Surface-induced non-equilibrium 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 $T_c$ 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.