Effects of zero van der Waals and zero electrostatic forces on droplet sedimentation

Effects of Zero van der Waals and Zero Electrostatic Forces on Droplet Sedimentation S. N. OMENYI AND R. S. SNYDER ES73, Space Sciences Laboratory, George C. Marshall Space Flight Center, Huntsville, Alabama 35812

C. J. VAN OSS Department of Microbiology, State University of New York at Buffalo, Buffalo, New York 14214 AND

D. R. ABSOLOM AND A. W. NEUMANN Department of Mechanical Engineering, University of Toronto, Toronto, M5S-IA4 Canada Received August 7, 1980; accepted October 29, 1980 The stability of concentrated suspensions of glutaraldehyde-fixed human erythrocytes layered on a I)20 cushion was studied by taking as a criterion the maximum cell concentration that could be sustained without giving rise to droplet sedimentation. Greatest stability of the cell suspensions prevailed under conditions of zero van der Waals attraction and high negative cellular surface potential. The van der Waals attraction between the cells could be reduced to zero by lowering the surface tension of the medium by the admixture of 12% (v/v) dimethyl sulfoxide (DMSO), corresponding to a surface tension of the liquid of ~65 ergs/cm z. This conforms closely to the surface tension of ~64.5 ergs/cm 2 found for the fixed erythrocytes by means of a freezing front technique. The electrostatic repulsion between the cells could be reduced to zero by the admixture of 5 × 10-8 M lanthanum nitrate. In the region of zero electric charge, maximum stability, although occurring at significantly lower cell concentrations, also was achieved at zero van der Waals attraction. Mechanisms other than electrostatic repulsion and van der Waals attraction, such as density differences, mass diffusion, etc., clearly also play a role in droplet sedimentation. I. INTRODUCTION

The fractionation of a mixture of biological particles or cells, e.g., in centrifugation, zone electrophoresis, or isoelectric focusing, frequently involves the layering of the particulate mixture on a solution of nonconducting gradient-forming molecules, e.g., sucrose or Ficoll, in an electrolyte. The particle suspension forms a zone of finite thickness, with a sharp interface between the sample and the liquid cushion. Under a field applied perpendicular to the layer, e.g., gravitational or electrical, different particle species within the mixture migrate to differ-

ent levels, thus allowing their separation. However, at particle concentrations above a given minimum, the particles in the starting zone, and/or the particles in different already separated sample bands, congregate together and separate out of the interface in clusters or droplets, which sediment toward the adjacent bands or into the liquid cushion. This leads to interface distortion and excessive band mixing, to the detriment of resolution. The above phenomenon is generally referred to a s " streaming" or "droplet sedimentation" (1-6). The formation of droplets of a more concentrated particle suspension at the sample 402

0021-9797/81/060402-08502.00/0 Copyright © 1981 by Academic Press, Inc. All fights of reproduction in any form reserved.

Journal of Colloid and Interface Science, Vol. 81, No. 2, June 1981

DROPLET SEDIMENTATION zone/liquid cushion interface is attributable to certain factors. The initial concentration of particles in the sample layer is a critical factor in initiating droplet formation (2, 4-6). If the particle concentration is sufficiently high, the average distance between adjacent particles is small and the frequency of collision among particles will be high. If there is adhesion or fusion of particles upon collision, a buildup of aggregates of particles enhances droplet formation. If the density of the particles in the sample zone exceeds that of the supporting liquid, the sample zone may become gravitationally unstable. A consequence of this instability is the sedimentation of droplets at the sample zone/liquid cushion interface. Ultimately, the interface becomes highly distorted and band mixing will occur. Droplet sedimentation also depends on the relative difference between the diffusivities of the particles in the sample zone and the solute molecules in the liquid cushion. If the solute molecules of the liquid cushion diffuse into the sample zone, a local increase in the density of the sample zone close to the interface results. Convection will then set in and may lead to the formation of droplets of particles, which ultimately sediment. However, a slow and uniform diffusion of the particles into the liquid cushion does not create serious problems provided that the sample zone/ liquid cushion interface remains sharp, i.e., no droplets of particles are formed. Under this condition, the sample zone may broaden somewhat without causing excessive band mixing (3). Apart from achieving optimal separation, in most particle fractionation experiments one aims to handle maximum quantities of sample. We intend to show in this paper that it is possible to determine the maximum particle concentration that can remain stable on a given liquid cushion. We also intend to show that it is possible to increase this particle concentration further by a modification of some of the operating con-

