A dynamic DFT approach to generalized diffusion equations in a system with long-ranged and hydrodynamic interactions

Interfacial Flow around Brownian Colloids

Understanding the flow created by particle motion at interfaces is a critical step toward understanding hydrodynamic interactions and colloidal self organization. We have developed correlated displacement velocimetry to measure flow fields around interfacially trapped Brownian particles. These flow fields can be decomposed into interfacial hydrodynamic multipoles, including force monopole and dipole flows. These structures provide key insights essential to understanding the interface's mechanical response. Importantly, the flow structure shows that the interface is incompressible for scant surfactant near the ideal gaseous state and contains information about interfacial properties and hydrodynamic coupling with the bulk fluid. The same dataset can be used to predict the response of the interface to applied, complex forces, enabling virtual experiments that produce higher order interfacial multipoles.

Dynamical density functional theory with hydrodynamic interactions in confined geometries

We study the dynamics of colloidal fluids in both unconfined geometries and when confined by a hard wall. Under minimal assumptions, we derive a dynamical density functional theory (DDFT) which includes hydrodynamic interactions (HI; bath-mediated forces). By using an efficient numerical scheme based on pseudospectral methods for integro-differential equations, we demonstrate its excellent agreement with the full underlying Langevin equations for systems of hard disks in partial confinement. We further use the derived DDFT formalism to elucidate the crucial effects of HI in confined systems.

Theory of anomalous collective diffusion in colloidal monolayers on a spherical interface

A planar colloidal monolayer exhibits anomalous collective diffusion due to the hydrodynamic interactions. We investigate how this behavior is affected by the curvature of the monolayer when it resides on the interface of a spherical droplet. It is found that the characteristic times of the dynamics still exhibit the same anomalous scaling as in the planar case. The spatial distribution, however, shows a difference due to the relevance of the radius of the droplet. Since for the droplet this is both a global magnitude, i.e., pertaining to the spatial extent of the spherical surface, and a local one, i.e., the radius of curvature, the question remains open as to which of these two features actually dominates in the case of a generically curved interface.

2D Stokesian Approach to Modeling Flow Induced Deformation of Particle Laden Interfaces

A Stokesian dynamics simulation of the effect of surface Couette flow on the microstructure of particles irreversibly adsorbed to an interface is presented. Rather than modeling both bulk phases, the interface, and particles in a full 3D simulation, known interfacial interactions between adsorbed particles are used to create a 2D model from a top down perspective. This novel methodology is easy to implement and computationally inexpensive, which makes it favorable to simulate behavior of particles under applied flow at fluid-fluid interfaces. The methodology is used to examine microstructure deformation of monodisperse, rigid spherical colloids with repulsive interactions when a surface Couette flow is imposed. Simulation results compare favorably to experimental results taken from literature, showing that interparticle forces must be 1 order of magnitude greater than viscous drag for microstructure to transition from aligned particle strings to rotation of local hexagonal domains. Additionally, it is demonstrated that hydrodynamic interactions between particles play a significant role in the magnitude of these microstructure deformations.

Velocity Gradient Power Functional for Brownian Dynamics

We present an explicit and simple approximation for the superadiabatic excess (over ideal gas) free power functional, admitting the study of the nonequilibrium dynamics of overdamped Brownian many-body systems. The functional depends on the local velocity gradient and is systematically obtained from treating the microscopic stress distribution as a conjugate field. The resulting superadiabatic forces are beyond dynamical density functional theory and are of a viscous nature. Their high accuracy is demonstrated by comparison to simulation results.

Collective colloid diffusion under soft two-dimensional confinement

This work presents a numerical and theoretical investigation of the collective dynamics of colloids in an unbounded solution but trapped in a harmonic potential. Under strict two-dimensional confinement (infinitely stiff trap) the collective colloidal diffusion is enhanced and diverges at zero wave number (like k^{-1}), due to the hydrodynamic propagation of the confining force across the layer. The analytic solution for the collective diffusion of colloids under a Gaussian trap of width δ still shows enhanced diffusion for large wavelengths kδ<1, while a gradual transition to normal diffusion for kδ>1. At intermediate and short wavelengths, we illustrate to what extent the hydrodynamic enhancement of diffusion is masked by the conservative forces between colloids. At very large wavelengths, the collective diffusion becomes faster than the solvent momentum transport and a transition from Stokesian dynamics to inertial dynamics takes place. Using our inertial coupling method code (resolving fluid inertia), we study this transition by performing simulations at small Schmidt number. Simulations confirm theoretical predictions for the k→0 limit [Phys. Rev. E 90, 062314 (2014)PLEEE81539-375510.1103/PhysRevE.90.062314] showing negative density-density time correlations. However, at finite k simulations show deviations from the theory.