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. This unexpected finding demonstrates that density functional theories that do not account for thermal fluctuations are incomplete even for ideal systems. 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. * Electronic address: donev@courant.nyu.edu

Classical dynamical density functional theory: from fundamentals to applications

“…Comparisons between DDFT and BD simulations are made frequently. Examples of studies combining DDFT and microscopic simulations consider active particles [20,[296][297][298][299][300], advected DDFT [132], anisotropic pair correlations [286], Brownian aggregation [190,191], canonical dynamics [38], capillary collapse [301], capillary interactions [302], cluster crystallization [244], colloidal fluids in a cavity [272,303], colloidal shaking [294], colloids in a DNA solution [304,305], demixing [306], diffusioncontrolled reactions [307], drag forces [308], driven particles [18,19,[309][310][311], dynamical correlations [312], dynamic mode locking [313], flowing colloids [314], hydrodynamic interactions [41,153,200,210,[315][316][317][318][319][320][321], inhomogeneous polymer systems [322], lane formation [323]…”

“…Regarding applications, the original hydrodynamic DDFTs were used to study sedimentation [133] and oscillations in optical traps [41]. Effects of hydrodynamics in confined systems have also been studied in DDFT [315,316,318,321,405]. Moreover, hydrodynamic DDFT allows to study hydrodynamic interactions in ion diffusion [406], wavenumber-dependent diffusion coefficients [316], crystal growth [189,407], glassy water [209], and velocities of particles subject to hydrodynamic stress [408].…”