Calculation of the wave-vector dependent diffusion constant in concentrated electrostatically stabilized dispersions

Dynamic simulation of concentrated macromolecular solutions with screened long-range hydrodynamic interactions: algorithm and limitations

Hydrodynamic interactions exert a critical effect on the dynamics of macromolecules. As the concentration of macromolecules increases, by analogy to the behavior of semidilute polymer solutions or the flow in porous media, one might expect hydrodynamic screening to occur. Hydrodynamic screening would have implications both for the understanding of macromolecular dynamics as well as practical implications for the simulation of concentrated macromolecular solutions, e.g., in cells. Stokesian dynamics (SD) is one of the most accurate methods for simulating the motions of N particles suspended in a viscous fluid at low Reynolds number, in that it considers both far-field and near-field hydrodynamic interactions. This algorithm traditionally involves an O(N(3)) operation to compute Brownian forces at each time step, although asymptotically faster but more complex SD methods are now available. Motivated by the idea of hydrodynamic screening, the far-field part of the hydrodynamic matrix in SD may be approximated by a diagonal matrix, which is equivalent to assuming that long range hydrodynamic interactions are completely screened. This approximation allows sparse matrix methods to be used, which can reduce the apparent computational scaling to O(N). Previously there were several simulation studies using this approximation for monodisperse suspensions. Here, we employ newly designed preconditioned iterative methods for both the computation of Brownian forces and the solution of linear systems, and consider the validity of this approximation in polydisperse suspensions. We evaluate the accuracy of the diagonal approximation method using an intracellular-like suspension. The diffusivities of particles obtained with this approximation are close to those with the original method. However, this approximation underestimates intermolecular correlated motions, which is a trade-off between accuracy and computing efficiency. The new method makes it possible to perform large-scale and long-time simulation with an approximate accounting of hydrodynamic interactions.

Sedimentation of Strongly and Weakly Charged Colloidal Particles: Prediction of Fractional Density Dependence

We report on calculations of the reduced sedimentation velocity U/U0 in homogenous suspensions of strongly and weakly charged colloidal spheres as a function of particle volume fraction φ. For dilute suspensions of strongly charged spheres at low salinity, U/U0 is well represented by the parametric form 1 - pφalpha with a fractional exponent alpha = 13 and a parameter p approximately 1.8, which is essentially independent from the macroion charge Z. This nonlinear volume fraction dependence can be quantitatively understood in terms of a model of effective hard spheres with φ-dependent diameter. For weakly charged spheres in a deionized solvent, we show that the exponent alpha can be equal to 12, if an expression for U/U0 given by Petsev and Denkov (1992, J. Colloid Interface Sci. 149, 329) is employed. We further show that the range of validity of this expression is limited to very small values of φ and Z, which are probably not accessible in sedimentation experiments. The presented results might also hold for other systems such as spherical proteins or ionic micelles. Copyright 1999 Academic Press.