403

ditions. An important factor that has to be considered is the effect of particle-particle interactions that cannot be avoided, especially when the particles are concentrated. Particle-particle interactions can be described in terms of the van der Waals, electrostatic, and hydrodynamic interaction forces. The van der Waals force between particles is always present, and for similar particles in a liquid medium this force is always attractive. It tends to bring close particles together to form aggregates, and therefore enhances the tendency for droplet formation and subsequent sedimentation. A reduction of this force to zero, however, will reduce droplet formation and thus sedimentation. With charged particles of the same sign of charge electrostatic forces play a role in keeping the particles dispersed, since these forces are repulsive. Therefore, the larger the electrostatic repulsive forces, the lower the probability of droplet formation and sedimentation. Hydrodynamic forces may arise due to particle or fluid motion. In such a case, the viscosity of the liquid may become an important parameter, influencing the stability of sample zones. If we assume that only the attractive van der Waals and the repulsive electrostatic forces are required to determine whether aggregates of particles are formed within the sample zone, then the total potential energy for the system is the sum of the attractive and repulsive energies. If an additive to the liquid medium reduces the van der Waals forces sufficiently, so that electrostatic forces predominate, the particles will remain well dispersed, and formation of aggregates of particles and hence droplet sedimentation will be minimized. If, on the other hand, an additive is used to reduce the repulsive electrostatic forces by charge neutralization, allowing the particles to approach each other to a distance that is sufficiently small for the attractive van der Waals forces to predominate, particle aggregates Journal of Colloid and Interface Science, Vol. 81, No. 2, June 1981

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O M E N Y I ET AL.

• ~ -,-.. ~L~~ ,,..,., ~ ,

I.

(e)

(b)

(c)

t=O

t=t 1

t>t 1

Fie. 1. Sequence in droplet formation and sedimentation. S is the sample suspension and L is the test liquid.

may be formed. In such a case droplet sedimentation will be enhanced. We intend to illustrate the effects of van der Waals and electrostatic forces on droplet sedimentation, with glutaraldehydefixed human erythrocytes suspended in unbuffered 0.15 M NaC1 aqueous solution. The liquid cushion on which the above particulate suspension will be layered is D20 made to ionic strength 0.15 with NaC1. Dimethyl sulfoxide (DMSO) will be used as an additive to reduce the van der Waals forces. Charge reversal will be accomplished by the addition of lanthanum nitrate. Initially, the critical concentration No (suspension concentration above which suspension layer instability occurs) of particles for droplet sedimentation will be determined experimentally in the absence of these additives. The experiment will finally be repeated in the presence of known amounts of these additives, and their effects on No will indicate whether droplet sedimentation is enhanced or reduced. ~II. D E T E R M I N A T I O N O F CRITICAL C E L L C O N C E N T R A T I O N FOR D R O P L E T SEDIMENTATION

The experimental setup used (7) consists of a rectangular Perspex chamber, 3 x 25 x 120 mm which, is two-thirds filled with the test liquid D20. Constant temperature (26°C) is maintained in the tank by circulating thermostat water through an external Journal of Colloid and Interface Science, Vol. 81, No. 2, June 1981

jacket. The sample (suspension ofglutaraldehyde-fixed human erythrocytes (8)) is brought to the same temperature as the test liquid in the chamber. After 30 min within which temperature equilibrium is assumed to be attained, about 0.025 to 0.18 ml of the sample is slowly layered on the test liquid with a pipet, the tip of which is placed at the inner side of the Perspex chamber, about 3 mm above the meniscus of the test liquid. After the sample has spread on the surface of the test liquid, visual observation is done through a microscope at a magnification of 40x. A lamp placed behind the tank provides illumination for the microscopic observation. Timing commences immediately after the sample is layered, and the time at which interface distortion starts is recorded. This incipient droplet formation time is denoted by tl, (see Fig. 1). If after a reasonable length of time, i.e., 200 to 240 sec, no droplets of particles are formed, the experiment is discontinued. To repeat the experiment, the used test liquid is siphoned out of the chamber, the chamber dried and refilled with the test liquid. Two or three experiments are performed for each given particle concentration, and the droplet formation time determined. The droplet formation times were found to vary by not more than ___8%. From these experiments a series of values of droplet formation times and the corresponding particle concentra-

DROPLET SEDIMENTATION 3

!

