Time-dependent active microrheology in dilute colloidal suspensions

Abstract

In a microrheological set-up a single probe particle immersed in a complex fluid is exposed to a strong external force driving the system out of equilibrium. Here, we elaborate analytically the time-dependent response of a probe particle in a dilute suspension of Brownian particles to a large step-force, exact in first order of the density of the bath particles. The time-dependent drift velocity approaches its stationary state value exponentially fast for arbitrarily small driving in striking contrast to the power-law prediction of linear response encoded in the long-time tails of the velocity autocorrelation function. We show that the stationary-state behavior depends nonanalytically on the driving force and connect this behavior to the persistent correlations in the equilibrium state. We argue that this relation holds generically. Furthermore, we elaborate that the fluctuations in the direction of the force display transient superdiffusive behavior.

Critical force in active microrheology

“…The schematic model defined by ( 7)- (10) has the free parameters τ s , κ , κ ⊥ , F ext , v s 1 , v s 2 and f b . The bath nonergodicity parameter f b will be parametrized through the distance ε to the critical point (viz.…”

“…With these differences in mind, we now turn to the simulation data, and analyze the tracer position correlation functions averaged over time in the range [10,25]…”

“…In this section, we will show how to derive an analytical expression for the critical force and the critical amplitude of the schematic model defined in Eqns. ( 7)- (10) for the case κ = κ ⊥ =: κ. The starting point is the iteration equations for the critical amplitude (18).…”

“…However, it was soon acknowledged that the technique could be significantly improved if the tracer is pulled externally (active microrheology), as both the linear and non-linear regimes can be studied [6,7]. Several models for active microrheology have been presented, based on an effective medium approach [8], the two-particle Smoluchowski equation (for low densities) for stationary [9] and transient regimes [10], the mode-coupling approach (applicable to high densities) [11], the continuous time random walk model [12,13], a kinetically constrained model [13,14]. Simulation studies [15][16][17] and first experimental studies confirmed that the dynamics becomes highly anomalous in glass-forming dispersions [18,19].…”

Transient nonlinear microrheology in hydrodynamically interacting colloidal dispersions: flow cessation

“…Microrheological experimental studies, theoretical models and dynamic simulations have recovered steady-state non-Newtonian behaviours, including force thinning and thickening, flow-induced diffusion, normal stress differences and response to oscillatory flows (Habdas et al 2004;Carpen & Brady 2005;Furst 2005;Squires & Brady 2005;Khair & Brady 2005, 2006, 2007Squires 2008;Gazuz et al 2009;Sriram et al 2009;Wilson et al 2009;Squires & Mason 2010;Zia & Brady 2010;Gnann et al 2011;Schultz & Furst 2011;DePuit & Squires 2012;Zia & Brady 2012, 2013Swan & Zia 2013;Voigtmann & Fuchs 2013;Swan, Zia & Brady 2014;Chu & Zia 2016Hoh & Zia 2016a,b;Nazockdast & Morris 2016;Leitmann et al 2018). But, in both theory and experiment, the majority of the focus thus far has remained on steady-state response of the material, with comparatively little focus devoted to temporal evolution.…”