Hydrodynamic fluctuations in quasi-two dimensional diffusion

Abstract

We study diffusion of colloids on a fluid-fluid interface using particle simulations and fluctuating hydrodynamics. Diffusion on a two-dimensional interface with three-dimensional hydrodynamics is known to be anomalous, with the collective diffusion coefficient diverging like the inverse of the wavenumber. This unusual collective effect arises because of the compressibility of the fluid flow in the plane of the interface, and leads to a nonlinear nonlocal convolution term in the diffusion equation for the ensemble-averaged concentration. We extend the previous hydrodynamic theory to account for a species/color labeling of the particles, as necessary to model experiments based on fluorescent techniques. We study the magnitude and dynamics of density and color density fluctuations using a novel Brownian dynamics algorithm, as well as fluctuating hydrodynamics theory and simulation. We find that hydrodynamic coupling between a single tagged particle and collective density fluctuations leads to a reduction of the long-time self-diffusion coefficient, even for an ideal gas of non-interacting particles. Using linearized fluctuating hydrodynamics theory, we show that for diffusion on a fluid-fluid interface, nonequilibrium fluctuations of the total density are small compared to the equilibrium fluctuations, but fluctuations of color density are giant and exhibit a spectrum that decays as the inverse cubed power of the wavenumber. We confirm these predictions through Brownian dynamics simulations of diffusive mixing with two indistinguishable species. We also examine nonequilibrium fluctuations in systems with two-dimensional hydrodynamics, such as thin smectic films in vacuum. We find that nonequilibrium fluctuations are colossal and comparable in magnitude to the mean, and can be accurately modeled using numerical solvers for the nonlinear equations of fluctuating hydrodynamics.

arXiv commentTo appear in J. Stat. Mech. (JSTAT)

References in corpus (25)

• Dynamic Density Functional Theory of Fluids
• Langevin Equation for the Density of a System of Interacting Langevin Processes
• Dynamical density functional theory for interacting Brownian particles: stochastic or deterministic?
• Rapid Sampling of Stochastic Displacements in Brownian Dynamics Simulations
• Hydrodynamic interaction in confined geometries
• Stochastic Eulerian Lagrangian Methods for Fluid-Structure Interactions with Thermal Fluctuations
• Correlated diffusion of membrane proteins and their effect on membrane viscosity
• Dynamical density functional theory with hydrodynamic interactions and colloids in unstable traps
• A reversible mesoscopic model of diffusion in liquids: from giant fluctuations to Fick's law
• Brownian Dynamics without Green's Functions
• Generalized Langevin equations for a driven tracer in dense soft colloids: construction and applications
• Dynamic Density Functional Theory with hydrodynamic interactions and fluctuations
• Inertial Coupling Method for particles in an incompressible fluctuating fluid
• A perturbative path integral study of active and passive tracer diffusion in fluctuating fields
• Fluctuating force-coupling method for simulations of colloidal suspensions
• Stochastic Simulation of Reaction-Diffusion Systems: A Fluctuating-Hydrodynamics Approach
• Brownian Dynamics of Confined Suspensions of Active Microrollers
• The Stokes-Einstein Relation at Moderate Schmidt Number
• Charged hydrophobic colloids at an oil/aqueous phase interface
• Multiscale temporal integrators for fluctuating hydrodynamics
• Finite element discretization of non-linear diffusion equations with thermal fluctuations
• Simulating Brownian suspensions with fluctuating hydrodynamics
• Coupling a nano-particle with isothermal fluctuating hydrodynamics: Coarse-graining from microscopic to mesoscopic dynamics
• Experimental Realization of an Incompressible Newtonian Fluid in Two Dimensions
• Onset of anomalous diffusion in colloids confined to quasi-monolayers

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