405

III. DETERMINATIONOF THE SURFACE TENSION OF GLUTARALDEHYDEFIXED HUMAN ERYTHROCYTES

The freezing front technique provides a general means of measuring the surface tensions of small particles; it has been ~ lo 7 I I I I used to obtain the surface tensions of 30 60 90 120 polymer (9) and coal particles (10), as well CLUSTER FORMATION TIME. 11 (SECONDS) as of biological cells (10). Briefly, the FIG. 2. Droplet formation times of fixed human particles are placed in the liquid phase of erythrocytes layered on D~O cushion, as a funca matrix material which is then solidified tion of erythrocyteconcentration. in a controlled fashion. The interactions between the particles and the advancing tions were obtained, see Fig. 2. The lower solid/melt interface are observed through a limit of the curve, i.e., where no droplets microscope with the aim of determining the of particles have been observed, was found critical velocity of engulfment, i.e., the to correspond to a particle concentration limiting velocity at which the particles are of 2.2 x 108 cells/ml. Since above this no longer pushed by the solidification front concentration under the prescribed condi- but, because of viscous drag, become entions, droplets of particles may form, while gulfed in the solid phase. A dimensional below it, no droplets are formed within a analysis is used to relate that critical reasonable length of time, it is designated velocity to the Helmholtz free energy of the critical particle concentration for droplet adhesion for the particle at the freezing formation. front (9, 11). The equation of state for From Fig. 2, it is clear that droplet forma- interfacial tension (12) then provides the tion and sedimentation strongly depend on means for calculating the particle surface particle concentration. The more concen- tension. This method has been applied to trated the particle suspension, the sooner measure the surface tension of glutaraldedroplet formation occurs. For very dilute hyde-fixed human erythrocytes in the particle suspensions the sample zone re- matrix material thymol. A value of 61.9 mains stable for long periods of time. From ergs/cm 2 was obtained at 51.5°C, the matrix Fig. 2 it is also possible to determine the melting point. In view of past experience maximum particle concentration that can be with many polymer particles, a surface supported on a given liquid. In this manner tension temperature dependence of -0.1 the maximum sample concentration can be erg/cm2/°C can be assumed. At 26°C the determined, for use in optimized particle fixed erythrocytes thus have a surface fractionation experiments. tension of approximately 64.5 ergs/cm 2. By determining the settling velocity of sedimenting droplets of various sizes, the IV. EFFECTS OF ZERO density of the droplets could be derived. VAN DER WAALSFORCES From these droplet densities it was established that the cell concentration inside the The effective van der Waals energy bedroplets was from 8.9 times (for the largest tween any two similar spherical particles 1 droplets) to 10.5 times (in the case of the embedded in a liquid 3, is given by (13) smallest droplets) higher than in the bulk of Alala the cell suspension (Omenyi et al., in AFlal - , [1] preparation). 12do z

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OMENYI ET AL.

where A,31 is the effective Hamaker coefficient, a is the particle radius, and do is the equilibrium separation distance between the particles. Equation [1] is valid for a >> do. Ala~ can be calculated from the individual H a m a k e r coefficients A,~ and A33 from the expression

A13,

109

o ,

~

( A l l 1/2

--

A331/2) 2.

[2]

,

I 20

,

I 30

% (v/,) DM$O

Thus the van der Waals interaction energy AF13~ is zero when A ~ equals A33. Aii can be calculated from the expression for two flat similar surfaces given by: A~i = -12~-d02(-2yiv),

