Rotational self-diffusion in suspensions of charged particles: Revised Beenakker-Mazur and Pairwise Additivity methods versus numerical simulations

To the present day, the Beenakker-Mazur (BM) method is the most comprehensive statistical physics approach to the calculation of short-time transport properties of colloidal suspensions. A revised version of the BM method with an improved treatment of hydrodynamic interactions is presented and evaluated regarding the rotational short-time self-diffusion coefficient, $D^r$ , of suspensions of charged particles interacting by a hard-sphere plus screened Coulomb (Yukawa) pair potential. To assess the accuracy of the method, elaborate simulations of $D^r$ have been performed, covering a broad range of interaction parameters and particle concentrations. The revised BM method is compared in addition with results by a simplifying pairwise additivity (PA) method in which the hydrodynamic interactions are treated on a two-body level. The static pair correlation functions re- quired as input to both theoretical methods are calculated using the Rogers-Young integral equation scheme. While the revised BM method reproduces the general trends of the simulation results, it systematically and significantly underestimates the rotational diffusion coefficient. The PA method agrees well with the simulation data at lower volume fractions, but at higher concentrations $D^r$ is likewise underestimated. For a fixed value of the pair potential at mean particle distance comparable to the thermal energy, $D^r$ increases strongly with increasing Yukawa potential screening parameter.Comment: 24 pages, 13 figure

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

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.Comment: 4 figure

High-frequency viscosity of concentrated porous particles suspensions

We determine the high-frequency limiting shear viscosity, eta(infinity), in colloidal suspensions of rigid, uniformly porous spheres of radius a as a function of volume fraction phi and (inverse) porosity parameter x. Our study covers the complete fluid-state regime. The flow inside the spheres is modeled by the Debye-Bueche-Brinkman equation using the boundary condition that fluid velocity and stress change continuously across the sphere surfaces. The many-sphere hydrodynamic interactions in concentrated systems are fully accounted for by a precise hydrodynamic multipole method encoded in our HYDROMULTIPOLE program extended to porous particles. A truncated virial expansion is used to derive an accurate and easy-to-use generalized Saito; formula for eta(infinity). The simulation data are used to test the performance of two simplifying effective particle models. The first model describes the effective particle as a nonporous sphere characterized by a single effective radius a(eff)(x)<a. In the more refined second model, the porous spheres are modeled as spherical annulus particles with an inner hydrodynamic radius a(eff)(x) defining the nonporous dry core and characterizing hydrodynamic interactions, and an outer excluded volume radius a characterizing the unchanged direct interactions. Only the second model is in a satisfactory agreement with the simulation data