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

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 Tc 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.

Dynamics of the critical Casimir force for a conserved order parameter after a critical quench

“…[22,52] and references therein). Based on the notion of a generalized force [38], the stress tensor approach can be naturally extended to nonequilibrium situations [30,31,41,42]. The present study follows this approach (see Sec.…”

“…Both in and out of equilibrium, the bulk pressure can be obtained from a scaling limit: 12) which is taken by keeping the relevant thermodynamic control parameters fixed (see Refs. [41,52,53] for further details concerning ensemble differences). The thermally averaged dynamical CCF K , in units of k B T , is expected to exhibit the following scaling behavior:…”

“…V is the system volume independent of l i . In the case of the bounding surfaces of the system, located at z = L and z = 0, respectively, the generalized force K i in direction i = z can be expressed as [41,42]…”

“…In Ref. [41], the noise-free dynamics of the CCF after a quench of a fluid film in the presence of surface adsorption has been investigated within mean-field theory. We also note that particular care must be taken in applying field-theoretic stress tensors when computing forces out of equilibrium [37,38,41,42].…”

Correlations and forces in sheared fluids with or without quenching

“…These models have been applied extensively in describing various dynamical situations, e.g. the approach of the critical point from non-equilibrium initial conditions [34][35][36][37], the coarsening following a temperature quench [38,39], or for driven systems at criticality [40,41]. They have also been used to study shearing of near-critical fluids [42][43][44][45][46][47][48], leading to a large variety of phenomena.The use of such models provides generic scenarios, which we expect to be relevant for physical systems which allow for shearing and/or quenching.…”