I 10

i = l, 3,

[3]

where ~/~vis the surface tension of material i with respect to vacuum, v (14). From Eq. [3], we can see that A~ is proportional to Yiv and that condition A1, = A33 occurs when Ylv = Y3v, if we may, for the moment assume that d% ~ d% (14, 15). We can then render the van der Waals attraction zero by reducing the surface tensions of the liquids to the same value as that of the erythrocytes. Referring back to Eq. [2], we can see that since A13, will always be positive or zero, (AI~ 1/~ -A331/2) 2 will reach a minimum (equal to zero) as A33 is reduced while A ~ is kept constant. This minimum occurs when A,1 =A33, i.e., when T~v = Y3v. If A33 is reduced further, (A~I 1/2 A33~/2)2 again increases. Small amounts of DMSO were added to both the suspending physiological saline and the D20 and for each amount of DMSO added, the critical particle concentration for droplet formation was determined experimentally. A maximum of 30% (v/v) DMSO was used. The results are plotted in Fig. 3. As the DMSO concentration increased, the critical particle concentration rose sharply until a maximum was attained at 12% (v/v) DMSO. This maximum corresponds to a critical particle concentration of 6.3 × l0 s cells/ml, which is by a factor of about three larger than the value at 0% DMSO (i.e., 2.2 × l0 s cells/ml). This therefore shows very clearly that by adding appro-

Journal of Colloid and Interface Science, Vol. 81, No. 2, June 1981

FIG. 3. Effects of a d d e d D M S O to the test liquids. M a x i m u m particle concentration (6.3 x I0 s cells/ml.) occurs at about 12% DMSO.

priate amounts of an additive, it is possible to minimize droplet sedimentation and therefore increase the concentration of particles that can be supported on a given liquid. B e y o n d the maximum, i.e., above 12% (v/v) DMSO, the critical particle concentration decreases, but at a somewhat slower rate, probably because of the increase in density of the solution with the addition of more DMSO. The maximum in Fig. 3 corresponds to A13, - 0; which is obtained by an addition of 12% (v/v) DMSO which, in the light of our previous discussion, then makes the surface tension of the liquids equal to that of the particle, i.e., Y3v = Y,v. The surface tension o f D20 and physiological saline (ionic strength/z = 0.15) were measured as a function of the DMSO concentration by the Wilhelmy plate technique (16). The results are given in Fig. 4. As seen from this figure the surface tensions of the saline and D20 solution are virtually identical. Interpolating at a DMSO concentration of 12% (v/v) gives a surface tension of ~65 ergs/cm 2. This surface tension value conforms rather closely to the value of 64.5 ergs/cm 2 for glutaraldehydefixed erythrocytes obtained by the freezing front technique, using thymol as the matrix, see above. Thus, droplet sedimentation experiments offer one more method for estimating the surface tensions of biological particles, in

DROPLET SEDIMENTATION addition to the freezing front technique and contact angle measurements (17). This can be quite useful since the simplest of the hitherto employed techniques, i.e., contact angle measurements (17) is not easily applicable to fairly rigid cells such as glutaraldehyde-fixed erythrocytes. V. E F F E C T S O F ZERO E L E C T R O S T A T I C (AND ZERO VAN DER WAALS) FORCES

The electrostatic interaction energy (hFe) may be determined from (18); assuming low potentials, AFe = 1/2ea~o In {1 + exp(-Kd0)},

[4]

where e is the relative permittivity, ~b0is the surface potential of the particle, and K is the reciprocal of the Debye length. Other parameters retain the definitions as given previously. Electrostatic interaction effects will become zero, i.e., AFe will be zero, if tk0 is zero. From the solution of the linear Poisson-Boltzmann equations, tk0 can b e estimated from (19) as 00 --~ ~(1 + z/a) exp Kz,

[5]

where z is the distance from the surface of the particle to the shearing plane and ~ is the potential which can be obtained from measurements of electrophoretic mobility u, i.e., from

75~

8

70

z

g

~o ~o

0

5L

I I I0 15 PERCENTAGE (V/V) DMSO

E 20

FIG. 4. Reduction in surface tension of D20 (=©) and water (=A), each of ionic strength = 0.15, by the addition of DMSO.

407

+20

~÷ ,o ~ o ~ ~o ,o ~ -20

I

}0-9

i 10-7

i ]0-5

i 10-3

l ~0-1 THANUM NITRATE

FIG. 5. Zeta potential against molar concentration of lanthanum nitrate for glutaraldehyde-fixed human erythrocytes in physiological saline.

