AN OPTICAL iNS’TRUMENT TO RECORD SEDlMENTATlON RATE OF AGGLUTINATING ERYTHROCYTES The“: for the Degree. of M. S. MICHIGAN STATE UNEVERSI’FY Henry Puryear Cole Jr. 1963 ssssss IlllllllilllllllllllNIHllllllllllIUIUIHIIIHHllllllllll 3 1293 01683 6276 LIBRARY Michigan State University ABSTRACT AN OPTICAL INSTRUMENT TO RECORD SEDIMENTATION RATE OF AGGLUTINATING ERYTHROCYTES by Henry Puryear Cole Jr. This thesis describes a quantitative method intended to determine the strength of the antigen-antibody reaction by measuring the sedimen— tation rate of red blood cells. A beam of polychromatic, unpolarized light sweeps a row of sample tubes; the transmission through each tube depends on the degree of settling. The settling, in turn, varies with the size of the settling aggregates formed in the immune reaction. By mounting the light source and photocell on a moving boom, samples placed in the path of the light beam can be studied simultaneously. The transmittance of each cell is recorded and a settling curve for each blood sample is obtained. The bulk of the thesis deals with the con- struction, operation and theory of the machine: The apparatus performs well. It records the optical density accurately, and provides direct comparisons between samples aggluti- nating under different experimental conditions. The settling rates of four types of suspensions were examined: blood mixed with anti-serum; blood with anti-B serum, blood with anti-D serum, both in and out of a magnetic field, and blood with saline. There is a difference in the curves for agglutinating and Henry Puryear Cole Jr. non—agglutinating blood, but more data are required before the instru- ment forms the basis of a precise method. A few runs were made on samples placed in a magnetic field, but the datavmutainsufficient to permit conclusions to be drawn. The process of sedimentation was found to be more complex than had been supposed. The experimental difficulties-—convection currents, hindered settling, multiple scattering of the light--could be overcome, but there remain serious theoretical problems to be resolved: develop- ment of the hydrodynamical laws for settling of non-spherical particles and estimation of the Mie scattering coefficient for the non spherical particles. These problems are discussed, and an approach to a solution is suggested. AN OPTICAL INSTRUMENT TO RECORD SEDIMENTATION RATE OF AGGLUTINATING ERYTHROCYTES BY Henry Puryear Cole Jr. A THESIS Submitted to Michigan State University in partial fulfillment of the requirements for the degree of MASTER OF SCIENCE Department of Physics and Astronomy 1963 ACKNOWLEDGMENTS It has been my good fortune to have been able to write my thesis under the supervision of Dr. Donald J. Montgomery. He has been an ex- cellent teacher whose insight into the problems of my research and whose ability to teach one how to think clearly have been of the greatest value. I am grateful for his help and the patience he has shown towards me. Warm thanks are due to the others who have helped me: Larry Knapp, Charlane Temple, Jerry Tomecek, and John Warren. Mr. Richard Hoskins and Mr. Nelson Rutter in the machine shop have also been most helpful and cooperative. The staff of the laboratory of Olin Health Center have been of the greatest assistance to me throughout the year. They and the volunteers who gave blood contributed materially to the success of the project. Thanks are due also to Dr. Emanuel Hackel for the donation of certain sera, and to Mr. Jack Carmichael, of the Department of Chemistry, for the loan of Spectrophotometer cells. This work was supported in part by the National Institutes of Health under Research Grant GM #08967. ii Chapter II. TABLE OF CONTENTS INTRODUCTION . Statement of Problem Description of Apparatus and Agglutination Summary of Solution THEORY OF AGGLUTINATION Description of Antigens and Antibodies Nature of the Antigen-antibody Reaction Discussion of Process of Agglutination III. THEORY OF LIGHT TRANSMISSION AND STOKES LAW Discussion of Losses Due to Scattering and Absorption Losses due to Reflection Stokes Law Hindered Settling Electroviscosity IV. PREPARATION FOR RUNS Preparation of Suspensions Machine Adjustments V. EXPERIMENTAL RESULTS . . VI. CONCLUSIONS APPENDIXES I. SURVEY OF METHODS OF PARTICLE-SIZING . II. BENCH DESIGN . III. OPTICAL DESIGN . IV. SWITCHING . . BIBLIOGRAPHY . . . . . . . . . . iii Page 14 23 27 39 40 45 48 51 S7 Figure 10. 11. 12. 13. 14. 15. 16. LIST OF FIGURES Diagram of the main components of the apparatus . Four phases of sedimentation process and corresponding light transmission curve. . . . . . . . . Conceptual representation of functional and haptenic antigens. . . . . . . . . . . . . . . . . . Radial distance the erythrocyte wanders under Brownian bombardment in scale with the actual distance between cells for a concentration of 27 x lOBerythrocytes/ml. . . . . The time course of the Optical density through a region slightly below the center of tubes containing a constant amount of red cells and varying quantities of influenza virus suspension. . . . . . . . . . Optical density against time curves for samples with varying quantities of influenza virus suspension. Plot of light transmitted against concentration in two serial dilutions. . . . . . . . . . . . . . . . . . Alignment of Beckman cell with respect to incident beam . Graph of percent of maximum possible transmission registered by recorder against sweep speed in volts A.C. Diagram showing arrangement of cell and slit. Plot-of four curves from run A - 13 compared to a single- cell run to illustrate similarity of shape and sloPe. . Plot of run A - 67 showing the abrupt rise of the saline samples due to convection compared to the steady rise of samples mixed with serum. Plot of run A - 72 showing comparative curves of saline and serum . Photograph of original recorder chart for run A - 73. . . Diagram of manometer. Photographs of apparatus. iv Page ll 13 13 16 18 25 27 33 36 37 38 42 47 Figure Page 17. Diagram of boom and measurement of distances. . . . . . . . 50 18. Design of bracket for eight Beckman Spectrophotometer cells 50' 19. Illustration of supporting yoke and microswitches . . . . . 51 20. Safety circuit diagram. . . . . . . . . . . . . . . . . . . 52 21. Illustration of cam and friction clutch for braking circuit 53 22. Braking circuit . . . . . . . . . . . . . . . . . . . . . . 54 23. Complete circuit diagram. . . . . . . . . . . . . . . . . . 56 CHAPTER I INTRODUCTION The experimental problem of this thesis is to measure the strength of the immune reaction by simultaneously recording the transmittance of light through several tubes of red cells (erythrocytes) settling in saline (physiological1y-equivalent) or serum. The associated analytical problem is to relate the time changes in transmittance to the size- distribution of the settling particles. This thesis deals with the solution of the first problem, and outlines the theoretical basis for the second. The introduction presents a sketch of the requirements for the machine, a survey of its construc- tion, and a description of the agglutination process. The second part discusses the biochemistry of agglutination, and gives a qualitative discus- sion of settling. The third deals with the scattering, absorption, Stokes Law, and particle size-distribution. The fourth gives experi- mental results and conclusions. The appendix is reserved for a survey of previous methods of measurement, and details of the construction of the apparatus and circuitry. The measurement of the strength of the agglutination reaction could be made in a number of ways. Sedimentation is a visible accom- paniment of agglutination and the rate of sedimentation depends in some fashion on the strength of the immunological reaction. Thus sedimentation may serve as the basis of an instrumental method which 1 2 for several reasons may be preferable to a subjective method. As factors in the choice of a Specific method, we note that the binding between the agglutinated cells is very weak, so the settling suspension should not be disturbed,and a number of samples must be studied simul— taneously and as a function of time. Finally, enough room must be allowed for the sample to be placed in a water jacket or magnetic field to suit Specified experimental conditions. These specifications are effectively met by use of optical transmittance to measure sedi- mentation rate. Since devices have been described previously which measure transmittance, what is original in this work is the ability to study samples simultaneously and automatically. For a discussion of the features of other existing methods, one may refer to Appendix 1. The antigen-antibody reaction has been chosen for study for several reasons. First, the sensitivity of the reaction permits the unequivocal detection of substances in amounts of hundreths of a micro- gram. And since a future aim of this project is to assay the effect of magnetic fields on biological reactions, this high sensitivity makes it likely that no magnetic effect would fail to be detected. Second, the antigen-antibody reaction may be easily observed in'vitro with only small amounts of blood and serum, and the test sample can easily be maintained in the desired experimental conditions. Third, since this reaction is one which is not entirely understood, the in- vention ofaaquantfiativenmthod to measure the rate and extent of agglutination (to supplement or to supersede the existing visual methods) will be a useful tool in determining the nature of the re- action. 