force on its collapse may be calculated by the use of the water hammer equation and Rayleigh*s equation (19). Assuming that the force F acts over an area on the fat globule equal to knr2 , k being a constant, the impact pressure P due to the water hammer action upon the collapse of a cavity is P = 1.04 Sjfr/kfrr2 - * |j. dynes/cm? The average size of milk fat globules is around 4 microns, and S at l6o°F is around 5 dynes/cm. Hence, P = 1.04 x 5/ 0 .0002k = 26000 k "1 dynes/cm? = 26 .6/k gms./cm? = 0.37A P sl* From the water hammer equation, p = PcU T W nsi* ps *Adapted from the water hammer equation on page 395 Hydraulics 2nd Ed., by Schoda & Dawson, McGraw Hill Book Co., New York. 1934. - 88 where p = mass density of liquid, slugs/cu.ft., r = specific density of liquid, lbs./cu.ft. (66 for milk), c = velocity of sound in liquid .(assumed to be the same as in water, 4700 ft./sec.), and U = velocity of the in-rushing liquid, The velocity of in-rushing liquid is U = 144 p/pc or = 144 x 0.37 x 32 .2/(66 x 4700k) = 0 .0055/k ft. per sec. If it is assumed that the cavity is a perfect vacuum at the moment of collapsing (i.e. all the vapor condenses and no other gases present), Rayleigh’s formula for the velocity of contraction of cavity (19 ) can be used to determine the size of the cavity necessary to produce a sufficient force at its collapse. where Rayleigh's formula states, P = the hydrostatic pressure, p = density of the liquid, (66 lb./cu.ft. for milk) Rq= initial radius of the cavity, R = radius of the cavity at the moment under consideration. Putting the value of U obtained on the top of this page into Rayleigh's formula, - 89 Remembering that kJjr^, or k(^- x surface area of a fat globule), is the area on the fat globule over which the water hammer acts, it can be readily seen that the value of k is somewhere between 0 and 4. If the hydrostatic pressure is near atmospheric (2.12 x 10^ lbs./sq/ft.) then the term 0 .003.Pk 2 will be significant only when the value of k is in the order of 10"^ or less. Therefore, the ratio ^0 should R be not very far from 1 if the assumptions are correct, i.e. the collapse of the cavity is instantaneous and there is no resistance due to uncondensed vapor or undissolved gases. The actual conditions can be expected to deviate greatly from what have been set forth in the above calculations. 1. The formation of the cavity requires the expenditure of energy to evaporate the water and to work against the hydro static pressure. Since it is a constant presspure process in a steady flow the source of energy would be the thermal energy of the surrounding milk. Hence, there must be a re­ duction in the temperature of the shell of the cavity. The reduction in temperature raises the surface tension and also may harden the fat globule to some extent. The force necessary to break the fat globule would thus be greater than just calculated. 2. It is known that in rapid operation, the elasticity of the liquid becomes significant. The work done in deforming the fat globule may not be negligible. - 90 - 3. Unless the milk is thoroughly deaerated, there are bound to be some gases present in the cavity, and unless the free gases go back into solution instantaneously as the Van Iterson (25 ) theory postulates such gases may serve as cushion at the moment of collapse of the cavity. Hence, the hammering action would be much weaker than calculated. 4. In the homogenization of milk the fat globules are supposed to break into more than just two smaller ones. The actual situation would be much more complicated than what is assumed in the calculations. 5. The fat globules in milk have a surface adsorption layer of proteinous material which no doubt affects the magnitude of the force necessary to break the fat globule. - 91 APPENDIX V Determining the Representativeness of the Milk Collected in the Steel Cylinder Inserted between the First- and Secondstage Valve Blocks of a Manton-Gaulin Laboratory Homogenizer In the investigation of the influence of exit side hydro­ static pressure on homogenization efficiency a steel cylinder which had a capacity of about one quart was inserted between the first- and the second-stage valve blocks of the homogenizer, It was necessary to determine the proper length of time that must elapse for getting a representative