-

47r~ u £

,

[61

assuming that the particles are large, (~ is the fluid viscosity). To reduce AFe to zero, therefore, one needs to attain the conditions under which the electrophoretic mobility u is zero. This was done by gradually decreasing the negative ~ potential through the addition of La 3+ ions and by monitoring the electrophoretic mobilities (20, 21) of the glutaraldehyde-fixed human erythrocytes suspended in physiological saline, as a function of lanthanum nitrate concentration. The solutions used were unbuffered to avoid possible interaction of buffer ions with either the cell surface or added cations. The pH for all solutions was found to be between 5.29 and 5.84. Within this range, pH variation is not likely to alter the electrophoretic mobilities to a significant degree (20). For each mobility determination, a minimum of at least eight cells was considered. The mobilities were found to vary by less than 12% from the mean values. Using ~ = 0.903 cP (at 26°C) and e = 76.7 for the liquids used, the electrophoretic mobilities were converted to potentials with Eq. [6] and were plotted against the molar concentration of lanthanum nitrate, as shown in Fig. 5. The molar concentration of lanthanum nitrate necessary for complete charge neutralization, as deduced from this figure was -~5 × 10-8 M. Journal of Colloid and Interface Science, Vol. 81, No. 2, June 1981

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OMENYI ET AL.

109 - -

o

10 8

¢J

10-9

10"7

10-5

MOLAR CONCENTRATION OF LANTHANUM

10-3

10-1

NITRATE

FIG. 6. Effect of lanthanum ions on critical particle concentrations for droplet formation, for human erythrocytes.

To determine the effects of zero electrostatic forces and zero van der Waals forces on droplet sedimentation, lanthanum nitrate ranging from zero to 10-8 M in concentration was added to 12% (v/v) DMSO in the test liquids. The experimentally determined critical particle concentrations were plotted against lanthanum nitrate concentration in Fig. 6. At 5 x 10-8 M lanthanum nitrate, No = 3.8 x 108 cells/ml which is lower than the value of 6.3 × 108 cells/ml when no lanthanum nitrate was added. It would be expected that neutralizing the charge on the surface of the particles would also reduce the electrostatic repulsion to zero. Since lower critical particle concentration was obtained, it appears that other effects, e.g., density difference, mass diffusion, etc., may be active in addition to the first two interaction forces. The value at zero van der Waals and in the region of zero electrostatic forces (i.e., 3.8 × 108 cells/ml) is an improvement over the value obtained when both the van der Waals and electrostatic forces are fully effective, i.e., 2.2 x 108 cells/ml. At lanthanum nitrate concentrations > 5 × 10-8 M, the critical particle concentration continues to decrease with increasing lanthanum concentration. We would have expected that, as the sign of charge is reversed, an increase in the charge on the surface of the particles with increasing lanthanum nitrate concenJournal of Colloid and Interface Science, Vol. 81, N o . 2, J u n e 1981

trations would lead to more repulsive electrostatic forces, and hence to larger critical particle concentrations which would mean reduced droplet sedimentation. The discrepancy probably is due to increased cation bridging involving excess cations (22), leading to particle aggregation and hence enhancement of droplet sedimentation. With lanthanum nitrate concentration fixed at 5 x 10-8 M, and thus in the region of zero ~ potential, the DMSO concentration was varied between 10% and 15%. At 10% (v/v) DMSO, No was 2.9 x 10s cells/ ml, at 12% DMSO it was 3.8 x 10s cells/ml and at 15% DMSO it was 3.6 × 10s cells/ml. As expected, a maximum in the value of No prevailed at 12% (v/v) DMSO, although the No value at 15% DMSO did only vary slightly from the value at 12%, the maximum of the graph reached in Fig. 3 is maintained in the region of zero electrostatic interaction. VI. CONCLUSION

The dependence of droplet sedimentation on particle concentration was confirmed. It was shown that it is possible to determine the maximum particle concentration that can remain stable on a given liquid from droplet sedimentation experiments. Droplet sedimentation can be reduced but not totally eliminated by the addition of appropriate amounts of DMSO to reduce the van der Waals forces to zero. It was found that, at 12% (v/v) DMSO, a maximum particle concentration of 6.3 × 108 cells/ml of glutaraldehyde-fixed human erythrocytes suspended in physiological saline can remain stable on a D20 cushion. This value is about three times the value obtained in aqueous media in which attractive van der Waals forces dominate. Experiments show that the surface charge of glutaraldehyde-fixed human erythrocytes is neutralized at lanthanum nitrate concentration of 5 × 10-s M. At zero van der Waals and in the region of zero electro-