3 In the apparatus, a boom holding the light source, two condensing lenses, and a photo-cell, swings above the samples which are placed on a semicircular table. (See Figure 1) As the boom swings, the light beam,which is blocked off between samples, shines through each sample tube and stimulates a voltage from the photo-cell on the other side. As the beam reaches a particular sample tube and light begins to enter the photocell, the ensuing mechanical motion of the recorder pen ener- gizes an eddy-current brake which decreases the sweep speed. This slowing gives time for the recorder to respond fully to the signal from the photocell. The total arc swept may vary from 10 degrees to 180 degrees, and may contain a maximum of thirty samples along the path. The boom is allowed to sweep forward slowly in one direction while collecting data, and then to return quickly. If the machine is sweeping 8 samples at a typical rate, the forward sweep would take two minutes and the return one—half minute. The runs last from half an hour to twelve hours, and the sweep rate just mentioned gives a sufficient number of points to determine a good curve. The sample is a suspension of human erythrocytes in saline or serum contained in a square glass cell from a Beckman - DK 2 Spectro- photometer. A window in a brass plate at a specific height on the cell governs the position and flux of the light beam traversing the cell. At the start of the run, the erythrocytes are evenly distributed throughout the saline, and the transmittance is at its lowest value. As the erythrocytes settle, the transmittance increases, and soon a division between the clear medium and the erythrocytes appears near the top of the tube. Settling continues for the next several hours, the 4 maximum transmission occurring when all the cells have settled into a dense mass at the bottom and the upper portion of the liquid is clear. Light Source [5 Boom 8 Optical Axis Of System \ Test Tube ‘\ Samples Lenses ‘ - - \ .-' \ - ‘\ éRecorder ,. . Photocell a;- Motor For Sweep Dflve <———— S omple Tobie Fig. 1.--Diagram of the Main Components of the Apparatus. .o>uoo scammwamcmuu unwwa wowvooamouuou cam mmoooun oofiumuooawwom mo mommsm usomuu.m .wwm mi; muooFmE woman a mmaoimqa .345 H .LHSI‘I 031. .LIWSNVHI CHAPTER II THEORY OF AGGLUTINATION An antigen is a foreign substance, usually a protein of a very wide class, which has the ability to induce the formation of antibodies when it is introduced into the blood stream of an animal. Antibodies are proteins of the class of serum globulins, with molecular weights on the order of 160,000 or 900,000,1 which have the ability to join with the specific antigen and render it inactive. This specificity is attributed to the presence of specialized combining sites, small areas of the antibody molecule which have a configuration complementary to the specific antigen. These sites of chemical activity which are re- Sponsible for bringing the antigen and antibody together in combination mayextend over only one percent of the antibody molecule. The active area consists of a series of amino acids arranged in a specific sequence and stereoconfiguration, but the rest of the molecule is inert in this reaction. It is this stereoconfiguration joining a spot of complementary configuration on the antigen which is responsible for the very high degree of specificity of the immunological reaction. Certain substances, called haptegg§3have the property of uniting with an antibody once it is formed. This union takes place because the haptenes possess the complementary configuration which matches the 1Advances in Biological and Medical Physics Vol III. p. 102. (Academic Press, 1953) 'T' i HAPTENE . HAPTENE COMPLETE FUNCTIONAL PORTION OF FUNCTIONAL ANTIGEN Pig. 3.--Conceptual representation of functional and haptenic antigens. The R group represents a single determinant of antibody specificigy and is the actual group that combines with the antibody molecule. active site of the antibody. Alone, however, the haptene is unable to stimulate=the production of antibodies. But when combined with a pro- tein molecule, it can not only stimulate the production of antibodies but join with them. In such a case, the haptene governs the speci- ficity of the reaction. For example, the pneumococcus owes its patho- genic preperties to an attached carbohydrate group which alone cannot _produce antibodies. Combined with the base protein, however, the carbohydrate group elicits the formation of an antibody which neutral- izes its own pathogenic prOperties.3 The ability to add functional groups to the base protein enables testing and altering the specificity fl '— *— 2Cushing, J. and D. Campbell, Principles of Immunology. p. 37. (McGraw Hill Book Co., Inc. New York. 1957). 3Houssay, Bernado A., Human Physiolggy. p. 79. (McGraw Hill Book Cod, Inc. New York. 1953). 8 and extent of a particular immunological reaction, and serves as an important tool with which to study the mechanism. Two theories have been proposed .to explain the formation of antibodies: one, called the template theory, suggests that poly- peptide chains .old and wrap themselves around the active sites of the antigen molecule and form a shape complementary to it, and thus create the antibody specific to this antigen. The other theory, called the clonal-selection theory, asserts that the body has previous information on the structure of the particular antigen, and that it uses this in- formation to manufacture the antibody to fit the specific antigen when stimulated by the antigen. References to the formation of antibodies may be found in Advances in Biological and Medical Physics, Cushing and Campbell, Kabat and Mayer.4 Human blood can be classified into four blood types according to the presence or absence of two antigens A_and §.on the wall (stroma) of the red cell. There are four combinations of the antigens resulting in the following blood types: Type AB, with é_and g antigens; Type A, with antigen Aialone; Type B, with antigen §_alone; and Type Q_with neither antigen A_or B. Existing in the serum of the blood and re- acting specifically with the foreign antigens A'or,§.on the cell, are the antibodies. In blood typing, these antibodies are called alpha and beta agglgtinins, and they react Specifically with the A and B antigens, respectively. The type AB blood contains neither alpha nor 4Advances in Biological and Medical Physics, 9p. cit. Kabat, Elvin A., and Manfred Mayer, Experimental Immunochemistry (Charles C. Thomas Pub., Springfield, Ill. 1948). Cushing and Campbell, op. cit. 9 beta agglutinin in its serum, for if it did it would react internally to agglutinate its own cells. Type A contains only the beta agglutinin, type B contains only alpha, and type 0 contains both alpha and beta agglutinins in its serum. These facts are tabulated below for each blood type.5 Reaction with Erythrocytes Blood Antigens on Antibodies Agglu- Anti A Anti B Group Red Cells in Serum tinins Antibody Antibody 0 None 22:1 A «,9 - - 1 B A A Anti B 6 + - B B Anti A (X - + AB A,B None 0 + For a large number of erythrocytes to agglutinate in a single aggregate the antibody molecule must be polyvalent. The rate of com- bination depends on the amount of antiserum available to form bonds be- tween erythrocytes, and on the extent and frequency of contact between erythrocytes. Brownian movement and gravitational descent are the two motions experienced by the erythrocytes which would cause them to come in con- tact. We can calculate the extent to which the cell wanders in a given time owing to Brownian movement, and we can calculate the distance between cells. 