Effective confinement as origin of the equivalence of kinetic temperature and fluctuation-dissipation ratio in a dense shear-driven suspension

Abstract

We study response and velocity autocorrelation functions for a tagged particle in a shear driven suspension governed by underdamped stochastic dynamics. We follow the idea of an effective confinement in dense suspensions and exploit a time-scale separation between particle reorganization and vibrational motion. This allows us to approximately derive the fluctuation-dissipation theorem in a "hybrid" form involving the kinetic temperature as an effective temperature and an additive correction term. We show numerically that even in a moderately dense suspension the latter is negligible. We discuss similarities and differences with a simple toy model, a single trapped particle in shear flow.

Resonant behavior of trapped Brownian particles in an oscillatory shear flow

“…In the static limit ( = 0), several aspects of this problem have been addressed previously, for example, diffusion [38], inertial effects [31], dynamic properties [33], fluctuationdissipation relations [34,39], the probability distribution in the overdamped limit [32], or retardation effects [40]. In the following, we focus on the oscillatory case with > 0 and explore the influence of the periodic flow on the dynamics of a single particle (Sec.…”

“…Compared to static shear flow [31,34], the coefficient matrix A(t) now becomes time dependent and reads…”

“…This could be pivotal to constructing new antenna systems, for example, ultrasonic emitters [30]. Second, more fundamentally, even the case of a single trapped particle is interesting since analytical solutions have been presented for the linear-shear case [31][32][33][34]. Due to the stochastic Brownian force, these solutions are nontrivial and exhibit interesting particle distribution functions and shearinduced cross-correlations.…”

Driven Brownian particle as a paradigm for a nonequilibrium heat bath: Effective temperature and cyclic work extraction

“…However, in complex fluids or biological matter this kind of dynamical time-scale separation is the exception rather than the rule. In this regime of mixed time scales, time-dependent FDRs have been studied, i.a., for active matter [5,11,[14][15][16][17][18][19], sheared colloidal suspensions [10,20,21] and single biomolecules [12]. In a heuristic approach introduced in the glassy context [2,7] and revisited for driven Brownian [15,16,22] and ageing [23] systems, the effective temperature is identified with the measurement by a thermometer.…”

Brownian systems perturbed by mild shear: Comparing response relations

“…One more fact is that underdamped Brownian particles have been investigated much less frequently than overdamped ones, because the latter model is more simple yet widely applicable in many practical cases. Even if the particle inertia is formally considered [19,26,32,[35][36][37][38][39], typically, little attention is paid to its effect on the system response. On the other hand, it was proven that inertial effects play an important role at short time scales [40][41][42][43][44][45].…”