DROPLET SEDIMENTATION

static forces, the droplet sedimentation effect is reduced compared to that when both forces are fully effective. Reduction of the electrostatic forces alone enhances droplet sedimentation. For optimally stabilized suspension and hence reduced droplet sedimentation, the van der Waals forces should be reduced to zero while the electrostatic repulsive forces should be enhanced to keep the particles well dispersed. Mechanisms other than electrostatic repulsion and van der Waals attraction such as density differences, mass diffusion, etc., clearly also are important in causing droplet sedimentation. The surface tension of glutaraldehydefixed human erythrocytes was estimated at 64.5 ergs/cm 2 by freezing front exclusion and at --~65 ergs/cm 2 by the technique of determination of maximum stability with respect to droplet sedimentation. This technique may serve as another alternative method for the study of surface tensions of biological particles. ACKNOWLEDGMENTS This work was supported in part by NRC (U. S. A.) Associateship to S.N.O., Ontario Heart Foundation Fellowships to D.R.A. and A.W.N. and NRC (Canada) Grant 8278. REFERENCES 1. Brakke, M. K., Arch. Biochem. Biophys. 55, 175 (1955). 2. Nason, P., Schumaker, V., Halsall, B., and Schevedes, J., Biopolymers 7, 241 (1969). 3. Meuwissen, J. A., and Heirwegh, K. P., Biochem. Biophys. Res. Commun. 41,675 (1970). 4. Peterson, E. A., and Evans, W. H., Nature 214~ 824 (1967). 5. Plesset, M. S., and Winet, H., Nature 248, 441 (1974).

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6. Halsall, H. B., and Schumaker, V. N., Biochem. Biophys. Res. Commun. 43, 601 (1971). 7. Omenyi, S. N., Snyder, R. S., van Oss, C. J., Absolom, D. R., and Neumann, A. W., "2nd Chemical Congress of the North American Continent, San Francisco, 1980." 8. Vassar, P. S., Hards, J. M., Brooks, D. E., Hagenberger, B., and Seaman, G. V. F., J. Cell Biol. 53, 809 (1972). 9. Omenyi, S. N., Smith, R. P., and Neumann, A. W., J. Colloid Interface Sci. 75, 117 (1980). 10. Spelt, J. K., Absolom, D. R., Neumann, A. W., van Oss, C. J., and Zingg, W., "54th Colloid and Surface Science Symposium," p. 135. Lehigh University, Bethlehem, Pa., 1980. 11. Omenyi, S. N., Neumann, A. W., Martin, W. W., Lespinard, G., and Smith, R. P.,J. Appl. Phys., in press. 12. Neumann, A. W., Good, R. J., Hope, C. J., and Sejpal, M.,J. Colloidlnterface Sci. 49, 2 (1974). 13. Hamaker, H. C., Physica 4, 1058 (1937). 14. Neumann, A. W., Omenyi, S. N., and van Oss, C. J., Colloid Polym. Sci. 257, 413 (1979). 15. Omenyi, S. N., "Attraction and Repulsion of Particles by Solidifying Melts," pp. 33, 34. Ph.D. Dissertation, University of Toronto, 1978. 16. Neumann, A. W., and Good, R. J., in "Surface and Colloid Science" (R. J. Good and R. R. Stromberg, Eds.), Vol. II, p. 31. Plenum, New York, 1979. 17. van Oss, C. J., Gillman, C. F., and Neumann, A. W., "Phagocytic Engulfment and Cell Adhesiveness as Cellular Surface Phenomena." Dekker, New York, 1975. 18. Verwey, E. J. W., and Overbeek, J. Th. G., "Theory of the Stability of Lyophobic Colloids." Elsevier, Amsterdam, 1948. 19. Hiemenz, P. C., "Principles of Colloid and Surface Chemistry," p. 465. Dekker, New York, 1977. 20. Seaman, G. V. F., and Pethica, B. A., Biochem. J. 90, 573 (1964). 21. Seaman, G. V. F., and Brooks, D. E., in "Electrokinetic Separation Methods" (P. G. Righetti, C. J. van Oss, and J. W. Vanderhoff, Eds.), p. 95. Elsevier/North-Holland, Amsterdam, 1979. 22. Curtis, A. S. G., Biol. Rev. 37, 82 (1962).

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