From the Liouville to the Smoluchowski equation for a colloidal solute particle in a solvent

Abstract

We show how the Smoluchowski dynamics of a colloidal Brownian particle suspended in a molecular solvent can be reached starting from the microscopic Liouvillian evolution of the full classical model in the high friction limit. The integration of the solvent degrees of freedom goes through a multiple time scale perturbation expansion which removes the secular divergences. A simple dynamical Monte Carlo scheme is then proposed to solve the resulting evolution equation for the colloid solute particle. In particular we study the approach to the equilibrium Boltzmann distribution at late times and its resilience behavior at shorter times as influenced by the steepness of the external potential and the friction coefficient around their respective minima. This is very important to understand the fate of the Brownian particle's random walk and its evolution history.

20 pages and 1 figure

References in corpus (16)

• Patchy sticky hard spheres: analytical study and Monte Carlo simulations
• Penetrable Square-Well fluids: Exact results in one dimension
• Multicomponent adhesive hard sphere models and short-ranged attractive interactions in colloidal or micellar solutions
• Bridging and depletion mechanisms in colloid-colloid effective interactions: A reentrant phase diagram
• The thermodynamic instabilities of a binary mixture of sticky hard spheres
• Stability boundaries, percolation threshold, and two phase coexistence for polydisperse fluids of adhesive colloidal particles
• The structure of colloidosomes with tunable particle density: simulation vs experiment
• Penetrable-Square-Well fluids: Analytical study and Monte Carlo simulations
• Janus fluid with fixed patch orientations: theory and simulations
• Phase behavior of weakly polydisperse sticky hard spheres: Perturbation theory for the Percus-Yevick solution
• Phase diagram of the penetrable square well-model
• A Numerical Test of a High-Penetrability Approximation for the One-Dimensional Penetrable-Square-Well Model
• Wertheim perturbation theory: thermodynamics and structure of patchy colloids
• Phase diagrams of Janus fluids with up-down constrained orientations
• Phase behavior of polydisperse sticky hard spheres: analytical solutions and perturbation theory
• Fluids of spherical molecules with dipolar-like nonuniform adhesion. An analytically solvable anisotropic model