5Houssay, op. cit., p. 60. 10 1) The motion due to Brownian Bombardment may be expressed by: 2 §_|_ RT where X = distance moved in time t t 3'Tf’17/L -16 R = 1.38 x 10 erg deg 2 T = 3 x 10 deg -2 = .9 x 10 dyne - sec 2 cm t = 30 min. = 1800 see. = .9 centipoises (viscosity) r = 10p x2 _ 1.38 x 10.16 x 300 x 1800 dyne x gm x deg x sec 3 x 3.14 x 9 x 10-2 x 10-4 deg x dyne xzsec x cm cm x2 = 1.38 x 1.8 x 10-5 cmZ x .9 2 5 2 x = .88 x 10' = 8.8 x 10‘6 cm Particle Moves X 2.96 x 10"3 cm = 29.6 n in 30 min. Particle Moves X 1.7 x 10-3 cm = 17 u in 10 min. 2) A cell count of 27 x 106 erythrocytes = 27,000.2 ml. (27 x 106)1/3 = 3 x 102 104 -———Ji-§ = 33p between centers of each cell. 3 x 10 We see that the effect of Brownian motion will be such as to make the particle wander in a area of radius 17u in a period of 10 6Moelwyn-Hughes, E. A., Physical Chemistpy. p. 64, equation 145. Qergamon Press, N.Y. 1950. 11 minutes. Thus after 10 min. there will be ample contact between erythrocytes for combination if contact alone insures it. Although the fraction of active sites is small, there are probably enough that a single contact will result in a union. .0. L; \ Fig. 4.--Radial distance the erythrocyte wanders under Brownian Bombardment in scale with the actual distance between cells for a concentration of.27 x 108 erythrocytes/m1. We may visualize the agglutination then in the following manner: In a sample mixed with the appropriate antiserum, certain erythrocytes become potentially reactive. Convection and Brownian motion bring them near enough to form dimers (a coupling of two erythrocytes); these descend through the solution faster than the single cells; they have a weight equal to that of two cells but a perimeter less than that of two 12 cells.7 As they fall, they will overtake and combine with other single erythrocytes and form larger aggregates. They will fall faster and an avalanche will occur if enough antiserum is present to make all cells potentially reactive. (See curves A and B Fig. 5 on the following page.) If there is only enough antiserum to supply antibodies for the union of half of the erythrocytes, then dimers mostly would be formed, and avalanching would not be important.8 (See.curve C Fig. 5 on the following page.) Fig. 6 curve B shows the increase in rate of settling due to the formation of dimers. As the dimers fall out of the path of the beam, the transmittance curve due to the settling of the residual single cells has the same slope as curve A with the virus absent. The effect of the concentration of the erythrocytes is simply to control the sensitivity of the transmission measurements. With high concentration, the opacity of the suspension makes it difficult to de- tect changes attributable to the formation of the relatively small number of dimers. A more important factor is whether there is anti- serum enough to agglutinate the erythrocytes present regardless of their concentration. Increased experimental time merely allows more collisions between erythrocytes, and thus formation of larger and more numerous aggregates, and attainment of a more advanced stage of settling. 7Kunkel, w. 1)., J. Appl. Phys. _1_9., 1056-8. (1948). 8Kabat and Mayer, o . cit., p, 117. Hirst, G. K., and E. G. Pickels, J. Immunol. 423 273 (1942). 13 in L0 0P TlCAL DENS! T Y 25 50 75 100 TlME (min.) Fig. 5.--The time course of the optical density through a region .slightly below the center of tubes containing a constant amount of red cells and varying quantities of influenza virus suspension. As the amount of virus decreases, the form of the curve changes from one with steep inflection (A and B) to a linearly falling optical density C. D is control with no virus. 30° )— virus 1- 2.5- A absent a z 0 Lu 0 2.0—- .J 3 B - IJS. E virus 0 present LG . 1 ' 50 ICC 150 200 TIME (min. 1 Fig. 6.--The lower curve illustrates that apprcgates larger than' dimers have not been formed in appreciable numbers. The break at 100 min. marks the time when the boundary of the dimers has passed out of the field scanned by the light beam. Thereafter the optical density of the tube containing the virus is parallel to the control. The dif- ference in cell density in the two tubes when the curves fall at parallel rates is a measure of the number of cells dimerized. 9Levine, Puck, and Sagik, J. Exper. Med. '28, 521 (1953). CHAPTER III THEORY OF SCATTERING AND STOKES LAW Most of this thesis is concerned with the experimental problem of designing a machine capable of differentiating between agglutinating and non-agglutinating suspensions of erythrocytes. This chapter, on the other hand, introduces a related and much more complicated problem, analytical in nature: What is the dependence of the transmittance on the size-distribution of the erythrocytes? We shall try to ougline a direction of solution by discussing first, what happens to the light beam as it penetrates the sample, and second, what are the factors affecting sedimentation. Consider an electromagnetic wave at any point in empty space. For its complete description we must know its wavelength, direction, intensity and state of polarization at each moment. Let I be the intensity, 5 wavevector, 5 position vector and t time. Then I = I( , IH , ) for horizontal polarization k t I = 1(kjr,£) for vertical polarization Since the intensities of the horizontally and vertically polarized com- ponents will be equal, and we are considering a steady state condition, I = King) When a beam of light impinges on a molecule, the energy may be absorbed in several ways: in rotational states if the molecule 14 15 possesses a dipole moment; in vibrational states, if the charged atoms could vibrate about a fixed position; and in vibrational states of the electrons. Some of the incident energy is reemitted and termed scattered radiation. If the atoms are sufficiently close as in a lattice, the reemission of the energy by the electrons takes place as a cooperative effect, and may result in reflection. The remaining energy is lost as kinetic energy of vibration in the molecule, and is termed ahsgzhed_radiation. These are the basic phenomena affecting the beam. The expression for the differential change in light intensity as the beam traverses a slab of thickness dx, containing n scatterers/ unit vol. with cross-sectional area A is d1 = I(Ksca + Kabs) nAdx + de The first term represents the energy removed from the beam; Keca and Kabs are the scattering and absorption coefficients respectively. The second term jdx represents processes which could add energy to the beamdflourescence and secondary scattering back into the beam of rays previously scattered out of the beam. Flourescence may be disregarded and if we neglect multiple scattering also then the jdx term does not appear. The integrated extinction formula for single scattering and absorption through a thickness 1 is I = IO exp-(KSC + Kabs) Anl a The coefficients KSca and K.£11 are both very complicated func— bs tions of the size and shape of the particle, wave number and the re- fractive index of the particle relative to the medium. To test the applicability of this expression, the following experiment was performed: Starting at concentrations of 5.7 x 108 .m. mam fl mCOMDSHIV fimuuom oau. afiomuuwsmoofla unws umcwmwm :Owumuuooocoo mo ”.03....“ .wwm l6 Es eo: 20.25.2328 o o c , n N _ o . / . A . _ . o / / 1 / / 1 / / .. / U / / 1o. / / m / / e / // .1. / 1 / / ow / / /. 