Critical force in active microrheology

Abstract

Soft solids like colloidal glasses exhibit a yield stress, above which the system starts to flow. The microscopic analogon in microrheology is the delocalization of a tracer particle subject to an external force exceeding a threshold value, in a glassy host. We characterize this delocalization transition based on a bifurcation analysis of the corresponding mode-coupling theory equations. A schematic model is presented first, that allows analytical progress, and the full physical model is studied numerically next. This analysis yields a continuous type A transition with a critical power law decay of the probe correlation functions with exponent −1/2. In order to compare with simulations with a limited duration, a finite time analysis is performed, which yields reasonable results for not-too-small wave vectors. The theoretically predicted findings are verified by Langevin dynamics simulations. For small wave vectors we find anomalous behavior for the probe position correlation function, which can be traced back to a wave vector divergence of the critical amplitude. In addition we propose and test three methods to extract the critical force from experimental data, which provide the same value of the critical force when applied to the finite-time theory or simulations.

Tracer dynamics in crowded active-particle suspensions

“…The fact that the effect of the nonequilibrium perturbation on the glassy dynamics of the host system, in fluidizing that system, is underestimated by MCT is in line qualitatively with previous applications of the theory to, for example, sheared colloidal suspensions 25 or active microrheology; [44][45][46][47] also there, the introduction of an empirical scaling factor allowed to bring the theory in quantitative agreement with simulation data. In general, one finds that MCT overestimates the glassiness of the relaxation dynamics, and hence it predicts too slow relaxation for a fixed density j and fixed self-propulsion strength v 0 .…”

“…For a tracer that is driven by an external force of fixed direction, this effect is known 43 and has been studied in the framework of MCT. [44][45][46][47] Here, the theory predicts that above a certain threshold force, the tracer motion delocalizes (as indicated by an MSD that grows without bound even when the host system is glassy). However, in the present theory the situation is less obvious, because the active tracer always has a finite persistence time if D r 4 0, and the limit D r -0 does not necessarily commute with the long-time limit of interest in studying glassy dynamics.…”

Tagged-particle motion in quasi-confined colloidal hard-sphere liquids

“…recent experiments for soft star polymers [81]. Non-monotonic confinement effects should also be present in driven systems like granular matter [82][83][84] and active microrheology [40,85].…”

Fluctuations and Pinning for Individually Manipulated Skyrmions

“…Examples include driving single colloids through assemblies of other colloids [24][25][26][27][28], as well as measuring the changes of the effective viscosity on the driven particle as the system goes through glass [24][25][26][27], or jamming transitions [29,30]. Other studies have explored how the depinning threshold changes in a clean system as the system parameters are varied [25,31,32], as well as the effect of quenched disorder on individually manipulated superconducting vortices and magnetic textures [33][34][35][36][37]. It is also possible to examine changes in the fluctuations as a function of drive while the density of the surrounding medium or the coupling to quenched disorder is changed [29,30,37,38].…”