milk in the steel cylinder after the pressures were adjusted. To do this, suc­ cessive quarts of milk discharging from the homogenizer were collected after the pressures became steady and tested for U. S.P.H.S. index and Farrall's index. The results, tabulated in Table All and plotted in Figure All, show that milk in the cylinder can be taken as a representative sample after at lease two quarts of milk have been discharged from the homo­ genizer after the pressures become steady. TABLE All DEGREE OF HOMOGENIZATION OF SUCCESSIVE QUARTS OF MILK DISCHARGED FROM A MANTON-GAULIN LABORATORY MODEL CGB 25 GPH HOMOGENIZER WITH A STEEL CYLINDER IN­ SERTED BETWEEN THE FIRST AND THE SECOND-STAGE VALVE BLOCKS Sample U.S.P.H.S. index Farrall's index lst.qt. 2nd.qt. 3rd.qt. 4th.qt. 5th.qt. 6th.q t . 41.3 18.1 11.0 11.0 11.0 12.0 362 l6l 47 62.3 37.1 43.1 * ft * 40 400 TJ.S.P.H.S* index Farrall’s index 300 200 cl •H CO to p] 10 100 CO to 1st. 2nd. 3rd. 4th. Sample number 5th. Farrall’s index 30 6th. Figure All Degree of homogenization of successive quarts of milk discharged from the Manton-Gaulin lab­ oratory homogenizer with a steel cylinder inserted between the first-stage and the second-stage blocks. - 93 APPENDIX VI Some Peculiarities in the Pressure Adjustment of the Single­ piston Two-stage Laboratory Model Homogenizer It is almost a rule that a two-stage homogenizer is pro­ vided with only one pressure gage, though there are two pres­ sures to be regulated. Because of this fact the customary way of adjusting the first- and the second-stage pressures is as follows: With the first-stage valve open, the second-stage valve is adjusted until the pressure gage indicates the de­ sired second-stage pressure, then the first-stage valve is turned in until the pressure gage indicates the sume of the desired first- and second-stage pressures. However, in one of the experiments using the Manton-Gaulin laboratory model homogenizer it was accidentally noticed that this conventional way of using one pressure gage for regulating two pressures did not seem to be reliable. It was noticed that after the pressures were adjusted the pressure gage did not fall to the desired first-stage pressure on the release of the secondstage valve, being higher than what was expected. Upon closer investigation, it was found that the higher the second-stage pressure the more greatly the first-stage pressure differs from the desired on the release of the second-stage valve. Table AIII shows such differences. Such differences might be an indication that the conven­ tional way of using the pressure gage In a two-stage homogenizer - 94 was not correct. Since the customary way of using a. single pressure gage in a two-stage homogenizer is based on the con­ stant delivery nature of the homogenizer pump., the next item checked was the rate of delivery at different pressures. results are shown in Table AIV. gallons per hour. The The average capacity was 21.0 The maximum fluctuation was less than 5fo from the average. TABLE AllI PRESSURE READINGS INDICATED BY A SINGLE PRESSURE GAGE OP A TWO-STAGE SINGLE-PISTON HOMOGENIZER WHEN THE VALVES WERE ADJUSTED IN THE CONVENTIONAL WAY Desired 2nd.-stage pressure, psi 500 1000 1500 2500 2500 2500 Gage reading when 2nd.-stage valve was adjusted, psi 500 1000 1500 Gage reading when 1st.-stage valve was also adjusted, psi 5000 5500 4ooo Gage reading when the 2nd.stage valve was released, psi 2700 5050 5500 Difference from desired 1ststage pressure difference, psi 200 550 1000 Desired 1st.-stage pressure difference, psi - 95 TABLE AIV CAPACITY OP THE TWO-STAGE SINGLE-PISTON LABORATORY HOMOGENIZER AT VARIOUS PRESSURES Pump press., psi 2nd.-stage press., psi Time for de­ livering one gallon, sec. 2500 5000 5500 5000 5500 4000 0 0 0 0 0 500 1000 1500 180 177 167 167 168 170 170 175 20.0 20.5 21.5 21.5 21.4 21.2 20.8 CM • t-i 2000 CM Capacity, gal./hr. 1500 TABLE AV BEHAVIOR OP THE READINGS OP TWO PRESSURE GAGES ■ OP A TWO-STAGE SINGLE-PISTON HOMOGENIZER - I (Method of manipulating the valves: The second-stage valve was adjusted first, then the first stage valve was ad­ justed to get a gage reading on the pump gage equal to the sum of the desired pressures, then the second-stage valve was released.) 2nd.-stage gage reading when the 2nd.