1 u < 1 1cm H 100. CON 17 erythrocytes/ml and again at concentrations of 1.8 x 108 erythrocytes/ ml, serial dilutions of the suspension were made and the transmittance of each dilution was recorded. ,The log of the transmitted intensity as ordinate was plotted against the concentration as abscissa (See Fig. 7). At low concentrations the plot is linear in conformity with the above law representing single scattering and absorption. The contribution by multiple scattering is small except at higher concentrations where the curve deviates markedly from the straight line. Here other factors such as the opacity of the cells may affect the curve. The problem of fully describing the transmitted intensity in terms of the parameters of the problem is extremely complicated and beyond the scope of this thesis. It does seem to be possible, however, to do experiments in the range of low concentration where the exponential extinction law seems to apply. There are many excellent references which deal with various facets of this problem. A lucid text which surveys the whole field of scattering is Light Scattering by Small Particlgs10 by VanderHulst. This is highly recommended as a general introduction to the problem. Mie's original papers develop the general expressions for the absorption and scattering coefficients from Maxwell's Equations.11 Max Born and Emil Wolf in their Optics12 and Stratton in Electromagnetic 10VanderHulst, H. C., Light Scattering by Small Particles. (John Wiley and Sons, Inc. N.Y. 1957). 11Mie, Gustav, Annalen der Physik (4) 25 (1908). 2Born, Max and Emil Wolf, Principles of Optics. (Pergamon Press, N.Y. 1959). Fifi 18 Theory13 also use this approach. Multiple scattering receives full theoretical treatment by Chandrasekar in Radiative Transfer14 and by V. V. Sobolev in A Treatise on Radiative Transfgr.15 Gumprecht and Sliepcevich16 develop specific application of these theories for a light-transmission experiment where loss by scattering alone is con- sidered. Their approach is nonetheless instructive since they intro- duce Stokes law and develop an expression relating transmission to particlewsize distribution. Let us consider losses due to reflection. The Beckman Spectrophotometer Cell is made of glass with 1 cm x 1 cm inner cross-section and wall thickness of 1/32". The filament image comes to focus at a spot 1/2" in front of the cell and the light beam diverges only 4 degrees in passing through the cell. Essentially then, the rays traverse the cell normally to the interfaces. Cell Incident —* 1 \ o Beam 1 / Lf Fig. 8.--Alignmln, of Beckman cell with reSpect to incident beam. Estimating losses due to reflection shows that they are constant with respect to time and concentration and reduce the amount of light by 8%. 13Stratton, Julius, Electromggnetic Theory. (McGraw Hill Book Co., Inc. N.Y. 1941). 14Chandrasekar, S., Radiative Transfer. (Dover Pub. Inc. N.Y. 1960). 15Sobolev, V. V., A Treatise on Radiative Transfer. (D. VanNostrand, Inc. N.Y. 1959). 16Gumprecht, R. 0., and C. M. Sliepcevich, J. Chem. Phys. 21, 95-97 (1953b). 19 n = 1.0 1.5 n = 1.33 1.5 n = 1.0 Air Glass Suspension Glass Air 2 (“1 ‘ “2) _ g;.0 - 1. 5): r = 2 - .04 A (“1 + “2) (1. 0 +1. 5)2 2 r3 2 (1.5 - 1.33) z .0004 (1.5 + 1.32) rC = .0004 rD = .04 Total Losses 9’.08 = 8% The limiting speed of spherical particles falling through a liquid is described by Stokes .13— (p - po )8 t effective diameter of particle viscosity density of saline density of erythrocyte acceleration due to gravity height fallen in time t which is the distance the light beam is below the interface. where d xtm-oo _3m u n n In our application, the Reynold's Number is low; .0001 to 2.0, and Stokes law may be used in the form given above which neglects inertial forces.17 For non-spherical particles, an effective diameter is used in the equation. Kunkel has pointed out that objects fall so 17Perry, J. H., Chemical Engineering Handbook. (McGraw Hill Book Co., Inc., N.Y. 1950). 3rd Ed. 20 as to offer the greatest possible viscous resistance, that is, with the major axis of inertia parallel to the velocity for typical particles.18 The deviation of the erythrocyte from sphericity thus results in its falling slower than a sphere of the same mass. The size estimates of maximum radius by Stokes Law therefore, would be erroneously small, perhaps by 50 percent.19 For fall times of the order of hours, the effect of Brownian bombardment on the rate of fall is negligible. For a time t = 60 min, the size of a critical radius for which the extent of motion under Brownian bombardment is equal to fall under gravity, is equal to Thus Brownian bombardment will not keep the erythrocyte of diameter 7H from falling. But as we noticed earlier, Brownian motion is a signifi- cant factor in the formation of dimers. The ionic strength of the saline solution is 0.14 N, which is strong enough to eliminate any electroviscosity effects of the descent of the erythrocytes.21 This problem is discussed in detail by Booth22 and Elton and Hirschler.23 Hindered settling refers to the phenomenon in settling concen- trations where a very sharp interface is formed between the settling particles and the supernatant liquid. In such a case, the rate of fall 18Kunkel, op. cit. 19Ibid. 20Alexander, Jerome, Colloidal Chemistgy. (Chemical Cat.Co.,N.Yu 1928). 21Orr, Clyde and J. M. Dallavalle, Fine Particle Measurement: Size, Surface and Pore Volume. (MacMillan Co. N.Y. 1960). 22Booth, F., J. Chem. Phys. 22, 1956—58. 23Elton, G. A. H. and F. G. Hirschler, Brit. J. Appl. Phys. Supp. 3 360-862. 1954. 21 of a sphere is less than that given by Stokes Law. If VS is Stokes Velocity, Q is the velocity in a vertical plane, and = the fraction of the total suSpension occupied by the supporting liquid, the rate of 24 fall would vary from that given by Stokes Law according to: _ 2 -l.82(1 -e) Q—VSE 10 For a .27 x 108 cell count, the fraction by volume of cells is: .27 x 108 x 70 x (10.4)3 = .00189 cc. Therefore 6 = .9981 And Q = VS(.9981)2 10—1.82(.00189) 0r 02vS Thus there are very small deviations from Stokes Law due to hindering at .27 x 108 cell count. The largest and at this time unknown dis- crepancy is due to the departure of the shape of the erythrocyte from that of a sphere. The conclusions which may be drawn from the above are as follows. 1) A simple exponential relationship between transmittance and concentration does exist at low concentrations (below .54 x 108 erythrocytes/ml.). At higher concentrations, the problem becomes much more complicated requiring accurate expressions for the scattering and absorption coefficients for non-spherical particles. 2) Reflection losses are not difficult to calculate and constant in time. Electroviscosity, brownian movement and hindered settling affect the sedimentation process by a negligible amount below .27 x 108 erythrocytes/ml. 3) Stokes Law is applicable but corrections still must be made to account for the non-spherical shape of the erythrocyte. 4Steinour, Harold, Industrial Engineering Chemistry. 39 840-7. 1947a. 22 When the above problems are solved, it will be possible to ex- press particle-size distribution in terms of light transmission measure- ments. CHAPTER IV PREPARATION FOR RUNS Ten ml of whole blood is removed from the arm of a volunteer, and preserved in 1 ml of sodium citrate under refrigeration. Before the run, 1 ml of whole blood is placed in a saline solution and washed by centrifuging three times for 3 min. at 3000 rpm. The various con- centrations of erythrocytes are prepared by using a certain amount of packed blood. cytes, cells to saline. In a normal human adult there are 5,400,000 erythrocytes/m1 of Since 30% of the volume of whole blood is occupied by erythro- then the count is: _ 9 egythrocytes .3 - 18 x 10 m1 of packed erythrocytes 3 ml of packed erypr 9 _ 8 egythrocytes 100 m1 of Saline x 18 x 10 ‘ 5'4 x 10 m1“ TABLE 1 AMOUNT OF PACKED ERYTHROCYTES IN ML. TO BE MIXED WITH SALINE FOR A DESIRED COUNT in Desired viii.“ 9—8;. 80‘ 108) 5.4 x 10 2.7 1.35 1.07 .54 .27 4 .12 ml .06 .03 .024 .012 .006 20 .60 .30 .15 .12 .06 .03 Amount 25 .75 .375 .186 .15 .075 .037 of 30 .90 .45 .225 .18 .09 .045 packed 35 1.05 .525 .26 .21 .105 .052 cells 50 1.5 .75 .375 .30 .150 .075 (m1) 100 3.0 1.5 .75 .60 .3 .15 23 24 Since anti—A and anti-B sera will cause agglutination at room temperatures, the desired blood suspension and the serum dilutions must be prepared separately just before the start of the run: 2 ml of double the desired cell concentration is added to 2 m1 of serum of half the desired dilution. The 2 ml of blood will dilute the serum concentration and the serum will halve the cell count, to make 4 m1 of the desired preparation. After the suspensions with anti-A and anti—B have been prepared, they may be placed directly in the machine, whereas the suspensions mixed with anti-B serum must be placed in the 37° water bath for the serum to react. Two methods were used to mix the erythrocytes and serum. The tubes for one group of anti-D suspensions were inverted every 10 minutes during an hour to mix the reactants, and the tubes for the other were centrifuged for 45 seconds at a half hour and returned to the bath for the rest of the hour before being pipetted into the sample tubes. Before the suspensions are pipetted into the cells, a certain number of adjustments must be made on the machine: 1) The cells must be washed with distilled water and dried, to prevent hemolysis of the erythrocytes. 