Strict simulations of non-equilibrium dynamics of colloids

Abstract We review our new direct numerical simulation scheme, called “smoothed profile (SP) method”, which is implemented for a full explicit time-marching simulations of colloidal dispersions. The SP method provides a way to couple continuum fluid dynamics with rigid-body dynamics through smoothed profile of colloidal particle. Our formulation includes extensions to colloids in multi-component solvents such as charged colloids in electrolyte solutions. This method enables us to compute the time evolutions of colloidal particles, ions, and host fluids simultaneously by solving Newton, advection–diffusion, and Navier–Stokes equations so that the electro-hydrodynamic couplings can be fully taken into account. The electrophoretic mobilities of charged spherical particles are calculated in several situations. The comparisons with approximation theories show quantitative agreements for dilute dispersions without any empirical parameters.

[1]  R. Yamamoto,et al.  Simulation method to resolve hydrodynamic interactions in colloidal dispersions. , 2004, Physical review. E, Statistical, nonlinear, and soft matter physics.

[2]  Efficient Simulations of Charged Colloidal Dispersions: A Density Functional Approach , 2004, cond-mat/0403350.

[3]  Robin Ball,et al.  A simulation technique for many spheres in quasi-static motion under frame-invariant pair drag and Brownian forces , 1997 .

[4]  Tanaka,et al.  Simulation method of colloidal suspensions with hydrodynamic interactions: fluid particle dynamics , 2000, Physical review letters.

[5]  Depletion forces in nonequilibrium. , 2003, Physical review letters.

[6]  H. Hasimoto.  On the periodic fundamental solutions of the Stokes equations and their application to viscous flow past a cubic array of spheres , 1959, Journal of Fluid Mechanics.

[7]  George M. Homsy,et al.  Stokes flow through periodic arrays of spheres , 1982, Journal of Fluid Mechanics.

[8]  C. Peskin,et al.  A three-dimensional computational method for blood flow in the heart. 1. Immersed elastic fibers in a viscous incompressible fluid , 1989 .

[9]  Hiroya Kodama,et al.  LETTER TO THE EDITOR: Fluid particle dynamics simulation of charged colloidal suspensions , 2004 .

[10]  J. Happel,et al.  Low Reynolds number hydrodynamics: with special applications to particulate media , 1973 .

[11]  J. Hansen,et al.  Basic Concepts for Simple and Complex Liquids , 2003 .

[12]  R Yamamoto.  Simulating particle dispersions in nematic liquid-crystal solvents. , 2001, Physical review letters.

[13]  Robin Ball,et al.  Continuous shear thickening transitions in model concentrated colloids—The role of interparticle forces , 2004 .

[14]  Christos N. Likos,et al.  EFFECTIVE INTERACTIONS IN SOFT CONDENSED MATTER PHYSICS , 2001 .

[15]  Lee R. White,et al.  Electrophoretic mobility of a spherical colloidal particle , 1978 .

[16]  Sangtae Kim,et al.  Microhydrodynamics: Principles and Selected Applications , 1991 .

[17]  A. Ladd,et al.  Lattice-Boltzmann Simulations of Particle-Fluid Suspensions , 2001 .

[18]  A. Malevanets,et al.  Mesoscopic model for solvent dynamics , 1999 .

[19]  David J. Jeffrey,et al.  Calculation of the resistance and mobility functions for two unequal rigid spheres in low-Reynolds-number flow , 1984, Journal of Fluid Mechanics.

[20]  A. Satoh.  Introduction to molecular-microsimulation of colloidal dispersions , 2003 .