-stage valve was adjusted, psi Pump gage reading when 1st.stage valve was also adjusted, psi 1st.-stage pressure difference, psi Pump gage reading when 2nd.stage valve was released, psi 500 1000 1500 5000 5500 4000 2500 2500 2500 2850 3200 3600 - 96 - TABLE AVI BEHAVIOR OF THE READINGS OF TWO PRESSURE GAGES OF A TWO-STAGE SINGLE-PISTON HOMOGENIZER - II (Method of manipulating the valves: The first-stage valve was first adjusted to get the desired pump pressure, then the second-stage valve was adjusted until the second-gage indicated the desired second-stage pressure, then the pump gage reading was again noted.) ..... — —, Pump gage reading when the first-stage valve was ad­ justed, psi Second-stage gage reading when the second-stage valve was adjusted, psi Pump gage reading after the second-stage valve was ad­ justed, psi Pump gage reading when second-stage valve was released, psi 2500 2500 2500 500 • 1000 1500 2650 2750 2950 2500 2500 2500 The next item investigated was to insert a pressure gage between the first-stage and the second-stage valves in addition to the one at the homogenizer pump and to note the behavior of the gage readings for different pressure combinations. The results are shown in Tables AV and AVI. Table AV seems to show that the valve clearance of the first-stage valve changes with different first- and secondstage pressure combinations though the pressure across fne valve is maintained the same. Table AVI seems to show that though the valve hand-wheel was kept at the same setting the pressure difference across the valve changes as the secondstage pressure changes. Such behavior of the homogenizer makes it difficult in the experiments to maincain constant - 97 shearing and. impingement and to vary the factors of cavitation. An investigation of such hehavior was carried out on a diff­ erent machine, a Manton-Gaulin triplex two-stage homogenizer at 125 gallons per hour capacity. The results shown in Table AVIX are quite different from that obtained by using the single­ piston homogenizer. The differences between the desired pump pressure and the gage reading upon the release of the secondstage valve were not so large as in the case of the singlepiston homogenizer. TABLE AVII BEHAVIOR OP THE READINGS OP A SINGLE PRESSURE GAGE OF A TWO-STAGE TRIPLEX HOMOGENIZER (Method of manipulating the valves: The second-stage valve was first adjusted to get the desired second-stage pressure., then the first-stage valve was adjusted until the pressure gage indicated the sum of the desired first- and secondstage pressures, then thesecond-stage valve was released and pressuregage reading againnoted.) Gage reading when second-stage valve was adjusted, psi Gage reading when first-stage valve was also adjusted, psi Pressure difference across the first-stage valve, psi Gage reading when the secondstage valve was released, psi 500 1000 3000 3500 2500 2500 2550 2500 2600 2700 (trial l) (trial 2 ) The principal structural differences between the singlepiston homogenizer and the triplex homogenizer are listed below. - 98 Single-piston homogenizer Triplex homogenizer 1. Single piston, pressure 1. Three pistons, pressure unsteady. 2. The outlet valve of the pump was also used as the relatively steadier. 2. Separate pump valves and homogenization valve. first-stage valve. Comparing the figures In Table AVII and Table AV, it can be seen that such behavior of the homogenizer Is likeljr an individuality of a particular type of homogenizer. - 99 APPENDIX VII Statistical Analysis of the Results Obtained from the Experi­ ments of Applying Pressure to the Exit Side of a Homogenizer Valve in a Manton-Gaulin Single-Piston Homogenizer Part 1 Pressure difference across the homogenizer valve kept constant. TABLE AVIII EFFECT OF THE APPLICATION OF PRESSURE ON THE EXIT SIDE OF A HOMOGENIZER VALVE ON HOMOGENIZATION EFFICIENCY - I (Milk samples were collected in a steel cylinder inserted be­ tween the first- and the second-stage blocks and their degrees of homogenization were expressed in terms of U.S.P.H.S. index., pressure difference across the homogenizer valve being maintained at 2500 psi.) Sums Means 5000 3500 4000 0 500 1000 1500 Run 1 8.75 15.3 CO U.S.P.H.S. indices 2500 M Homo. pump press. psi. Cylinder pressure psi. 14.6 53.45 Run 2 8.4 12.9 12.3 10.9 44.5 Run 5 7.6 13.8 13.1 11.6 46.1 24.75 42.0 40.2 37.1 144.05 