2) The slit heights should be adjusted for each sample to give a uniform amount (i 10%) of light through each. 3) The pen slide must be cleaned and oiled for quick response, and the friction clutch must be tightened enough to maintain contact during pen rise, and to break contact during pen fall. 4) The light source should be turned on at least a half hour before the start of a run to stabilize the intensity. Slight differences in flux through each cell offer no great difficulties since these 25 variations are constant during the course of a run, the resulting curves can each be normalized by a suitable factor and replotted. 5) The reversing arms on the shaft should be adjusted to reverse the sweep 2" beyond the end samples._ I. 6) The variac setting should be set to give a sweep speed slow enough. for full record response as the light traverses the sample, but fast enough to collect an adequate amount of data. C3 LIJ 33 :2 p— 100":K £52 -0 1— 2‘3: 2 96- (r is: - C3 65‘: 528 92" P2“; aw . ”<2: 51:)- 88p 1 L 1 l I I ,1 4O 50 60 70 SWEEP SPEED (V.A.C.) Fig. 9.--Plot of Percent of Maximum possible transmission registered by recorder against Sweep Speed in Volts A.C. 7) Typical Running Values are: Recorder Scale: 12.5 mv., 25 mv. Recorder Speed Chart: 0.2"/min. Variac Setting: 55 vac., 60 vac. Steady Brake Current: 1.7 amp. Pulse Brake Current: 3.0 amp. Capacitance: 2000 pf. Recorder response with clear saline in Beckman 3/4 of full scale Height Number Number Number 26 of Light Beam of Samples Run of Spaces for Samples of Spaces for Magnetic Samples 1/8" below meniscus 3/8" below meniscus 8 8 3 CHAPTER V EXPERIMENTAL RESULTS Because of the gradual development of the machine, it is con- venient to describe the results and innovations on the machine in chronological order. A run consists of preparing a blood suspension of the desired count, diluting it in serum or saline, and placing it in the machine. The on-off timers are set so the machine will stop sweeping when all particles have definitely settled and the trans- mittance is maximum. In tabulating the runs, the numbers in the columns of Saline, Anti D, Anti-A, Anti-B, denote the number of samples in the corres- ponding soluent. ‘Slip refers to the height of the rectangular window in front of the Beckman Cell. The available sizes are .03 x 3/16", .06 x 3/16", .02 x 3/16". £3131 means the distance between the top of the light beam and the meniscus of the suspension. SLIT OR 'I wmoow\ ? i_——7 ’ \___/.a———MENlSCUS LIGHT" BEAM TOP OF BEAM BRAS S PLATE L——— Fig. 10.--Diagram showing arrangement of cell and slit. -—-—D G—SAMPLE CELL a) C - lgto C - 16 Each run consists of two samples of erythrocytes with saline 27 28 and two samples with Anti-D serum, counts of 5.4 x 108 erythrocytes/m1 in a 4 mm. round test tube. Because it was difficult to position the cell so the light beam would be undeviated in passing through and the sweep was not retarded, these runs were invalid for collecting data. b) T - 1 to_T - 40 A series of T (test) runs were devised to test the machine Opera- tion but not to collect data. The effects tested and corrected werejfor example: source constancy (of the arc lamp in use at this time) elec- trical noise in the photocell circuit, transformer noise, recorder re- sponse with control Specimens in the tubes, effect of sweep speed on recorder response. c) C - 17 to C - 42 Number of Samples Count in Medium of Run (lOBe/ml ) Saline Anti-D Remarks C -17 5.4 3 Used round 4-mm. test tubes C -19 5.4 10 6 test tubes, 4 Beckman C ~20 5.4 4 4 Beckman C -21 5.4 4 4 Beckman C -22 4.6 4 4 Beckman C -23 4.6 single 4 Beckman C ~24 4.6 single 4 Beckman C -25 2.7 5 Round Tubes and Beckman C -26 2.7 4 Beckman C -27 2.7 4 Beckman C -28 2.7 single Beckman C ~29 2.2 2 2 Beckman C -30 1.2 2 2 Beckman C -31 2.2 2 2 Beckman C -32 1.3 2 2 Beckman C -33 2.7 2 2 Beckman C -34 3.2 4 Latex Suspension: No settling, C -35 3.2 4 colloidal. C -36 3.2 4 C -41 3.2 4 Brake on C —42 5.4 4 Brake on 29 This series was run with high erythrocyte count suSpensions con- tained in the Square Beckman Cells at sweep speeds of 60 vac (sweep cycle time c 2 min.). The light beam was located 1/8" below the meniscus, and was powered by a 6v. storage battery; and the eddy-current brake was not utilized until the last runs. No meaningful data were collected; the curves were not smooth, and the individual ordinates fluctuated owing to the lack of an eddy current brake. d) C — 43 to C ~ 55 For these runs the machine was improved considerably. A pen motor with the faster response time (1/2 sec. full scale) was installed; the eddy-current brake, with 3-a. pulse for 1.3 sec. and a 1.5—a. steady current, was devised to retard the sweep at the time of measure- ment; the light beam was collimated by a 0.03" x 3/16" aperture in front of the cell. Number of Samples in Medium of Count Run (108e/m1.) Saline Remarks C ~43 5.4 4 1.5 amp. steady brake current C ~44 5.4 4 1.5 amp. steady brake current C ~45 5.4 4 1.5 amp. steady brake current C ~46 5.4 4 1.5 amp. steady brake current C ~47 2.7 7 1.5 amp. steady brake current C ~49 2.7 C ~50 2.7 4 1.5 amp. steady brake current C ~51 2.7 .03" slits C ~52 2.7 4 Introduction of Pulse C -53 2.7 4 brake C ~54 2.7 4 .04" slits C ~55 2.7 4 .04" slits The results were considerably better. The machine worked well, and the improvements enabled us to obtain a number of reliable curves 30 of the settling interface. The curves were normalized and replotted on smaller linear graph paper to facilitate comparison. The extent of agglutination could not be determined from the comparison of slopes, since with counts of 5.4 x 108 erythrocytes/ml and 2.7 x 108 erythro- cytes/m1 the interfaces are composed mainly of unagglutinated single cells. Run §_;23_demonstrated the first evidence of the formation of convection currents: The transmission increased as the interface fell, then decreased as convection in the Beckman Cell lifted the erythro- cytes back into the path of the light beam. e) To eliminate convection which could be due to heat from the source, an infra-red filter and a 2"-thick water cell was used to filter out the infra-red in a series of runs with 1 or 2 samples each: A - 1 to A ~ 13. The resulting settling curves were smooth and valid for 60 to 90 minutes, before convection disturbed the curve. If the beam is 1/8" below the meniscus, the convection currents take longer to cir- culate the erythrocytes into the path of the light beam than if the beam were farther below the meniscus. f) A ~ 14 to A - 49 These runs were similar to C - 14 to C - 55 (d) in experimental set up. The purpose was to check a filling procedure standardized so all samples would settle at the same time. The curves were normalized and replotted. A t run A - 42, the source storage battery was replaced by a 6.3-v. filament filament transformer. 