Driven colloidal fluids: construction of dynamical density functional theories from exactly solvable limits

Abstract

The classical dynamical density functional theory (DDFT) provides an approximate extension of equilibrium DFT to treat nonequilibrium systems subject to Brownian dynamics. However, the method fails when applied to driven systems, such as sheared colloidal dispersions. The breakdown of DDFT can be traced back to an inadequate treatment of the flowinduced distortion of the pair correlation functions. By considering the distortion of the pair correlations to second order in the flow-rate we show how to systematically correct the DDFT for driven systems. As an application of our approach we consider Poiseuille flow. The theory predicts that the particles will accumulate in spatial regions where the local shear rate is small, an effect known as shear-induced migration. We compare these predictions to Brownian dynamics simulations with generally good agreement.

Microstructure of Flow-Driven Suspension of Hardspheres in Cylindrical Confinement: A Dynamical Density Functional Theory and Monte Carlo Study

“…32,35,36 In the presence of transient diffusion or applied flows, the nonequilibrium effects may be incorporated in the DFT formalism and this generalized procedure is referred to as the dynamical density functional theory (DDFT), 37–40 which has been successful in predicting the flow-driven particle correlations with weak or no hydrodynamic interactions. 41–44 …”

“…In order to account for the fluid inertia in the framework, we apply rigorous ensemble averaging to relate the single-particle migration velocity to the flow-perturbed average particle distribution through the consideration of an additional work term in the total free energy functional. Other DDFT studies in the past have similarly investigated the microstructure of colloidal fluid flows in the limit of zero Reynolds number confined between boundaries by including the distortion of the particle pair correlation due to the flow in the limit of zero Reynolds number, 41,44 Our current effort is an attempt to bridge the prevailing physics of the system over various fluid hydrodynamic time scales with its long-time configuration by employing appropriate free energy descriptions. We also put forward a complimentary approach to predict the spatially varying densities under flow conditions using Monte Carlo (MC) simulations.…”

Shear-induced migration in colloidal suspensions

“…In Refs. [7,16] a dynamical density functional theory was developed, which incorporates the physics of shear-induced migration in a mean-field fashion. It would be interesting to exploit the numerical data presented in this work to optimize the approximations employed in the theory -particularly for the case of attractive interparticle interactions.…”

“…Since the original phenomenological theory of Leighton and Acrivos [13] there have been a variety of theoretical, simulation and experimental studies addressing migration physics [14][15][16][17][18][19][20][21].…”

Structural Nonequilibrium Forces in Driven Colloidal Systems

“…From the time evolution in the exact (Smoluchowski) low-density limit, Brownian dynamics simulations and a novel power functional approximation, we obtain a quantitative understanding of viscous and structural forces, including memory and shear migration.It is a very significant challenge of Statistical Physics to rationalize and predict nonequilibrium structure formation from a microscopic starting point. Primary examples include shear banding [1][2][3], where spatial regions of different shear rate coexist, laning transitions in oppositely driven colloids [4,5], where regions of different flow direction occur, as well as migration effects in inhomogeneous shear flow [6][7][8][9][10][11]. In computer simulations, discriminating true steady states from slow initial transients can be difficult [12,13].…”