8.25 14.0 13.4 Sum 9.28 Correction term = (144.05)^/12 = 1729.2002 Total sum of squares = 8.75^ + 8.4^ -1 - ..... + 11.6^ - correction term = 95.0925 - 100 Treatment (cylinder pressure) sum of squares = (24.752 + 42.02 + 40.2^ + 37*l^)/3 - correction tern = 60.4706 Run sum of squares = (53.45^ + 44.5^ + 46.1^)/4 - correction term = 11.5904 Discrepance = 95.0923 - 60.4706 - 11.3904 = 23.2313 TABLE AIX ANALYSIS OP VARIANCE OP THE EXPERIMENT OF APPLYING PRESSURE TO THE EXIT SIDE OP A HOMOGENIZER VALVE WHILE THE PRESSURE DIFFERENCE ACROSS IT WAS KEPT CONSTANT Sources of Variance Degree of Freedom Total Sums of Squares Mean Squares P ratio 5 .21* 11 95.0923 Treatments (cylinder pressures) 3 60.4706 20.157 Runs 2 11.3904 5.695 Discrepance O 23.2313 3.872 1 .46 trai *Significance level equal to 5$. For six degrees of freedom t = 5.707 L o s = 2 -447 Least significant difference between treatment means at 1>3 level = a/ 2 x 5. B"7273_ x 3.707 = 5.98 Least significant difference between treatment means at 5/5 level = fJ2 x 3 .072/3 x 2.447 = 3.94 Hence, when keeping the pressure difference across the homogenizer valve constant and discharging the milk into a pressure chamber of 500 psi and 1000 psi there was a significant - 101 lowering of homogenization efficiency. This was not true when the chamber pressure was at 1500 psi. Part 2 Homogenizer valve setting kept constant. TABLE AX EFFECT OF THE APPLICATION OF PRESSURE ON THE EXIT SIDE OF A HOMOGENIZER VALVE ON HOMOGENIZATION EFFICIENCY - II (Milk samples were collected in a steel cylinder inserted be­ tween the first- and the second-stage blocks and their degrees of homogenization were expressed in terms of U.S.P.H.S. index, homogenizer valve setting being kept constant.) Homo. pump press. psi. Cylinder pressure psi. U.S.P.H.S. INDICES 2500 2650 2750 2900 0 500 1000 1500 Run 1 14.4 Run 2 6.7 Run 3 12.3 Run 4 8.65 Sums 20.0 20.4 71.0 13.2 17.0 46.53 14.5 15.9 24.4 67.10 12.2 14.1 23.0 57.95 242.58 16.2 9.63 Sums 42.05 52.53 63.2 84.8 Means 10.51 13.12 15.80 21.18 Correction term - 242.582/l6 = 3677.816 Total sum of squares = 14.42 -1 - 6.72 + ---- + 23.02 - correction term = 370.193 Treatment (cylinder pressure) sum of squares = (42.05 2 + 52.53 + 6 3 .22 + 84.82 )/4 - correction term = 250.405 2 - 102 Run sum of squares = (7 1 .02 + 46.55 2 + 67.102 + 57.952 )/4 correction term = 88.847 Discrepance = 5 7 0 .195 - 250.405 - 88.847 = 50.941 TABLE AXI ANALYSIS OP VARIANCE OP THE EXPERIMENT OF APPLYING PRES­ SURE TO THE EXIT SIDE OP A HOMOGENIZER VALVE VJHILE ITS SETTING NAS KEPT CONSTANT Degree of Freedom Sums of Squares 15 570.195 Treatments (cylinder pressures) 5 Runs Discrepance Sources of Variance Total Mean Squares F Ratio 250.405 85.468 24.478* 5 88.847 29.616 8.614 Q s 50.941 5.^58 *Significance level equal to 1$. For 9 degrees of freedom t qi = 5-250 t ^ = 2.262 05 Least significant difference between treatment means at 1fo level . = r/2 X5-^5^/^ X 5.250= 4.27 Least significant difference between treatment means at 5^ level = ^2. x5.458/4 x 2.262= 2.97 Hence , the samples obtained when the cylinder pressure was 1000 psi or 1500 psi were very significantly different from the sample when the cylinder pressure was zero (atmospheric). - 103 APPENDIX VIII Statistical Analysis of the Results Obtained from the Bleeding Valve Experiments Part 1 Pour-hole valve. -TABLE AXII DEGREES OF HOMOGENIZATION (IN TERMS OF FARRALL1S INDEX) OF MILK AT FOUR DIFFERENT LOCATIONS IN THE HOMOGENIZER VALVE Locations Distance from Inner Edge of Valve Homo. 0.008" 0 .010" 0 .013" 0 .016" Outlet Slides series I 77.8 94.6 78.4 67.6 42.4 23.8 26.4 34.2 29.2 97.4 32.4 15.6 8.0 2.6 2.6 5.2 5.2 7.8 10.6 5.2 318.4 126.8 174.6 18.4 28.8 me an 79.6 31.7 4.6 7.2 nr O f .O Farrall1s indices 57.4 86.2 6l .4 45.2 32.6 26.2 15.6 57.8 34.4 44.4 24.4 5.2 5.2 2.6 10.8 5.2 13.6 15.6 13.0 250.2 82.2 161.0 23.8 47.4 Farrall’s indices sum Slides series II sum mean Sum 62.55 568.6 20.55 209.0 43.65 40.25 335.6 5.95 42.2 Mean 71.07 26.12 41.95 5.27 Diff. be­ tween series sums 68.2 4 4 .6 13.6 5.4 Sums 667.0 33.35 564.6 11.85 76.2 9.52 18.6 Means 28.23 1231.6 30.79 - 104 Correction term = 1231.62/4o = 37920.964 Total sum of squares = 77. 