First-order virial expansion of short-time diffusion and sedimentation coefficients of permeable particles suspensions

TL;DR

This paper develops a theoretical first-order virial expansion to evaluate short-time diffusion and sedimentation coefficients of permeable particle suspensions, considering hydrodynamic interactions and particle permeability effects.

Contribution

It introduces a high-accuracy method for calculating two-body hydrodynamic interactions in permeable particle suspensions using virial expansion up to the two-particle level.

Findings

Virial coefficients are accurately computed for various permeability ratios.

Hydrodynamic radius model effectively approximates coefficients for large particle-to-screening length ratios.

Results extend understanding of transport properties in porous particle suspensions.

Abstract

For suspensions of permeable particles, the short-time translational and rotational self-diffusion coefficients, and collective diffusion and sedimentation coefficients are evaluated theoretically. An individual particle is modeled as a uniformly permeable sphere of a given permeability, with the internal solvent flow described by the Debye-Bueche-Brinkman equation. The particles are assumed to interact non-hydrodynamically by their excluded volumes. The virial expansion of the transport properties in powers of the volume fraction is performed up to the two-particle level. The first-order virial coefficients corresponding to two-body hydrodynamic interactions are evaluated with very high accuracy by the series expansion in inverse powers of the inter-particle distance. Results are obtained and discussed for a wide range of the ratio, x, of the particle radius to the hydrodynamic screening length inside a permeable sphere. It is shown that for x >= 10, the virial coefficients of the transport properties are well-approximated by the hydrodynamic radius (annulus) model developed by us earlier for the effective viscosity of porous-particle suspensions.