31 Number of Samples Count in Medium of Runs (108e /m1 ) Saline Anti-D Anti—A 81 it Level Remarks A ~14 2.7 4 .059" 1/8" Good curves A ~15 2.7 4 .059" 1/8” Good curves A ~16 2.7 4 .059" .05" Good curves A ~17 2.7 4 .059" .05" Good curves A ~18 2.7 4 .059" .05" Good curves A ~19 5.4 4 .059" .05" Good curves A ~20 stirred 19 6 .059" .05" Good curves A ~21 5.4 4 .030" .18" A ~22 5.4 4 .030" .12" A ~23 5.4 8 .040" A ~24 5.4 8 .060" .10" A ~25 5.4 .060" .10" A ~26 5.4 .060" .10" Good run A ~27 5.4 .060" .10" Bad run A ~28 5.4 .030" .10" Bad run A ~29 5.4 .030" .10" A ~30 5.4 .030" .10" A ~31 5.4 .030" .10" A ~32 5.4 .030" .10" A ~33 5.4 .030" .10" Bad pulse A ~34 5.4 2 2 .030" .10" Bad pulse A ~35 5.4 2 2 .030" .10" Bad pulse A ~36 5.4 2 2 .030" .10" Bad pulse A ~37 5.4 8 .030" .10" Bad pulse A ~38 5.4 8 .030” .18" Bad pulse A ~39 5.4 4 4 .030” .12" Bad pulse A ~40 5.4 4 4 .030" .12" Good curves A ~41 2.7 4 .030" .12" Good curves A ~42 2.7 4 .030" .12" Good curves A ~34 2.7 4 .030" .12" Good curves A ~44 5.4 4 .030" .12" Good curves A ~45 2.7 4 .030" .12" Good curves A ~46 5.4 4 .030" .12" Good curves A ~47 5.4 4 .030" .12" Good curves A ~48 5.4 4 .030" .15" Good curves A ~49 5.4 4 4 .030" .15" Good curves The performance is now quite reliable. No striking differences in the curves between the agglutinating and unagglutinating blood samples appear as yet. 3) The beam was allowed to set on 7 single—sample runs to see if the fluctuations in curves were due to machine operation. The runs were 32 1.35 x 108 erythrocytes/ml. count, level was 1/8" below meniscus, with saline and Anti-D. The curves from these stationary runs were similar in shape and slope to those where the beam was sweeping several samples of suspension made with saline and Anti-D. This similarity, plus the ability of the machine to register the same value of light intensity for a sample which had completed settling, together with the reliability of the in- dividual operations of the machine (switching, braking, recording, constancy of the light intensity) demonstrates that this machine pro- vides an accurate method of measuring the optical transmittance through any number of samples over an indefinite period. (See Fig. 11.) h) Runs A ~ 53 to A ~ 62 were made under the same experimental conditions as the (e) series, but with serial dilution of serum: 1:8, 1:16, 1:32, 1:64. Number of Samples Counts in Medium of Runs (lOSe/ml ) Saline Anti-D Anti-A Level Slit Results A ~53 1.35 1 3 8:1 .18" .03" Good run A ~54 1.35 2 2 8:1 .18" .03" A ~55 l.35,.9,.6 l 3 .18" .03" Fair run A ~56 1.35,1.07 5 .15" .03" Good run A ~57 1.35 l 6serial .15" .03" Good run A ~58 .27 1 6s .15" .06" Good run A ~59 1.07 65 .15" Good run A ~60 .54,.27 2 4 .15" Good run A ~61 .54, .27 63 .15" Fair run A ~62 .54, .27 .15" Incomplete 5101 5.4, .27 6 .15" Inc. Owing to the blocking power of the erythrocytes at these high concentrations and the convection, no difference between agglutinating and unagglutinating samples was ascertainable. de 33 . .omofim mom macaw mo zuwumdweww museungflm cu can flaoonoawcfim m on moummEoo Md 1 4 com Scum mo>uoo snow mo uoam--.H~ .wwm €55. .22.... seem um RN 3 s. m. e. .e. om me 0... mm on 3 om e. o. _ _ . _ . . n. V . .AU b 13 loo 13. 22:83 :8 295 100. 4 4 :8. 4 4 4 > . 4 4 p . a 4 p . ..-... . on. H .LtiOl-I ALISNEI 34 I.) A.;64 to A - 73 These runs were made at 0.54 x 108 to 0.27 x 108 erythrocytes/ml counts. The beam was now 3/8" below the top of the meniscus, in order to observe the change in transmittance as the dimers dropped from the center of the tube. Anti-A and Anti-B sera were used, since they would react at room temperatures and would not need to be incubated. Number of Samples Counts _in Medium of Runs (lOSe/ml ) Saline Anti-D Anti-A Level Slit Remarks $101 5.4, .27 6 .18" .06" Inc. run 5.4 .3" A ~63 5.4 1 53erial .3" Inc. run 5.4 .3" A ~64 1.07,.54 1 58 .3" Fair run 1.07,.54,.27 A ~65 .54,.27 2 4s 4s .3" Good run .54,.27 .3" A ~66 1.07,.54 2 4s 4s .3" Good run A ~67 1.07,.54 2 4s 4s .3" Good run A ~68 .54,.27 2 6s 6s .3" Good run A ~69 .54,.27 2 6s .3" Good run A ~70 .54,.27 8 .3" Good run A ~71 .54,.27 3 5s 55 .3" Good run A ~72 .54,.27 3 SS SS .3" Good run A ~73 .54,.27 2 6s 6s .3" Good run Graphs of A ~67, A ~72, A ~73 are included as figures 12, 13, 14. The curves are now generally excellent, and some difference in slope is evident between the antiserum samples and the saline samples. Convection still causes a decrease in intensity of the suspensions after the initial rise in intensity. The agglutinating samples settle at a steadier rate, and their curves do not show the initial sharp rise which is characteristic of the saline. These differences, however, have not been observed frequently enough that they can be used to differentiate between samples. These results show, however, that the machine is 35 capable of measuring the transmittance through a sample,a1though it is premature to use it in differentiating between agglutinating and non- agglutinating samples. 36 .e:uom cows most mw~QEom mo omwu mvmoum ago on moumoeoo moduoo>coo On one mofimsmm meadow may we moan umouoo ego mowsosm so u < cam mo uon11.- .wwm manor 0. m m h m n o m N _ o . _ a _ is _ . _ . . O .. ~ _ . .. ..\.- -8 ..\\ \ \ . : .\\. 10w H \. ... . .. cs ._ n _ . Q _. . 1. .\/ lerlQl/ __ 10h W x \ , .. w. \ x \ /.. . w . \.\x\ l. u \ \ \ \ \ u. l. \‘IIIII \\ \\ 1100— 3 e\$\ II .s \\ N . nu “UH“1\ \\V&H \\\. a . \ \ _/\ \\ / ~ \ \\\III \\ \ \\\\\\\ \X‘ I!".\\ o - \ \i? x 2 |\\o 111\ \\\\\s \WN II) \ mafiamm .s\m.\\.\mm\\ 11\\ . 100. 37 m b w m .asuom mom ocwfimm uo mo>u=o o>wumummsoo wow305m Nu . < com mo uofim11.mH .wwm manor w n N . J - u mean eaaom--aeaaam 1H ..e.\ \s \ \.\\\ N sx am On ab 00. 0N. on. "03111WSNva1 1H9V1 moan mama wmwm I) SM (0,000 A m, fines 1:21 “84 (12.9 [256 l fleet; E (5’6 a; ‘1 9 1.) 1.4 ~73 2.00 D s Iii/2— % ill-ll Twin-ii big. . ill-I Ill-III he'll! . 1.1.1.111 glee-III . 1..» guilt: «Id-I all! in. II .II -.I .i 1'1 1111...!“ . kill . 111 11.1181 1|? 11...“? I 5% 111i.111.11l[11|1~.|l.1|.1 111111111 ISO IOO A ~ 73. l4.~-Photograph of original recorder chart for run Fig. CHAPTER VI CONCLUSIONS 1) The apparatus which this thesis describes is able to accurately and simultaneously measure the transmittance of light through a number of samples and permit direct comparisons of trans- mittance of samples under differing experimental conditions. 2) There seems to be some difference in the curves of samples of erythrocytes mixed with saline and erythrocytes mixed with serum, but many more data must be collected to use the machine as the basis of a precise method of differentiating between samples and estimating their degree of agglutination. 3) Settling is a more complex phenomenon than was originally thought. The analytical problem of expressing the particle-size dis- tribution in terms of the light—transmittance measurements will re- quire knowledge of scattering and absorption, and the effect of the non-sphericity of the erythrocytes on Stokes Law. 39 APPENDIX 1 SURVEY OF METHODS OF MEASURING SIZE-DISTRIBUTION For solving the analytical problem of this thesis, that is, measuring the particle-size distribution of the erythrocytes, the ex- perimental method chosen should have certain features: ability to handle multiple samples; enough room to place the sample in controlled environment, e.g., water bath, magnetic field. The suspension should not be disturbed and the amount of sample required should be small. Further, the tube holding the sample should be large enough such that wall effects are negligible?5 and the concentration of the particles in the suspension should be low so that the tendency to hindered settling is reduced. For the reader to get perspective on the problem, this section describes critically some of the methods of measuring particle size distribution. There are two basic methods of measurement: incremental, where the changes in the concentration of particles in a certain portion of suspension are measured i.e., pipette, diver, hydrometer, photo~ extinction, and light scattering; and cumulative methods,which measure the overall changes in concentration over the whole testing period: 25Donoghue, J. K., Brit. J. Appl. Phys. 2, 333-6 (1956). 40 41 e.g. manometer. a) The pipette method consists in weighing a small volume of the sample from a specific height in the suspension at a Specific time. If C(O) represents the concentration at the start of settling, and C(t) at the time of sampling, from a plot of C(t)/C(O) against a particle~ size distribution curve could be drawn.26 Suitable Particle-Size Range 0—45u Initial Dust Concentration 1% by weight Accuracy of Concentration Determination : 0.5% Remarks: Simple, though much weighing is involved if many points on the size-concentration curve are required. It is the most accurate method tested.27 b) In the hydrometer method, the density (the volume doncen~ tration) of the suspension is measured at a specific depth. Particle Size Range 0-25u (may be extended to 35) Initial Dust Concentration .01 suspension 1.6% by wt. Accuracy of Determination 0-25u i_1.5% 25-35u i 2.5% Remarks: A very simple method. Hydrometer bulb affects the density reading, eSpecially where comparatively large particles are present. The upper size to which the method is applicable is limited by this affect. c) The diver method consists of placing a number of small glass divers of known density in the sample. They settle at the levels in the suspension whose densities are equal to that of the divers them~ selves. The divers are located electronically or visually, and thus give the density and rate of fall of a series of levels. 26 Orr, Dallavalle, o . Cltq p. 52. 