How are mobility and friction related in viscoelastic fluids?

TL;DR

This study explores the relationship between mobility and friction in viscoelastic fluids, combining theoretical models and experiments to generalize Einstein's relation and understand how these properties vary with concentration.

Contribution

The paper introduces a generalized Einstein relation for viscoelastic fluids and links recoil and MSD to separate memory kernels, supported by theoretical models and experimental validation.

Findings

Recoil and MSD reveal different behaviors of friction and mobility kernels with concentration.

A Volterra relation connects the two kernels, explaining their differing timescales.

Generalized Einstein's relation applies to viscoelastic fluids, unifying mobility and friction concepts.

Abstract

The motion of a colloidal probe in a viscoelastic fluid is described by friction or mobility, depending on whether the probe is moving with a velocity or feeling a force. While the Einstein relation describes an inverse relationship valid for Newtonian solvents, both concepts are generalized to time-dependent memory kernels in viscoelastic fluids. We theoretically and experimentally investigate their relation by considering two observables: the recoil after releasing a probe that was moved through the fluid and the equilibrium mean squared displacement (MSD). Applying concepts of linear response theory, we generalize Einstein's relation and thereby relate recoil and MSD, which both provide access to the mobility kernel. With increasing concentration, however, MSD and recoil show distinct behaviors, rooted in different behaviors of the two kernels. Using two theoretical models, a linear two-bath particle model and hard spheres treated by mode-coupling theory, we find a Volterra relation between the two kernels, explaining differing timescales in friction and mobility kernels under variation of concentration.