82 + 94.62 + ... + l? .o2 - correction term = 30476.88 Location sum of squares = (568.62 + 209.02 + .... + 76.22 )/8 - correction term = 22979.24 Series sum of squares = (667.02 + 564.62 )/20 - correction term = 262.14 Subclass sum of squares = (318 .4 2 + 250.22 + .... + 47.42 )/4 - correction term = 23879.3 Location x series interaction = 23879.3 - 22979.24 - 262.14 = 637.92 Slide sum of squares = (68 .22 + 44.62 + 13.62 + 5.42 4 l8 .62 )/8 - - correction term = 900.06 TABLE AXIII ANALYSIS OP VARIANCE OP THE BLEEDING VALVE EXPERIMENT USING A FOUR-HOLE VALVE Source of variance Degree of freedom Sum of squares Mean square P ratio 27.81* 39 30476.88 Locations 4 22979.24 5744.81 Slides 5 900.06 180.01 0.87 1 262.14 262.14 1.27 4 637.92 159.48 0.77 30 6197.29 206.57 Total Series Location x series interaction Discrepance *Significance level equal to Vfo - 105 If the hypothesis Is that all the samples came from the same population, the mean square of location may be compared with that of the slides. Then F ratio for location = 4°cation mean square slide mean square - 5744.81/180.01 = 31.913 P = 11.39 for 4 and 5 degrees of freedom Hence the hypothesis that all samples were from the same population cannot be established. The next step is to use t test to compare the samples from the bleeding holes with the sample collected at the outlet of the homogenizer. t for 30 degrees of freedom = 2.042 t for 30 degrees of freedom = 2.750 Standard error of difference between means = J 2 x 206.57/8 = 7.2 Therefore, least significant difference between means at 5^ level = 7.2 x 2.042 = 14.7 least significant difference between means at ifo level = 7.2 x 2.750 =' 19.8 Samples from the first and the third holes were significantly different from the sample from the homogenizer outlet at level. Tfo Sample from the second hole was significantly different from the sample from the homogenizer outletat5% level. Sample from the fourth hole was insignificantly different fromthe sam­ ple from the outlet of the homogenizer. - 106 - • 0 O rH X pq Pd 0 W S tS3 H H CO pq - C5 pj O B s S S S ^ w O S H ft I i> H X <3 a 9 B CO S co Ph S ft O B H Eh S < H '- 'O O S o H Eh < P3 EH tSJ f t H ft 525ft § s £ o gw ffiO 0 > ft 0 > ft ft ft O EH CO ft O o 0 g i—I X < SP O ? ft O O O CO CVJ00 CO • • • • m m m m CVJ f t CVJ f t in m vo•ft• voft • •voft « • o•n• vo• oo• VO cv VOft Cbift CM O co ft b— ft KVKNCM CM cm m ov CVJ ft ft O cvioo • • LT\ mm CVJ f t ft inft o ft 00 COCO ftoo*CVJ • • • • • * H b-C O LTV00 0m o in ft ft ft VO ft > ft o ft O O VO O O CVJ voft • I * ■ • • CQ KAft00 Ch ft o Hence, s = r = 4 P1= 33.3 + 29.2 + Pj= 32.2 + 28.3 -1- 29.2 = 89.7 Qh= 39.8 + 32.2 + 34.2 = 106.2 Qk= 36.5 + 35.2 + 43.3 = H 5.0 43.3 = 105.8 - 113 Substituting Into the above formulas, the following values are obtained. X = 38 .I (for W = 34.4 (for P-l = 600 psi, P2 = 50 psi, and d = 1/2") = 600 psi, P2 = 150 psi, and d = 3/16") The formula for one missing value is y _ tT-bB-S (t-l)(b-l)" where t is the number of treatments, b Is the number of blocks, T Is sum of items with same treatment as missing item B is sum of items In same block as missing item, S is sum of all observed items. To estimate the index for P^ = 800 psi, P2 = 50 psi, and d = 3/16" t = b = 4 T = 34.62 B = 31.55 S = 183.77 Putting these values into the above formula, X = 8.99 or 9.0, say. To estimate the index for P^ = 1000 psi, P2 = 150 psi, and d = 1/2 t = b = 4 T = 19.3 B = 34.7 S = 159.1 Putting these values into the above formula, X = 6.3 - 114 Following is the statistical analysis of the results. Correction term (C.T.) = (910)2/48 = 17252 .08333 Total sum of squares = 39.82 + 12.72 + ___ + 6.32 - C.T. = 6197.27667 2nd.-stage pressure sum of squares _ (28l.92 + .... + 219.22 ) _ r 12------------ m = 342.77500 1st,-stage pressure sum of squares = (543.5 2 4 - ---- + 165.42 ) _ C.T. lB = 5447.33042 Valve diameter sum of squares = 227.4 2 +....4- 252.22 - C.T. 12 1st. and 2nd-stage pressures interaction sum of squares = 150.82 + .... 4- 25.62 --------- 4----------- ?2 sum - P-, sum of sqs. 1 sqs. - C.T. = 123.98125 Interaction between diameter and 1st.-stage pressure sum of squares = 144.32 + .... 4- 4l.02 - diam. s.s. Zr~ - P-L S.s. - C.T. = 109.77792 - 115 TABLE AXVIII ANALYSIS 0.F VARIANCE Degrees of Freedom Source Total Sum of Squares Mean Square F Ratio 691 43 6197.27667 1st.-stage pressure 2 5447.33042 2723.66 2nd.