27Jarrett, B. A., and H. Heywood, Brit. J. Appl. Phys. Supp. 3) 21 (1954). 42 Particle Size Range 0-30u Initial Dust Concentration .01 suSpension Accuracy of Determination i;l% Remarks: 'Very simple. 0n larger particle sizes, rapid readings must be made, before deposition of dust on the diver affects the accuracy. Use of a large diver facilitiate readings for larger particle sizes. d) In the manometer method, the difference in density at two points in a suspension is measured by two indicator tubes immersed at different levels in the settling suspension. /:::‘\ i I I: C ' i I / r TELESCOPE v i "1 SUSPERSION TO VIEW (humus... ‘ ‘gl / DIFFERENCES ”unununJ 1 IN LEVELS : Fig. 15.-~Diagram of Manometer. Suitable Size Range Tested over range 12-53u, but unsatisfactory Initial Dust Concentration .01 suspension Accuracy of Determination .i 15% Remarks: Equipment is difficult to use, and very inaccurate; unsuitable to analysis. ~It is of interest to include the following method which is net 43 based on a sedimentation process but has proved to be very successful in measuring particle size-distribution. e) Electrical Resistance method or Coulter Counter determines particle size by measuring the resistance of particles as .5 ml. of the suspension flows between two electrodes. The resistance measured is proportional to the volume of the erythrocyte. Suitable Size Range 2-15u Initial Concentration .01 Accuracy of Determination i 2% Remarks: This is an extremely easy and fast method. All the above methods have a common shortcoming: the instruments are in the suspension, and distort the property which they are trying to measure. f) Photoextinction, an incremental technique, avoids this problem. In this method, the optical transmission of a number of samples is measured simultaneously at any height and as a function of time. This transmittance may then be related to particle size. Suitable Size Range 0-25u Initial Concentration .01 by volume Accuracy of Determination 0~25u i3% 0-53u‘i6% Remarks: Equipment is very simple to operate. It is the only method which can be used if only a very small sample is available. The method is suitable for comparative tests, such as are required for industrial control, but the theory is complex when absolute measurements are required. Coarse particles have relatively Small surfaces, and are difficult to detect; slight errors in reading the photocell output can cause large divergencies in the calculated size-particle distribution curves in this region. Excellent references on the present methods of measurements are Orr and DallaValle,28 who discuss the practice and theory of a variety 28Orr, Dallavalle, op. cit., p. 38-133. 44 of methods in detail; Donaghue,29 who discusses primarily the cumulative methods; The Physics of Particle Size Analysis Symposium?0 where a variety of industrial methods and their theory are discussed in detail. 29Donoghue, o . cit. p. 333. 30"The Physics of Particle Size Analysis Symposium." Brit. J. Appl. Phys. Supp. 3, 1954. APPENDIX 2 BENCH DESIGN The boom is fastened to the top of a steel shaft mounted ver- tically in ball bearings in a yoke of 1—1/2" thick magnesium stock -standing 24-1/2" high. An 8" drive gear is mounted near the bottom end of the shaft and is driven through a worm gear by a 1/80-th hp. series- wound Bodine Motor, Frame type NSE- 11R, 4.0 inch lbs. torque and 324:1 downgearing ratio. The sample bench is in the Shape of a semicircular annulus: 6" wide with a center-line radius of 22-1/2". One quadrant of the annulus stands 17-1/8" high and the other quadrant stands 12~1/8" high. The light from the boom hits 1-1/2" above the upper level and 6~l/2" above the lower. This split level is necessary so that the control specimens and the test specimens (resting in magnets) will be at a common height for the sweep of the light beam. (See Fig. l.) The top surface of the bench is made of 1/4" aluminum plate bolted to four wooden platforms 11-7/8" high, each made of four 2" x 4" boards which are further stabilized by 30-lb. lead bricks resting on the cross supports. The annular bench is centered with respect to the center yoke by two l-1/2" x l-l/2" 1/4" thick aluminum L-angles bolted to the bench and yoke. The bench and the yoke rest on a leveled 1/4" masonite Slab, 1/2" ~ thick blackboard slate, and a table built from 3/4" plywood with legs and cross-braces of 4" x 4" beams. 45 46 To maintain a temperature of 370 for the anti-D studies, a water bath has been built to circulate water through the cells holding the sample tubes. The pump, a l/4-hp. Westinghouse Motor Type FZ, circu- lates the water through a Sargent Thermal bath whose temperature is regulated by a resistance sensor made by the Yellow Springs Instrument Co. Although the equipment has been built and tested, it has not been yet possible to use it during a run. 47 Fig. 16.~-Photographs of apparatus. APPENDIX 3 OPTICAL DESIGN The optical system is the heart of the apparatus. Suspended 6~l/2" below the free end of the boom is a 32~watt GE 1184 single- filament incandescent lamp. The image projected is that of two spots of light one 1/8" above the other. The filament is 6" from the center of the first 3" condensing lens (f = 3.64 cm.) whose aparture is stopped to l-1/4" diameter to reduce Spherical aberration. The image comes to a focus 9-1/4" beyond the center of the first lens at a spot 1/2" in front of the center line of the bench, at the point where the samples are placed. After passing through a sample cell, the light hits another 3" lens (f = 3.64") located 8" beyond the center line. This final lens serves to focus the light on a 1.44" x 0.64" selenium photocell from International Rectifier. Model B5pl. The leads from the photocell go directly to the input of the Sargent Model SR Recorder, the negative lead grounded. The Sargent Recorder is a self-balancing potentiometer with a full-scale balancing Speed of 1/2 sec. ranges from 5 mv. to 125 mv., and chart speeds from 5"/min to 0.2"/min. The sample tubes are 1/2" x 1/2" x 1—3/4" square Beckman- DK2 Spectrophotometer Cells mounted on a 1/2"~ thick brass plate. This plate holds eight cells, and rests on three rubber phonograph shock mounts that eliminate some of the vibration from the motor. 48 49 Small windows (cut from brass sheet) of dimensions .03" x 3/16", .06 x 3/16", and .02 x 3/16", may be fastened in place at any height in front of the samples to control the amount of incident light. The 32~watt source is powered from the line through a Sola Isolation Transformer and a 6.3-volt. filament transformer. 50 .moocmumwm mo acoEOLSmmoE mom Soon «0 Emuwmfinun.w_ .wwm teem 9:5 \ :oooaozc zocom outsom to; mm s\ _ _ . . 235.com 50' -\ « TOP VIEW -\ I Inch l——-| Beckman Cell Brass Window SIDE VIEW ‘5.--" Beckman Cell . _—___— - - Brass Bracket Direction of 3"“? Light Beam "Brass Wlndow C3 Collimatlng,/w @ i FRONT VIEW Fig. 18.-~Design of bracket for eight Beckman cells. APPENDIX 4 SWITCHING TO reverse the direction of sweep of the boom, two 4" brass rods are mounted on the main shaft just above the drive gear. They stick radially away from the shaft, and the angle between them is adjustaHles When the boom reaches one end of its sweep, one arm trips a microswitch, ISMl Mbdel L4, which changes the direction of the motor drive for the return. These microswitches are mounted on the magnesium yoke, one to the right and one to the left of the shaft. Fig. 19.—~Illustration of supporting yoke and microswitches. Magnesium —-———t> <: Shaft Yoke l Reversing . Arm 8, , Rezersmga . rm Smtch Switch . J: / / \ksomy “m 81 Switch Safety Arm n I 81 Switch 51 52 If these two reversing microswitches fail to reverse the motor direCtion, limit switches mounted just below them are tripped by other arms. When failure OCcurs at the end of a sweep, the safety micro- switch will be tripped after the.boom has been driven an additional 5 degrees in the same direction. This action will break the drive circuit for the motor and prevent the boom from being driven into the supporting post. Before operation can be resumed, however, the relay in the safety microswitch circuit must be reset by hand to complete the drive circuit. To series wound motor .1 l l l I l I l I I l I .J Reset by hand ______ _Z_.___ N.C. m.s. o o—J 120 VAC Fig. 9.0.~~Safety circuit diagram. 