Transient nonlinear microrheology in hydrodynamically interacting colloidal dispersions: flow cessation

Abstract

Relaxation of a colloidal dispersion following flow shutoff occurs over distinct time scales, providing a useful method for identifying microscopic forces that are otherwise difficult to detect. Active microrheology facilitates such interrogation for small-scale systems such as biological cells, where a Brownian probe is driven by an external force through the dispersion and its motion is tracked to infer flow properties. An interplay between external forces, Brownian motion, hydrodynamic interactions and interparticle forces deforms the microstructure surrounding the probe, which alters probe speed. Application of the Stokes drag law relates mean probe speed to the effective viscosity of the embedding medium. We present a micromechanical theoretical model for this relationship during nonlinear transient relaxation upon removal of the external force. Upon cessation, contributions to viscosity linear in the force vanish instantly, but hydrodynamics influences subsequent relaxation, as well as the pre-cessation structure that sets the initial condition. Stronger pre-cessation flow drives faster relaxation of both structure and rheology. Non-equilibrium entropic contributions persist after shutoff, decaying over time. Hydrodynamic interactions slow this relaxation by hindering relative Brownian and interparticle displacements. The dissipation of entropically stored energy produces a deterministic force that drives deterministic probe motion even after the external force is removed, giving a natural connection to the chemical potential. Using this idea, we show that probe back-travel gives a direct measure of the osmotic pressure and the time scale over which entropically stored energy is dissipated. Modelling a range of repulsions provides a platform for particle formulation tuned to desired transient response.