A pairwise additive description of sedimentation and diffusion in concentrated suspensions of hard spheres

• Published in: Journal of colloid and interface science 1982-09, Vol.89 (1), p.124-143
• Main Authors: Glendinning, A.B, Russel, W.B
• Format: Article
• Language: English
• ISSN: 0021-9797; 1095-7103
• DOI: 10.1016/0021-9797(82)90127-8

Both general and specific results are presented for the sedimentation velocity and the mutual and self-diffusion coefficients in concentrated suspensions of monodisperse spheres. A statistical mechanical analysis of sedimentation-diffusion equilibrium affirms the generalized Stokes-Einstein equation relating the mutual diffusion coefficient to the sedimentation coefficient and the osmotic compressibility. An integral representation of velocities within a homogeneous suspension of particles subject to an external force leads to the mean sedimentation velocity in terms of ensemble averages of nearfield hydrodynamic interactions plus far-field contributions arising from the renormalization of non-convergent integrals. A simpler analysis determines the self-diffusion coefficient. All three results apply to arbitrary volume fractions and interaction potentials. To evaluate these explicitly we assume particle velocities to be pairwise additive and thus determined from the exact two sphere mobilities. Then the equilibrium radial distribution function for hard spheres, available from the Percus-Yevick theory for dense fluids, characterizes the microstructure, in the absence of long-ranged potentials, for low Peclet numbers. The results conform to the known dilute limits and deviate correctly at slightly higher volume fractions. Unfortunately, at still higher concentrations all three coefficients become negative, indicating the failure of pairwise additivity. Nonetheless, the formal approach provides an exact and general treatment of these transport processes in concentrated suspensions. Furthermore the shortcomings of pairwise additivity, which arise from screening due to intervening particles, can be corrected by either an ad hoc mean-field treatment suggested here or systematic inclusion of three-body effects.