53 Another set of switches actuates the eddy-current brake to reduce the sweep speed as the light hits a sample. The brake is a 0.150"~thick aluminum disc of diameter 4-7/8" mounted on the motor shaft and rotating between the poles of a small electromagnet. When the electromagnet is energized, the eddy currents induced in the disc set up fields to oppose the original field; this repulsion causes the disc to slow down. The electromagnet is energized by a switch mounted on the recorder frame. Micro [—7 Friction Cl ctch Switch _% C am N.C. . __J. Fig. 21.-~I11ustration of cam and friction clutch for breaking circuit. 54 As the pen responds to the voltage rise from the photocell, this switch energizes the magnet which remains Closed until the pen has reached a maximum value.‘ This action allows the brake to operate during the rise of the pen. A friction clutch keeps the contacts of the switch together while the pen rises to a maximum and breaks the contact when the pen- starts to return to zero. The steady current through the electromagnet is 1.7 a. at 9 v., from a Heathkit Battery Eliminator. For effective braking at sweep Speeds of 60 VAC., 1.7a was found to be insufficient, and a higher current was needed at the start of the braking. Therefore, a 3 a. pulse for .8 sec. in now produced the following fashion: A 2000-pf.capacitor with a 6 v. relay across it is charged to 15 v; this charge holds the relay shut, shorting out a 5~ohm resistor in the electromagnet brake circuit. When the recorded pen starts to reSpond the brake current is NC. 9 ESV ELECTRO MAGNET “Fig. 22.-~Braking circuit. 55 3a. and the capacitor begins to discharge with a time constant of 1 sec. When the voltage across the capacitor drops to less than 6 v., the relay opens and the 5~ohm resistance is put into the braking circuit to reduce the current from 3 a to 1.7a. The Bodine Motor is series-wound, with external controls arranged to provide 120 v. for one direction of rotation, and variable voltage in the other. .amuwmfiw uwooufio ouoamaoouu.m~ .wwm mw10k_3w emu—S us...— o<> 0N. >hwu ON. 08.m¢u>u¢ 56 _ _ 52:84: _ 5 2:28.: _ _ _ — '1 I I | J ——:—q+——d— “I :Q 3,15; 5 on. t. a” a 5.20.»— .0... >o 5&2» on .3 .0... 7:350 2:255 BIBLIOGRAPHY Advances in Biological and Medical Physics, Vol. III. New York: Academic Press, 1953. , A pertinent discussion of the reactions and formation of antigens and antibodies. Alexander, Jerome, Colloid Chemistgy, Vol. I. New York: The Chemical Catalogue Co., 1928f“ Booth, F., Sedimentation Potential and Velocity of Solid Spherical Particles. J. Chem. Phys. 22, (1958). Theoretical discussion of Modification of Stokes Law due to Double-layer Effect on Zeta Potential: not of great use for this thesis. Born, Max, and Emil Wolf, Principles of Optics. New York: Pergamon Press, 1959. A rigorous discussion of Mie Theory. Chandrasekar, S., Radiative Transfer. New York: Dover Publishers, Inc., 1960. A rigorous theoretical treatment of multiple scattering. Cushing, J., and Donald Campbell, Principles of Immunology. New York: McGraw-Hill Book Co., Inc., 1957. Donoghue, J. K., The Accuracy of Particle Size Determination of Cumulative Sedimentation Methods. Brit. J. App. Phys. 1, 333-6 (1956). A good discussion of available methods of sizing. Elton, G. A. H., and F. G. Hirschler, Electroviscosity in Dilute Hyper- disperse Suspensions. Brit. J. Appl. Phys. Supp. 3, 360-2 (1954). A good discussion of effects of electroviscosity on sedi- mentation. Gucker, F. T., Jr., A Photoelectric Instrument for Counting and Sizing Aerosol Particles. Brit. J. Appl. Phys. Supp. 3, 8138—43 (1954). , An Improved Photoelectric Counter for Colloidal Particles Suitable for Size Distribution Studies. J. Colloid Sci. 5, 541-60 (1949). 57 58 Gumprecht, R. 0., and C. M. Sliepcevich, Measurements of Particle Sizes in Polydispersed Systems by Means of Light Transmission Measure- ments Combined with Differential Settling. J. Phys. Chem. 519 95-7 (1953). A clear and pertinent discussion relating transmitted light intensity to particle-size distribution by use of Mie Theory. , Scattering of Light by Large Spherical Particles. J. Phys. Chem. 51, 90-95 (1953). Development and tables of Kt’ Ka and R coefficients for Mie theory. Hawksley, P. G. W., The Design and Construction of a Photoelectric Scanning Machine for Sizing Microscopic Particles. Brit. J. Appl. Phys. Supp. 3, 3125-32 (1954). , Theory of Particle Sizing and Counting by Track Scanning. Brit. J. Appl. Phys. Supp. 3, 3125-32 (1954). Heiss, J. F., and J. Coull, Jr., The Effect of Orientation and Shape on the Settling Velocity of Nonisometric Particles in a Viscous Medium. Chem. Eng. Progr. ‘48, 133-40 (1952). Hirst, G. K., and Pickels, E. C., A Method for the Titration of In- fluenza Antibodies with a Photodensitometer. J. Immunol. 32) 273 (1942). A very useful article discussing the nature of agglutina- tion and the formation of aggregates and the corresponding transmittance curves. Houssay, Barnado A., Human Physiology. New York: McGraw-Hill Book Co., Inc., 1953i This contains several very useful chapters on detailed descriptions of erythrocytes and immunity. Jarrett, B. A., and H. Heywood, The Physics of Particle Analysis Symposium. Brit. J. Appl. Phys. Supp. 3, 21 (1954). A detailed survey of many industrial methods of sizing, and studies connected with the field. Kabat, Elvin A., and Manfred Mayer, Experimental Immunochemistgy. Springfield, 111.: Charles C. Thomas, 1948. Detailed discussion of all phases of immunochemistry. Kermack, W. 0., A. G. McKendrick, and Eric Ponder. Proc. Roy. Soc. Edinburgh 42, 170-97 (1928). Involved mathematical discussion of fall of variously shaped particles, cataphoresis, and Stokes' Law. Not directly applicable. 59 Kunkel, W. D., Magnitude and Character of Errors Produced by Shape Factors in Stokes' Law Estimates of Particle Radius. J. Appl. Phys. 12, 1056-8 (1948). A good discussion of the effect of shape factors on rate of fall based on the use of metallic plates descending through oil. Levine, S., T. T. Puck, and B. P. Sagik, An Absolute Method for Assay of Virus Hemagglutinins. J. Exper. Med. ‘28, 521 (1953). A useful article dealing with light-transmission techniques to determine particle-size distribution. Mie, Gustav, Beitrage zur Optik Truber Medien, Speziell Kolloidaler Metallosungen. Annolen der Physik (4)‘2§, 8 (1908). The original paper on scattering theory. Moelwyn-Hughes, E. A., Physical Chemistpy. New York: Pergamon Press, 1957. Contains a thorough development of the theory of Brownian Movement. Orr, Clyde, and J) M. Dallavalle, Fine Particle Measurement: Size, Surface and Pore Volume. New York: MacMillan, 1960. An excellent general reference for most methods and theories of particle sizing. Perry, I. H., Chemical Epgineering Handbook. New York: McGraw-Hill Co., 3rd Ed., 1950. Phillips, J. W., Some Fundamental Aspects of Particle Counting and Sizing by Line Scans. Brit. J. Appl. Phys. Supp, 3, 8133 (1954). Scanning by a microscope over a slide of particles. Richardson, E. G., Turbidity Measurements by Optical Means. Proc. Phys. Soc. 55, 578 (1943). SuperfiEIal discussion of a variety of current methods of particle-sizing. Robins, W. H. M., The Significance and Application of Shape Factors in Particle Size Analysis. Brit. J. Appl. Phys. Supp. 3, s82 (1954). Discussion of the relation between projected area and Stokes' Law diameter. Rose, H. E., Calculation and Particles-Size Distribution from Sedimen- tation Observations. Nature 179, 774-5 (1957). Use of the slope of the transmittance curve to determine size distributions. 0f some use. Sobolev, V. V., A Treatise on Radiative Transfer. New York: D. VanNostrand, Inc., 1963. 6O Steinour, H. H., Rate of Sedimentation: Suspensions of Uniform-size Angular Particles. Ind. Eng. Chem, 3p, 840-7 (1944). , Rate of Sedimentation: Nonflocculated Suspensions of Uniform Spheres. Ind. Eng, Chem. 39, 618-624 (1944). , Flocculated Suspensions. Ind. Eng. Chem. 39, 901-7 (1944). Good treatment of sedimentation, hindered settling, and electroviscosity. Stratton, J. A., Electromagnetic Theopy. New York: McGraw-Hill Book Co., 1941. Accessible treatment of Mie Theory. VanderHulst, H. C., Light Scattering by Small Spherical Particles. New York: John Wiley and Sons, Inc., 1957. An excellent discussion of this field. Wolff, H. S., An Apparatus for Counting Small Particles in Random Dis- tribution, with Special Reference to Red Blood Corpuscles. Nature 165. Short article on the use of microscope scanning technique. lllllHillIllllllIllllllllllllllllllllllllllllllllllllllllllll 016836276