Brownian particles at different times scales: a new derivation of the Smoluchowski equation

Abstract A derivation of the Smoluchowski dynamics for colloidal suspensions from molecular laws of motion is presented, in which a fluctuating hydrodynamics description of the fluid and the solid particles is a crucial step. This procedure, unlike the standard ones, does not make use of the questionable assumption of time-scale separation between fluid and particle velocities underlying the Fokker-Planck equation.

[1]  A. Masters.  TIME-SCALE SEPARATIONS AND THE VALIDITY OF THE SMOLUCHOWSKI, FOKKER-PLANCK AND LANGEVIN-EQUATIONS AS APPLIED TO CONCENTRATED PARTICLE SUSPENSIONS , 1986 .

[2]  P. Mazur,et al.  Many-sphere hydrodynamic interactions and mobilities in a suspension , 1982 .

[3]  C. Beenakker.  The effective viscosity of a concentrated suspension of spheres (and its relation to diffusion) , 1984 .

[4]  B. Cichocki,et al.  ON THE MEMORY FUNCTION FOR THE DYNAMIC STRUCTURE FACTOR OF INTERACTING BROWNIAN PARTICLES , 1987 .

[5]  Banavar,et al.  Molecular dynamics of Poiseuille flow and moving contact lines. , 1988, Physical review letters.

[6]  C. W. J. Beenakker,et al.  Diffusion of spheres in a concentrated suspension II , 1984 .

[7]  Robbins,et al.  Simulations of contact-line motion: Slip and the dynamic contact angle. , 1989, Physical review letters.

[8]  P. Mazur,et al.  Self-diffusion of spheres in a concentrated suspension , 1983 .

[9]  W. Hess,et al.  Generalized hydrodynamics of systems of Brownian particles , 1983 .

[10]  G. Wilemski.  On the derivation of Smoluchowski equations with corrections in the classical theory of Brownian motion , 1976 .

[11]  Pierre Resibois,et al.  Time dependent correlation functions and mode-mode coupling theories , 1975 .

[12]  Irwin Oppenheim,et al.  Molecular Theory of Brownian Motion for Several Particles , 1971 .

[13]  T. J. Murphy,et al.  Brownian Motion of N Interacting Particles. I. Extension of the Einstein Diffusion Relation to the N‐Particle Case , 1972 .

[14]  J. Happel,et al.  Low Reynolds number hydrodynamics , 1965 .

[15]  Lev Davidovich Landau,et al.  Mécanique des fluides , 1989 .

[16]  E. J. Hinch,et al.  Application of the Langevin equation to fluid suspensions , 1975, Journal of Fluid Mechanics.

[17]  Dieter Forster,et al.  Hydrodynamic fluctuations, broken symmetry, and correlation functions , 1975 .

[18]  C. Broeck,et al.  Stochastic descriptions of the dynamics of interacting brownian particles , 1986 .

[19]  D. Ermak,et al.  Brownian dynamics with hydrodynamic interactions , 1978 .

[20]  Fluctuating hydrodynamics and Brownian motion , 1990 .

[21]  B. U. Felderhof.  Virtual mass and drag in two-phase flow , 1991, Journal of Fluid Mechanics.

[22]  J. Banavar,et al.  Computer Simulation of Liquids , 1988 .