Non equilibrium inertial dynamics of colloidal systems

TL;DR

This paper investigates the inertial dynamics of one-dimensional colloidal systems with damping and collisions, deriving evolution equations that extend existing theories to include inertial effects and validating them numerically.

Contribution

It introduces a kinetic theory approach to derive density evolution equations for inertial colloidal particles, extending beyond the dynamic density functional theory (DDF) to include inertial effects.

Findings

Derived a generalized density evolution equation incorporating inertia.

Showed agreement with DDF in high friction/mass limit.

Numerically validated inertial corrections at moderate friction values.

Abstract

We consider the properties of a one dimensional fluid of brownian inertial hard-core particles, whose microscopic dynamics is partially damped by a heat-bath. Direct interactions among the particles are represented as binary, instantaneous elastic collisions. Collisions with the heath bath are accounted for by a Fokker-Planck collision operator, whereas direct collisions among the particles are treated by a well known method of kinetic theory, the Revised Enskog Theory. By means of a time multiple time-scale method we derive the evolution equation for the average density. Remarkably, for large values of the friction parameter and/or of the mass of the particles we obtain the same equation as the one derived within the dynamic density functional theory (DDF). In addition, at moderate values of the friction constant, the present method allows to study the inertial effects not accounted for by DDF method. Finally, a numerical test of these corrections is provided.