Memory-induced motion reversal in Brownian liquids

Abstract

We study the Brownian dynamics of hard spheres under spatially inhomogeneous shear, using event-driven Brownian dynamics simulations and power functional theory. We examine density and current profiles both for steady states and for the transient dynamics after switching on and switching off an external square wave shear force field. We find that a dense hard sphere fluid (volume fraction ≈ 0.35) undergoes global motion reversal after switching off the shear force field. We use power functional theory with a spatially nonlocal memory kernel to describe the superadiabatic force contributions and obtain good quantitative agreement of the theoretical results with simulation data. The theory provides an explanation for the motion reversal: Internal superadiabatic nonequilibrium forces that oppose the externally driven current arise due to memory after switching off. The effect is genuinely viscoelastic: in steady state, viscous forces oppose the current, but they elastically generate an opposing current after switch-off.

Shear-induced deconfinement of hard disks

“…The adiabatic construction was used to identify these superadiabatic force contributions. The concept of superadiabatic forces [31,32,44] allows systematic classification [42] of flow and structural effects, including viscous [39][40][41] and structural [41][42][43] force contributions. Future work could be directed at the behavior at low shear rates.…”

“…Functional integration methods were developed [38], and the relevance of local particle number conservation was demonstrated [56,57]. Expressing the superadiabatic free power functional via the velocity gradient [39][40][41][42][43] has facilitated the description of viscous [39,40,42] and of structural superadiabatic force contributions [41][42][43]. Superadiabatic forces are accessible in many-body simulations [32,44,45].…”

Dynamic Decay and Superadiabatic Forces in the van Hove Dynamics of Bulk Hard Sphere Fluids

“…The phenomenological equation of motion (23) of DDFT does not capture the full non-equilibrium dynamics of many-particle systems. Important physical effects such as drag [59], viscosity [58,75] and structural non-equilibrium forces [59,[76][77][78][79][80][81][82]82] are absent. PFT provides a formally exact method for including such effects and for calculating the full current in a non-equilibrium system [52]; see Ref.…”

“…Recently, we have combined viscoelastic, draglike and structural forces to obtain an approximation for superadiabatic forces in the dynamics of the hard sphere van Hove function [57]. This work builds upon an approximation developed for viscolelastic forces in a sheared system of hard spheres [58] and approximations developed for drag-like and structural forces in a binary system of counterdriven hard spheres [59]. In [57], we have shown that superadiabatic forces contribute significantly to the internal force field at all times.…”

Power functional theory for Newtonian many-body dynamics

“…In the light of much recent interest in the study of memory kernels as fundamental objects for collective dynamics (Jung and Schmid, 2016;Jung et al, 2017;Lesnicki et al, 2016), Treffenstädt and Schmidt (2020) considered the hard sphere fluid exposed to transient switching phenomena under shear. Both the spatial variation of the shear field and its time dependence were highly idealized and chosen to trigger strong response of the system.…”