-stage pressure 3 342.77500 114.26 Valve diameter 3 82.88333 27.62 7.01 Interaction "between 1st. and 2nd.-stage pressures 6 123.98125 20.66 5.25 Interaction between 1st.-stage press, and valve diameter Error 29.0 * 6 109.77792 18.29 23 90.52875 3.94 4.63 All the F ratios are significant at the Vfo level. t-test for diameter and second-stage pressure For error of 23 degrees of freedom A 05 = 2.069 t.01 = 2 '°°7 The standard diviation of the mean for either the secondstage pressure or the diameter is S = /v/2(3.9^)/12 = 0.811. Hence, the least significant differences are L.S.D. = 0.811 x 2.069 = 1.68 L.S.D. 01 = 0.811 x 2.807 = 2.28 - 116 - Using these values to check the mean indices of the various diameters and second-stage pressures, it is found that there was significant difference at l/ level between the 1/ 2 " valve and the rest, and between Pg = 0 and the other second-stage pressures. - 117 APPENDIX XI A Comparison of the U.S.P.H.S. Method and Farrall»s Method of Judging the Degree of Homogenization of Milk In the "bleeding^ valve'1 experiments the samples of milk obtained were small. It was necessary to have some method of determining the degree of homogenization of very small samples. The microscopic method devised by Farrall, Walts, and Hanson (11) seemed to be the answer. A number of milk samples were tested for the purpose of getting familiar with the operations of this method and at the same time providing some idea of the relationship between this microscopic method and the U.S. P.H-.S. method. The results of eleven samples over a wide range of degree of homogenization are presented in Table AXIX and plotted in Figure A12. TABLE AXIX THE DEGREE OF HOMOGENIZATION OF ELEVEN SAMPLES OF MILK MEASURED BY THE U.S.P.H.S. AND FARRALL‘S METHODS Sample No. 1 2 3 4 5 6 7 8 9 10 11 Fat Test,$ U.S.P.H.S. Index Farrall*s Index 3.7 41.3 3.7 18.1 11.0 11.0 11.0 12.0 362 l6l 47 62.3 37.1 43.1 3.70 3.70 3.70 3.70 3.65 3.65 3.65 3.65 3.65 i4.6 28.2 34.8 18.8 38.8 15.6 47.0 8.47 14.8 8.86 - 118 350 300 Farrall*s index 250 200 150 100 50 0 10 20 30 40 50 U.S.P.H.S. index Figure A12 Farrall*s index versus U.S.P.H.S. index of the degrees of homogenization of eleven samples of milk. - 119 - 0) CM | O q> >5 to w c o 3 in •p o 2 | W ! G CV cd fw Q) | ’ CV INDEX ON FARR AIL* S INDEX OF HOMOGENIZATION •H v £ 5 s rH O ' , 0 0 O ' , OO I —1 s t CV C V P O • \C vD e ' ­ c o , vIT O, s t vC ! •H S jq REGRESSION v£> vO CV 1 1 1 I I I -st 1 & ! > v CO vCOO o- r i O H CO CO CM CV CO P- to fl § o •H •H £ TO *- ! •POO }>3 CO •H to m • o CO I c O CQ •C HQ~ CQrH X CD C D CG r t f ~ f C >. P t fsM Q )C d W cv « to rH CO G' • ■ —! «H O K H:• K in 05 * * P P • CV m p . CV in I I CV vo I vO to I Pi I C \ ! CO CV rH CV rH P s t rH Ch CV in P i —! to m vO to c s r p rH in O' CO CV in rH in P \C r i vC sC in CO CO n r —! n CV 05 CV CO • CV v £ ) rH 0 e ' ­ en iH 0 O ' , s t Cl to • s t CO to 0 to t 1 to • to O ' , o . s t rH . O & O' O ♦ CV rH vO • s t rH vO 0 IT vC c I —' cr CO -p V p to <15 O fH *rt o Ot & c •H £ o i r . O' s t rH C Q iH 05 C dTS P ( m fi cm T—l p s t sO CO sC rH en 0 rH H . to rH o• r~! H o• iH O • rH rH rH CV CO s t in 0 to CV et? Pn C O ! W K a (D P-: TJ » c co w ® rH • Pr © i CO H P • s t to P to 0 s ' rH tc vC e x . * 0 to O' r-! CO p» vC sC rn i-r i • cn ! - 120 From the results shown in Table AXIX the mathematical relationship between the two methods of measuring the degree of homogenization may be derived by applying the least square method as follows. Let the least square line be y» = a + m(x - x), x = observed U.S.P.H.S. index, y = observed Farrall1s index, and n = number of samples. a = y = sy/n = 980.1/11 = 89.1 x = zx/n = 166.75/11 = 15.16 m = (nixy - sxsy)/[n^x 2 - (zx)2] = (11 x 22211 - 166.7 x 980.1 )/(ll x 3566.07 - 166.732 ) = 8.764 Hence, the lease square line is y' = 89.1 + 8.764(x - 15.16 ) y 1 = 8.76x - 43 .7 or This equation Is the experimentally derived relation be­ tween Farrall's index and the U.S.P.H.S. index of degree of homogenization. From this equation the value of Farrall's index corresponding to a U.S.P.H.S. index of 10, which is the common upper limit of homogenized milk, was calculated to be 44. * Doan, Josephson and Adams (9) found that a Farrall's in­ dex of 20 corresponds to a U.S.P.H.S. index of 5. Later Doan, and Mykleby (10) recommended a Farrall's index of 12 as sat­ isfactory