2017-07-05
10:15 at HCI D 8

Brownian dynamics of colloids in quasi two-dimensional confinement

Aleksandar Donev

Courant Institute of Mathematical Sciences, New York University, United States

Recent theoretical work has lead to the discovery that diffusion of colloids confined to a two-dimensional flat interface between two fluids is anomalous in a number of unusual ways (see, for example, Bleibel et al., Soft Matter 10(17):2945-2948, 2014). This is because the quasi two-dimensional (q2D) fluid flow on the interface is not divergence free, even though the three dimensional fluid flow in the whole system is divergence free. In particular, this means that the divergence of the hydrodynamic mobility matrix M is not zero, even within the Rotne-Prager approximation, as it is for diffusion in three dimensions. Rather, the Ito stochastic drift term proportional to kT*div(M) looks like a long-ranged electrostatic repulsion between the colloids. This has a number of nontrivial consequences such as a short-time collective diffusion coefficient that diverges as 1/k, where k is the wavenumber.

I will describe an algorithm that can effectively perform Brownian Dynamics of as many as one million colloidal particles confined to diffuse on a planar interface. The algorithm, which is a q2D version of the fluctuating Force Coupling Method (FCM), uses fluctuating hydrodynamics to incorporate Brownian motion and uses two-dimensional FFTs to achive a dramatic speedup over fully three-dimensional simulations. I will present results obtained using this algorithm on diffusive mixing of a binary mixture of particles in q2D, including enhanced collective diffusion, as well as results on giant nonequilibrium fluctuations in q2D. I will discuss the differences with truly two-dimensional systems, as well as particles confined near boundaries, and point to several interesting physical questions that arise from the unusual nature of diffusion in q2D.