Rotational and translational self-diffusion in concentrated suspensions of permeable particles

TL;DR

This paper calculates the rotational self-diffusion coefficient in concentrated suspensions of permeable particles using hydrodynamic simulations, revealing scaling relations and providing analytic approximations for experimental analysis.

Contribution

It introduces the first evaluation of rotational self-diffusion in permeable particle suspensions and establishes scaling relations with impermeable particles.

Findings

Rotational self-diffusion can be scaled to that of impermeable particles.

Scaling applies similarly to translational diffusion.

Generalized Stokes-Einstein-Debye relation is not satisfied.

Abstract

In our recent work on concentrated suspensions of uniformly porous colloidal spheres with excluded volume interactions, a variety of short-time dynamic properties were calculated, except for the rotational self-diffusion coefficient. This missing quantity is included in the present paper. Using a precise hydrodynamic force multipole simulation method, the rotational self-diffusion coefficient is evaluated for concentrated suspensions of permeable particles. Results are presented for particle volume fractions up to 45%, and for a wide range of permeability values. From the simulation results and earlier results for the first-order virial coefficient, we find that the rotational self-diffusion coefficient of permeable spheres can be scaled to the corresponding coefficient of impermeable particles of the same size. We also show that a similar scaling applies to the translational self-diffusion coefficient considered earlier. From the scaling relations, accurate analytic approximations for the rotational and translational self-diffusion coefficients in concentrated systems are obtained, useful to the experimental analysis of permeable-particle diffusion. The simulation results for rotational diffusion of permeable particles are used to show that a generalized Stokes-Einstein-Debye relation between rotational self-diffusion coefficient and high-frequency viscosity is not satisfied.