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The effect of particle interactions on dynamic light scattering from a dilute suspension

Published online by Cambridge University Press:  21 April 2006

J. M. Rallison  and
E. J. Hinch
J. M. Rallison
Affiliation:
Department of Applied Mathematics & Theoretical Physics, University of Cambridge, Silver Street, Cambridge CB3 9EW
E. J. Hinch
Affiliation:
Department of Applied Mathematics & Theoretical Physics, University of Cambridge, Silver Street, Cambridge CB3 9EW
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Abstract

The calculation of dynamic laser-light scattering by dilute suspensions of Brownian particles is reviewed. It is shown that present theories of diffusion can provide approximations for the autocorrelation of the intensity of the scattered light that are only uniformly accurate for correlation times up to order (D0k2)−l where D0 is the diffusivity of a single particle and k is the scattering wave vector. The meanings of, and connections between, down-gradient, self- and tracer diffusion for both short and long times are established and it is shown how these may be inferred from light-scattering experiments for optically monodisperse and polydisperse systems.

For dilute systems, equations giving the time evolution of the intermediate and self-intermediate scattering functions, F(k, t) and Fs(k, t), accurate to first order in the volume concentration of particles are constructed, and are solved for suspensions of hard spheres with and without hydrodynamic interaction. For short and long times (semi-) analytic solutions are given; for intermediate times numerical results are presented. The formal correspondence of the limiting values of the time-dependent solutions with the results of Batchelor (1976, 1983) and others for steady sedimentation in polydisperse systems is established.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 167 , June 1986 , pp. 131 - 168
Copyright
© 1986 Cambridge University Press

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References

Ackeeson, B. J. 1976 Correlations for interacting Brownian particles. J. Ghent,. Phys. 64, 242.Google Scholar
Ackebson, B. J. & Fleishman, L. 1982 Correlations for dilute hard core suspensions. J. Chem. Phys. 76, 2675.Google Scholar
Akcasu, Z. & Gurol, H. 1976 Quasielastic scattering by dilute polymer solutions. Polymer Phys. 14, 1.Google Scholar
Altenbekger, A. R. 1979 On the wave vector dependent mutual diffusion of interacting Brownian particles. J. Chem. Phys. 70, 1994.Google Scholar
Altenbebger, A. R. & Deutsch, J. M. 1973 Light scattering from dilute macromolecular solutions. J. Chem. Phys. 59, 894.Google Scholar
Batchelor, G. K. 1972 Sedimentation in a dilute dispersion of spheres. J. Fluid Mech. 52, 245.Google Scholar
Batchelor, G. K. 1976 Brownian diffusion of particles with hydrodynamic interactions. J. Fluid Mech. 74, 1.Google Scholar
Batchelor, G. K. 1982 Sedimentation in a dilute polydisperse system of interacting spheres.Part 1. General formulation. J. Fluid Mech. 119, 379.Google Scholar
Batchelor, G. K. 1983 Diffusion in a dilute polydisperse system of interacting spheres. J. Fluid Mech. 131, 155 and Corrigendum J. Fluid Mech. 137, 1983, 467.Google Scholar
Batchelor, G. K. & Wen, C. S. 1982 Sedimentation in a dilute polydisperse system of interacting spheres. Part 2. Numerical results. J. Fluid Mech. 124, 495 and Corrigendum J. Fluid Mech. 137, 1983, 467.Google Scholar
Berne, B. J. & Pecora, R. 1976 Dynamic Light Scattering. Wiley.
Boon, J. P. & Yip, S. 1980 Molecular Hydrodynamics. McGraw Hill.
Ermak, D. L. & Yeh, Y. 1974 Equilibrium electrostatic effects on the behaviour of polyions in solution: polyion-mobile ion interaction. Chem. Phys. Lett. 24, 243.Google Scholar
Felderhof, B. U. 1978 Diffusion of interacting Brownian particles. J. Phys. A: Math. Gen. 11, 929.Google Scholar
Felderhof, B. U. & Jones, R. B. 1983 Diffusion in hard sphere suspensions. Faraday Discuss. Chem. Soc. 76, 179.Google Scholar
Fijnaut, H. M. 1981 Wave vector dependence on the effective diffusion coefficient of Brownian particles. J. Chem. Phys. 74, 6857.Google Scholar
Hanna, S., Hess, W. & Klein, R. 1981 The velocity autocorrelation function of an overdamped Brownian system with hard-core interactions. J. Phys. A 14, L493.Google Scholar
Hanna, S., Hess, W. & Klein, R. 1982 Self diffusion of Brownian particles with hard core interactions. Physica A 111, 181.Google Scholar
Hess, W. & Klein, R. 1976 Theory of light scattering from a system of interacting Brownian particles. Physica A, 85, 509.Google Scholar
Hess, W. & Klein, R. 1983 Generalized hydrodynamics of systems of Brownian particles. Adv. Phys. 32, 172.Google Scholar
Hinch, E. J. 1975 Application of the Langevin equation to fluid suspensions. J. Fluid Mech. 72, 499.Google Scholar
Jeffrey, D. J. & Onishi, Y. 1984 Calculation of the resistance and mobility functions for two unequal spheres in low-Reynolds-number flow. J. Fluid Mech. 139, 261.Google Scholar
Jones, R. B. & Btjrfield, G. S. 1982 Memory effects in the diffusion of an interacting polydisperse suspension. Parts 1 and 2. Physica A 111, 562.Google Scholar
Koppel, D. E. 1972 Analysis of macromolecular polydispersity in intensity correlation spectro-scopy: the method of cumulants. J. Chem. Phys. 57, 4814.Google Scholar
Lekkerkerker, H. & Dhont, J. K. G. 1984 On the calculation of the self diffusion coefficient of interacting Brownian particles. J. Chem. Phys. 80, 5790.Google Scholar
Phillies, G. D. & Wills, P. R. 1981 Light scattering spectrum of a suspension of interacting Brownian macromolecules. J. Chem. Phys. 75, 508.Google Scholar
Pusey, P. N. 1975 The dynamics of interacting Brownian particles. J. Phys. A 8, 1433.Google Scholar
Pusey, P. N. 1978 Intensity fluctuation spectroscopy of charged Brownian particles: the coherent scattering function. J. Phys. A 11, 119.Google Scholar
Pusey, P. N. & Tough, R. J. A. 1982 Langevin approach to the dynamics of interacting Brownian particles. J. Phys. A 15, 1291.Google Scholar
Pusey, P. N. & Tough, R. J. A. 1983 Hydrodynamic interactions and diffusion in concentrated particle suspensions. Faraday Discuss. Chem. Soc. 76, 123.Google Scholar
Rahmen, A., Singwi, K. S. & SJölander, A. 1962 Theory of slow motion scattering by liquids. Phys. Rev. 126, 986.Google Scholar
Rallison, J. M. & Leal, L. G. 1981 Dynamic light scattering from macromolecules: the separation of translation from rotational and deformational modes. J. Chem. Phys. 74, 4819.Google Scholar
Russel, W. B. & Glendinning, A. B. 1981 The effective diffusion coefficient detected by dynamic light scattering. J. Chem. Phys. 74, 948.Google Scholar
Wills, P. R. 1981 Wavevector dependence of effective diffusion coefficient for solutions of macromolecular. J. Phys. A 4, 3093.Google Scholar