Transport properties of suspensions–critical assessment of Beenakker-Mazur method

Abstract

The Beenakker-Mazur method of calculation of transport coefficients for suspensions has been analyzed. The analysis relies on calculation of the hydrodynamic function and the effective viscosity with higher accuracy and comparison of these characteristics to the original Beennakker-Mazur results. Comparison to numerical simulations is also given. Our calculations go along with the idea of Beenakker and Mazur, but avoid unnecessary approximations. Our higher accuracy results differ significantly from results obtained initially by Beenakker and Mazur for volume fractions φ > 25%. Moreover, our results agree with the precise numerical simulations of Abade and Ladd for volume fractions φ < 15% and volume fractions φ ≈ 45%, whereas for volume fractions 15% < φ < 40%, we observe pronounced discrepancies.

Rotational self-diffusion in suspensions of charged particles: simulations and revised Beenakker–Mazur and pairwise additivity methods

“…In the works by BM on the hydrodynamic function and the high-frequency effective viscosity, and in the work by Treloar and Masters on rotational diffusion, due to technical difficulties severe truncations of these matrices have been made as discussed in detail in Ref. [24]. In our revised method, we also truncate the infinite dimensional hydrodynamic matrices, but different from earlier works an extrapolation to infinite dimension has been included.…”

“…The details of this extrapolation procedure are along the lines described in Ref. [24] and are thus not repeated here.…”

“…These inaccuracies can be partially attributed to the approximate treatment of the HIs in the δγ method, and partially to the invoked mean-field approximation. In recent work by Makuch and Cichocki [24], the approximation steps in the original derivation of the δγ method have been reduced, in particular by accounting for a large number of hydrodynamic multipoles in the truncated multipolar matrices which are extrapolated to infinite order. The observation that the revised δγ method by Makuch and Cichocki, with its improved hydrodynamic mobility tensor treatment, has not resulted in a systematic improvement of the hydrodynamic function and high-frequency viscosity predictions points to a fortuitous cancellation of errors in the various approximation steps of the original method by Beenakker and Mazur.…”

Short-time diffusion in concentrated bidisperse hard-sphere suspensions

“…(15), (25), and (26). Extending the δγ scheme to the more general case of bidisperse suspensions is a non-trivial task.…”

“…[13][14][15] Each of these simulation methods is rather involved, which is one reason for the on-going development of approximate (semi-) analytical theoretical schemes for colloidal short-time dynamics. [16][17][18][19][20][21][22][23][24][25] In spite of extensive simulations and analytical theoretical studies, substantial gaps remain in the colloidal suspension parameter space that has yet been explored, which is due to both the large number of tunable parameters in soft matter systems and the complexity of the salient hydrodynamic interactions (HIs) among the suspended particles. The purpose of the present work is to assess the short-time diffusive dynamics in mixtures of hard spheres with two different hardcore diameters using a generalization of SD simulations and an analytical-theoretical scheme.…”