limit of homogenized milk. In the same year Doan (8 ) - 121 found that a Farrall's Index ranging from 5 to 7 corresponded to a U.S.P.H.S. index ranging from 2 to 7. The variation in the findings was more likely due to the unstandardized method of performing the U.S.P.H.S. method of determining the homogenization efficiency. Various methods of separating the top 100 ml. of milk after 48 hours of stand­ ing at a certain temperature can be found in the literature. Those methods may yield very different results. Farrall’s method should serve as a quick and convenient way of determining the degree of homogenization. However, the method may show variable results because 1. There may be variation in the thickness of the milk films on the slides. 2. There may be variation in the abilities of the operators to differentiate globules of neighboring size classes. 3 . There may be variation introduced in the calculation of the index by neglecting the variation in fat content of the milk samples. A richer milk would have more fat globules than a less rich milk if the globules are of the same size distribution. - 122 APPENDIX XII Statistical Analysis of the Results of Homogenizing Milk with Air Injection Using the Knife-edged Valve TABLE AXXI EFFECT OF ADDING AIR TO MILK ON HOMOGENIZATION EFFICIENCY (U.S.P.H.S. indices of milk homogenized hy the knife-edged valve at a homogenizer pump pressure of 800 psi, secondstage pressure of 50 psi, and four different air sat­ uration pressures, temperature of milk at l40° F . ) Air Saturation Press., psi Sum Mean 11.8 46.2 11.5 11.5 10.2 45.9 11.5 11.9 10.9 11.4 44.0 11.0 55.8 56.7 50.2 55.4 156.1 11.9 12.2 10.1 11.1 25 20 10 Run 1 i4.i 12.5 7.8 Run 2 11.9 12.5 Run 5 9.8 Sum Mean 0 11.5 Correction term = 156.1^/12 = 1545.6008 Total sum of squares = l4.1^ + .... + 11.4^ - C.T. = 27.1492 Treatment sum of squares = (55.8 P 2 + .... + 55.4 )/5 - C.T. = 8.4425 Run sum of squares = (46.2^ + 45.9^ + 44,0^)/4 - C.T. = 0.7117 - 123 TABLE AXXII ANALYSIS OP VARIANCE OP THE EFFECT OP ADDING AIR TO MILK ON HOMOGENIZATION EFFICIENCY Source Degree of Freedom Sum of Squares 11 27.1492 Treatments 3 8.4425 Runs 2 0.7117 Discrepance 6 lV.9950 Total Mean Square F ratio 2.8l4l 0.938 2.9991 The small value of F ratio for treatments Indicates that no significant effect on the efficiency of homogenization was produced by the particular air saturation pressures used. - 124 - APPENDIX XIII Statistical Analysis of the Results of Homogenizing Ice Cream Mix with Air Injection Using the Knife-edged Valve TABLE AXXIII EFFECT OF ADDING AIR TO ICE CREAM MIX ON HOMOGENIZATION EFFICIENCY (Farrall’s indices of ice cream mix homogenized by the knife-edged valve at 150° F.) Homo. Pump Press. psi 800 800 800 800 800 800 Air Sat. Press. psi 0 0 50 50 75 75 2nd.stage Press. psi 100 200 100 200 100 200 Total Mean 1000 1000 1000 1000 1000 1000 Total Mean Total 0 0 50 50 75 75 100 200 100 200 100 200 Run 1 2 Total 5 259.2 277.1 191.7 118.5 212.1 88.2 168.1 241.0 97.1 147.5 97.4 56.8 55.2 84.0 80.9 95.8 584.1 554.5 468.4 422.4 254.8 298.5 1214.0 607.6 720.9 2542.5 202.55 101.2 120.1 212.6 51.1 56.5 25.4 52.0 90.6 256.9 20.0 56.2 55.5 5.7 24.1 55.2 66 .9 524.8 155.7 101.5 124.5 599.6 142.8 557.8 1280.2 99.9 25.8 89.6 1815.6 750.4 1258.7 175.1 62.5 57.5 60.6 Mean 155.2 158.9 194.7 178.1 156.1 140.8 78.5 99.5 l4l .25 295.7 500.2 98.5 100.1 108.5 44.6 55.8 4l.4 71.12 5822.7 - 125 TABLE AXXIV THREE TWO-WAY TABLES OF THE EFFECT ADDING AIR TO ICE CREAM MIX ON HOMOGENIZATION EFFICIENCY Air Sat. Press. A Total Mean 834.5 1714.3 142.8 793.2 556.1 ■1349.3 112.4 75 556.3 422.8 759.1 63.2 Total 2009.3 1813.4 3822.7 100 200 0 879.8 50 Second-stage Press. B j First-stage Pressure 860 Total Mean 1000 100 1287.3 722.0 2009.3 111.5 200 1255.2 558.2 1813.4 100.7 Total 2542.5 1280.2 3822.7 Air Sat. Pre ss. C Second-stage pressure OF First-stage Pressure 1000 800 Total Mean 0 1118.4 595.9 1714.3 143.0 50 890.8 458.5 1349.3 112.3 75 533.3 225.8 759.1 63.2 Total 2542.5 1280.2 3822.7 Correction term = 405,917.64694 Total sum of squares = 239.2^ + .... + 124.3^ - C.T. = 197,439.1431 - 126 Run sum of squares = (1813.62 + ____ + 1258.72 )/12 - C.T. = 47,129.9206 Air saturation pressure sum of squares = (1714.2 2 + --- + 759.I2 )/l2 - C.T. = 58,721.5356 First-stage pressure sum of squares = (2542.5 