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.

arXiv comment25 pages, 10 figures

References in corpus (28)

• Critical Phenomena and Renormalization-Group Theory
• Critical Casimir effect in classical binary liquid mixtures
• The Casimir effect: from quantum to critical fluctuations
• Filler-Induced Composition Waves in Phase-Separating Polymer Blends
• Nonequilibrium critical Casimir interactions in binary fluids
• Critical dynamics in thin films
• Relaxation phenomena at criticality
• Universal Short-Time Behavior in Critical Dynamics near Surfaces
• The out of equilibrium behavior of Casimir type fluctuation induced forces for free classical fields
• Stresses in non-equilibrium fluids: Exact formulation and coarse grained theory
• Aging phenomena in critical semi-infinite systems
• Structure and dynamics of binary liquid mixtures near their continuous demixing transitions
• Long-time traces of the initial condition in relaxation phenomena near criticality
• Relaxation of the thermal Casimir force between net neutral plates containing Brownian charges
• Critical adsorption and critical Casimir forces in the canonical ensemble
• Transient Casimir forces from quenches in thermal and active matter
• Dynamical Relaxation and Universal Short-Time Behavior in Finite Systems: The Renormalization Group Approach
• Generalized Casimir forces in non-equilibrium systems
• Dynamic critical behavior of model A in films: Zero-mode boundary conditions and expansion near four dimensions
• Fluctuating Multicomponent Lattice Boltzmann Model
• Statistical field theory with constraints: application to critical Casimir forces in the canonical ensemble
• Non-equilibrium Dynamics Following a Quench to the Critical Point in a Semi-infinite System
• Out of equilibrium thermal Casimir effect in a model polarizable material
• Direct calculation of the critical Casimir force in a binary fluid
• Dynamical approach to the Casimir effect
• Dynamic surface critical behavior of systems with conserved bulk order parameter: Detailed RG analysis of the semi-infinite extensions of model B with and without nonconservative surface terms
• First-passage dynamics of linear stochastic interface models: numerical simulations and entropic repulsion effect
• First-passage dynamics of linear stochastic interface models: weak-noise theory and influence of boundary conditions

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• Dynamics and steady states of a tracer particle in a confined critical fluid
• Dynamics of the critical Casimir force for a conserved order parameter after a critical quench
• Correlations and forces in sheared fluids with or without quenching
• Critical surface adsorption of confined binary liquids with locally conserved mass and composition
• Fluctuations of the critical Casimir force
• Interplay of quenching temperature and drift in Brownian dynamics
• The role of dimensionality and geometry in quench-induced nonequilibrium forces