Surface-induced non-equilibrium dynamics and critical Casimir forces for model B in film geometry

TL;DR

This paper investigates the non-equilibrium dynamics of a conserved order parameter and the resulting critical Casimir forces in a fluid film following a quench to the critical temperature, using analytic and numerical methods within mean field theory.

Contribution

It provides exact dynamic scaling functions for the evolution of the order parameter and Casimir force in model B, including asymptotic regimes and boundary effects.

Findings

Identification of asymptotic regimes in order parameter dynamics

Exact expressions for dynamic scaling functions of the Casimir force

Analysis of surface effects on non-equilibrium critical dynamics

Abstract

Using analytic and numerical approaches, we study the spatio-temporal evolution of a conserved order parameter of a fluid in film geometry, following an instantaneous quench to the critical temperature $T_c$ as well as to supercritical temperatures. The order parameter dynamics is chosen to be governed by model B within mean field theory and is subject to no-flux boundary conditions as well as to symmetric surface fields at the confining walls. The latter give rise to critical adsorption of the order parameter at both walls and provide the driving force for the non-trivial time evolution of the order parameter. During the dynamics, the order parameter is locally and globally conserved; thus, at thermal equilibrium, the system represents the canonical ensemble. We furthermore consider the dynamics of the nonequilibrium critical Casimir force, which we obtain based on the generalized force exerted by the order parameter field on the confining walls. We identify various asymptotic regimes concerning the time evolution of the order parameter and the critical Casimir force and we provide, within our approach, exact expressions of the corresponding dynamic scaling functions.