Memory-based mediated interactions between rigid particulate inclusions in viscoelastic environments

TL;DR

This paper develops a formalism to describe the history-dependent interactions between rigid particles in viscoelastic media, covering both fluid-like and elastic behaviors, with applications to particle dragging, magnetic switching, and microswimmer dynamics.

Contribution

It introduces a unified approach to model mediated interactions between particles in viscoelastic environments, encompassing both fluid-like and elastic responses.

Findings

Describes history-dependent particle interactions in viscoelastic media.

Applies the formalism to particle dragging, magnetic switching, and microswimmer behavior.

Provides a foundation for future quantitative studies.

Abstract

Many practically relevant materials combine properties of viscous fluids and elastic solids to viscoelastic behavior. Our focus is on the induced dynamic behavior of damped finite-sized particulate inclusions in such substances. We explicitly describe history-dependent interactions that emerge between the embedded particles. These interactions are mediated by the viscoelastic surroundings. They result from the flows and distortions of the viscoelastic medium when induced by the rigid inclusions. Both, viscoelastic environments of terminal fluid-like flow or of completely reversible damped elastic behavior, are covered. For illustration and to highlight the role of the formalism in potential applications, we briefly address the relevant examples of dragging a rigid sphere through a viscoelastic environment together with subsequent relaxation dynamics, the switching dynamics of magnetic fillers in elastic gel matrices, and the swimming behavior of active microswimmers in viscoelastic solutions. The approach provides a basis for more quantitative and extended investigations of these and related systems in the future.