Dynamic Density Functional Theory with hydrodynamic interactions and fluctuations

Abstract

We derive a closed equation for the empirical concentration of colloidal particles in the presence of both hydrodynamic and direct interactions. The ensemble average of our functional Langevin equation reproduces known deterministic Dynamic Density Functional Theory (DDFT) [Rex and Löwen, Phys. Rev. Lett., 101(14):148302, 2008], and, at the same time, it also describes the microscopic fluctuations around the mean behavior. We suggest separating the ideal (non-interacting) contribution from additional corrections due to pairwise interactions. We find that, for an incompressible fluid and in the absence of direct interactions, the mean concentration follows Fick's law just as for uncorrelated walkers. At the same time, the nature of the stochastic terms in fluctuating DDFT is shown to be distinctly different for hydrodynamically-correlated and uncorrelated walkers. This leads to striking differences in the behavior of the fluctuations around Fick's law, even in the absence of pairwise interactions. We connect our own prior work [A. Donev, T. G. Fai, E. Vanden-Eijnden, J. Stat. Mech., P04004, 2014] on fluctuating hydrodynamics of diffusion in liquids to the DDFT literature, and demonstrate that the fluid cannot easily be eliminated from consideration if one wants to describe the collective diffusion in colloidal suspensions.

Submitted to J. Chem. Phys. See also arXiv:1312.1894

References in corpus (16)

• Anomalous transport in the crowded world of biological cells
• Dynamic Density Functional Theory of Fluids
• Langevin Equation for the Density of a System of Interacting Langevin Processes
• Lattice Boltzmann simulations of soft matter systems
• Dynamical density functional theory for interacting Brownian particles: stochastic or deterministic?
• A Stochastic Immersed Boundary Method for Fluid-Structure Dynamics at Microscopic Length Scales
• Dynamical density functional theory for molecular and colloidal fluids: a microscopic approach to fluid mechanics
• Stochastic Eulerian Lagrangian Methods for Fluid-Structure Interactions with Thermal Fluctuations
• Generalized dynamical density functional theory for classical fluids and the significance of inertia and hydrodynamic interactions
• 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
• Inertial Coupling Method for particles in an incompressible fluctuating fluid
• Fluctuating force-coupling method for simulations of colloidal suspensions
• The overdamped limit of dynamic density functional theory: Rigorous results
• On the controversy over the stochastic density functional equations

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