Shear-flow-induced distortion of the density distribution and transition from a stationary to an instationary non-equilibrium state of a colloidal particle in a trap

Abstract

The motion of a colloidal particle in a liquid, confined within an optical trap and subjected to a shear flow, is modeled as an overdamped harmonic oscillator in n dimensions. The first n_obs components are associated with the observable variables, while the remaining n_int = n - n_obs components are treated as "internal" or auxiliary variables intended to model complex fluid behavior. Coupling between the components drives the system into a non-equilibrium state. The Smoluchowski equation for the positional density distribution function is used to derive relaxation equations for the relevant averages. Specific results are presented for a plane Couette flow and for the case n_obs = 2 and n_int = 1. The shear-flow-induced effects on the observable averages and on the deformation and preferential orientation of the density distribution are analyzed and compared with numerical data from Brownian Dynamics simulations. A transition from a stationary to a transient state, corresponding to a delocalization of the particle or an escape from the trap, is found when the shear rate of the imposed stationary flow exceeds a critical value.