Dynamics and steady states of a tracer particle in a confined critical fluid

Abstract

The dynamics and the steady states of a point-like tracer particle immersed in a confined critical fluid are studied. The fluid is modeled field-theoretically in terms of an order parameter (concentration or density field) obeying dissipative or conservative equilibrium dynamics and (non-)symmetry-breaking boundary conditions. The tracer, which represents, e.g., a colloidal particle, interacts with the fluid by locally modifying its chemical potential or its correlations. The coupling between tracer and fluid gives rise to a nonlinear and non-Markovian tracer dynamics, which is investigated here analytically and via numerical simulations for a one-dimensional system. From the coupled Langevin equations for the tracer-fluid system we derive an effective Fokker-Planck equation for the tracer by means of adiabatic elimination as well as perturbation theory within a weak-coupling approximation. The effective tracer dynamics is found to be governed by a fluctuation-induced (Casimir) potential, a spatially dependent mobility, and a spatially dependent (multiplicative) noise, the characteristics of which depend on the interaction and the boundary conditions. The steady-state distribution of the tracer is typically inhomogeneous. Notably, when detailed balance is broken, the driving of the temporally correlated noise can induce an effective attraction of the tracer towards a boundary.

42 pages, 17 figures, v4: minor corrections

References in corpus (18)

• State-dependent diffusion: thermodynamic consistency and its path integral formulation
• A self-propelled particle in an external potential: is there an effective temperature?
• Effective Interactions in Active Brownian Suspensions
• Multidimensional Stationary Probability Distribution for Interacting Active Particles
• The Casimir effect: from quantum to critical fluctuations
• Lateral diffusion of a protein on a fluctuating membrane
• Applicability of Effective Pair Potentials for Active Brownian Particles
• Fractional Brownian motion in a finite interval: correlations effect depletion or accretion zones of particles near boundaries
• Thermodynamic Casimir Forces between a Sphere and a Plate: Monte Carlo Simulation of a Spin Model
• Effective forces between colloids at interfaces induced by capillary wave-like fluctuations
• Critical Casimir Forces and Colloidal Phase Transitions in a Near-Critical Solvent : A Simple Model Reveals a Rich Phase Diagram
• The Importance of Boundary Conditions for Fluctuation Induced Forces between Colloids at Interfaces
• Relaxation phenomena at criticality
• Transient coarsening and the motility of optically heated Janus colloids in a binary liquid mixture
• Three-body critical Casimir forces
• Critical and near critical phase behaviour and interplay between the thermodynamic Casimir and van der Waals forces in confined non-polar fluid medium with competing surface and substrate potentials
• Probing interface localization-delocalization transitions by colloids
• Bridging transitions and capillary forces for colloids in a slit

Cited by in corpus (9)

• Critical Casimir Effect: Exact Results
• Dynamics of a colloidal particle coupled to a Gaussian field: from a confinement-dependent to a non-linear memory
• Memory-induced oscillations of a driven particle in a dissipative correlated medium
• Stochastic thermodynamics of a probe in a fluctuating correlated field
• Tracer particle in a confined correlated medium: an adiabatic elimination method
• Inducing oscillations of trapped particles in a near-critical Gaussian field
• Structure and dynamics of a Rouse polymer in a fluctuating correlated medium
• Recoil of a driven tracer in a correlated medium
• Nonequilibrium relaxation of a trapped particle in a near-critical Gaussian field