(414i) Structural and Rheological Relaxation upon Flow Cessation in Colloidal Dispersions: Transient, Nonlinear Microrheology

We study the impact of particle roughness, Brownian motion, and hydrodynamic interactions on the relaxation in colloidal dispersions by theoretical study of structure and viscosity evolution following the cessation of an imposed flow. In particular, we focus on the disparity in timescales over which microscopic forces – hydrodynamic, Brownian and interparticle – act and influence the structural and rheological behavior utilizing the theoretical framework of active microrheology. In our recent work, we studied the formation of structure during flow startup and its impact on transient evolution of viscosity, finding that the transient rheology is a manifestation of a time evolving balance between microscopic forces, which leads to many interesting rheological behaviors, including transient viscosity overshoots, even for dilute colloidal dispersions. However, open questions remain about how the microscopic forces affect the structure and rheology after the external flow is removed, and how the structural relaxation and the probe motion varies with the external flow strength and strength of hydrodynamic interactions upon flow cessation. We formulate a time dependent Smoluchowski equation that governs the spatiotemporal evolution of the bath particle configuration around a probe particle, and solve it numerically for arbitrary strengths of pre-cessation external flow, and arbitrary strengths of hydrodynamic interactions. Upon flow cessation the stresses arising directly due to the external/hydrodynamic forces dissipate instantaneously, as expected, while the entropic Brownian and interparticle stresses take a finite time to relax. These entropic stresses relax via two processes: (i) the probe springs back immediately after flow cessation, and (ii) Brownian motion drives the bath particles towards an isotropic configuration relieving the concentration gradients in the structure. The rheological behavior shows at least two relaxation modes: an early-time fast relaxation, where the majority of the stresses relax, and a later time slow relaxation. We investigate the relaxation rates for arbitrary strengths of pre-cessation external flow and hydrodynamic interactions, and find that these factors have opposing effects on the relaxation process. While increasing pre-cessation flow strength enhances the relaxation rate, hydrodynamic interactions slow down relaxation as the relative motion between particles decreases. The connection between structural and rheological relaxation is studied, and the dissipation of stored entropic energy upon flow cessation is discussed.