2 + 1280.22 )/18 - C.T. = 44,261.1470 Second-stage pressure sum of squares = (2009.3 2 + 1813.42 )/l8 - C.T. = 1,066.0225 Total sum of squares of table A = (879.82 + + 422.82 )/6 - C.T. = 44,200.5648 Air saturation pressure and second-stage pressure interaction sum of squares = 44,200.5648 - 38,721.3356 - 1,066.0225 = 4,413.2067 Total sum of squares of table C = (1118.4 2 + ___ + 225.82 )/6 - C.T. = 84,925.1514 Air saturation pressure and first-stage pressure interaction sum of squares = 84,925.1514 - 38,721.3356 - 44,261.1470 = 1,942.2688 Total sum of squares of table B = (128T.32 + ___ + 558.22 )/9 - C.T. = 45,808.97X9 - 127 First-stage pressure and second-stage pressure interaction sum of squares = 45,808.9719 - 44,261.1470 - 1,066.0225 = 481.8024 Sum of squares of pressure combination = (584.I2 + 554.5 2 + ___ + 124.32 )/5 - C.T. = 92,543.9898 Air saturation pressure, second-stage pressure and first-stage pressure interaction sum of squares = 92,543.9898 - 38,721.3356 - 44,261.1470 - 1,066.0225 = 8,495.4847 TABLE AXXV ANALYSIS OF VARIANCE O F ‘THE EFFECT OF ADDING A IR TO ICE CREAM MIX ON HOMOGENIZATION EFFICIENCY Source Total Degree of Freedom Sum of Square s 35 197,439.1431 Mean Square F ratio Run 2 47,129.9206 23,564.96 IO.36** Air saturation pressure 2 38,721.3356 19,360.67 First-stage pressure 1 44,261.1470 44,261.15 19.25** Second-stage pressure 1 1,066.0225 Air x 1st.-stage press. 2 1,942.668 Air x 2nd.-stage press. 2 4,413.2067 2,206.60 1 481.8024 481.80 2 8,495.4847 4,247.74 50,927.5548 2,314.88 1st.-stage press, x 2nd. stage press. 1,066.02 971.33 1st.-stage press, x 2nd. stage press, x air sat uration press. Discrepance 22 **Significance level equal to ifo. 8.37** - 128 Standard deviation = ^2314.888 = 48.2 t .05 for degrees of freedom = 2.064 t^Qi f>or degrees of freedom = 2.797 Least significant difference between treatment means at 5$ level - x 2 .064 = 40.7 Least significant difference between treatment means at Vfo level 4^ B8 2L_g. x 2.797 = 55 The test of significance indicates that the use of 75 psi air saturation pressure produced results different from using no air at a significance level of Vfo and from using 50 psi air saturation pressure at a significance level of 5 The use of 50 psi air saturation pressure was insignificantly different from using no air. There was no significant difference between the two second-stage pressures. - 129 APPENDIX XIV Statistical Analysis of the Results of Homogenizing Concen­ trated Milk with Air Injection Using the Knife-edged Valve TABLE AXXVI EFFECT OF ADDING AIR TO CONCENTRATED MILK ON HOMOGENIZATION EFFICIENCY (Farrall's indices of concentrated milk homogenized by the knife-edged valve at a homogenizer pump pressure of 900 psi and second-stage pressure of 100 psi at a temperature of l4o° F . ) Deaerated Air Saturation Pressure 20 Sample 50 Atmos­ 10 25 pheric Sum Mean 127.8 63.1 35478 114.4 242.2 129.4 2 213.0 172.2 385.2 102.7 19471 125.3 117.9 133.5 93.5 65.0 124.0 85.9 117.0 91.0 65 .5 249.3 203 .8 250.5 184.5 130.5 1597.9 114.1 Sum- 740.0 436.3 378.7 300.8 355.1 376.7 274.5 2862.1 Mean 185.0 109.1 Run 1 Run 188.0 166.8 75 91.4 66.3 94.7 43.1 64.0 99.6 79.6 53.9 4o.6 92.6 64.4 97.0 10-4.6' 192.2 144.0 1264.2 75.2 88.8 94.2 68.6 90.3 102.2 Correction term = 2862.1^/28 = 292,557.7289 Total sum of squares = 188.0^ + 166.8^ + . . . . + 65.5 - C.T. = 51,219.7811 Run sum of squares = (1246.2^ + 1597.9^)/l4 ~ C.T. = 3,976.9890 Treatment sum of squares = (740.0^ + .... + 274.5^)/4 - C.T. = 36,242.5636 - 130 TABLE AXXVII ANALYSIS OP VARIANCE OF THE EFFECT OF ADDING AIR TO CONCENTRATED MILK ON HOMOGENI­ ZATION EFFICIENCY Degree of Freedom Source Total Sum of Squares Mean Square F ratio 27 51,219.781 Runs 1 3,976.989 3,976.989 7.23* Treatments 6 36,242.564 6,040.427 10.98** Discrepance 20 11,000.228 550.114 * Significance level equal to 5^. ^Significance level equal to ifo. t t qcj for 20 degrees of freedom= 2.086 for 20 degrees of freedom = 2.845 Least significant difference between treatment means at 5f level a / x 2.086 = 34.60 Least significant difference between treatment means at 1# level = y = 47.18 2 j r Hence there was significant deaerated and ^ m x 2 .845 difference at ifolevelbetween the all the other samples in favor of the latters. 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