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Mykola Zharkikh (Kyiv)

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Stokes friction coefficient of spherical particles in the presence of polymer depletion layers

E. Donath, A. Krabi, M. Nirschl,
V. M. Shilov, M. I. Zharkikh, B. Vincent

The Stokes friction coefficient has been calculated for the case of polymer depletion near a spherical particle surface, to provide a theoretical background for the interpretation of dynamic light scattering data. In a quasi-flat Newtonian approximation an analytical solution for arbitrary viscosity profiles was obtained. Numerical integration of the Navier-Stokes equation confirmed the large range of applicability of the approximate analytical solution. Explicit equations for an exponential and a step viscosity profile are given.

To compare experiment and theory, dynamic tight scattering data of liposomes with different radii in 110 kDa dextran are presented. For the first time evidence of a depletion layer relaxation effect has been obtained. This relaxation caused an effective reduction of the depletion layer thickness for small particles. A linear correction for the relaxation effect is suggested.


1. G. J. Fleer, J. M. H. M. Scheutjens, M. A. Cohen Stuart, T. Cosgrove and B. Vincent, Polymers at Interfaces, Chapman and Hall, London, 1993.

2. R. I. Feigin and D. H. Napper, J. Colloid Interface Sci., 1980, 75, 525.

3. H. Müller-Mohnssen, D. Weiss and A. Tippe, J. Rheol., 1990, 34, 223.

4. H. Bäumler and E. Donath, Stud. Biophys., 1987, 120, 113.

5. F. K. Li-in-on, B. Vincent and F. A. Waite, J. Colloid Interface Sci., 1987, 116, 305.

6. S. Emmett and B. Vincent, Phase Transitions, 1990, 21, 197.

7. G. J. Fleer, J. M. H. M. Scheutjens and B. Vincent, in Polymer Adsorption and Dispersion Stability, ed. E. D. Goddard and B. Vincent, ACS Symp. Ser. 240, 245, American Chemical Society, Washington, DC, 1984.

8. D. E. Brooks and G. V. F. Seaman, J. Colloid Interface Sci., 1973, 43, 670.

9. H. Bäumler, E. Donath, L. Pratsch and D. Lerche, in Hemo-rheologie et Agregation Erythrocytaire, ed. J. F. Stoltz, M. Donner and A. L. Copley, Editions Medicales Internationales, Cachan Cedex, 1991, p. 24.

10. E. Donath, P. Kuzmin, A. Krabi and A. Voigt, Colloid Polym. Sci, 1993,271,930.

11. E. Donath, A. Krabi, G. Allan and B. Vincent, Langmuir, 1996, 12, 3425.

12. H. Bäumler, E. Donath, A. Krabi, W. Knippel, A. Budde and H. Kiesewetter, Biorheology, in the press.

13. N. Ostrowsky, Chem. Phys. Lipids, 1993, 64,45.

14. G. Happel and H. Brenner, Low Reynolds Numbers Hydrodynamics. Nijhoff, The Hague, 1983.

15. L. D. Landau and E. M. Lifschitz, Lehrbuch der Theoretischen Physik, Hydrodynamik, Akademie-Verlag, Berlin 1981, p. 77.

16. H. Nirschl, VDI Fortschrittberichte, 1994, 7, 248.

17. H. Nirschl, H. A. Dwyer and V. Denk, J. Fluid Mech., 1995, 283, 273.

18. H. Nirschl, H. A. Dwyer and V. Denk, A Chimera grid scheme for the calculation of particle flows, AIAA 94-0519,1994.

Received 2 May 1999

Published : J. Chem Soc. Faraday trans, 1997, vol. 93, № 1, p. 115 – 119.

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