Effective medium theory for viscoelasticity of soft jammed solids

¹ Graduate School of Arts and Sciences, The University of Tokyo - Tokyo 153-8902, Japan
² Research Center for Complex Systems Biology, Universal Biology Institute, The University of Tokyo Tokyo 153-8902, Japan

Received: 30 August 2024
Accepted: 15 October 2024

Abstract

The viscoelastic properties of soft jammed solids, such as foams, emulsions, and soft colloids, have been extensively studied in experiments. A particular focus has been placed on the phenomenon of anomalous viscous loss, characterized by a storage modulus and a loss modulus , where ω represents the frequency of the applied strain. In this work, we aim to develop a microscopic theory that explains these experimental observations. Our approach is based on effective medium theory (EMT), also referred to as coherent potential approximation theory. By incorporating the effects of contact damping, a key characteristic of soft jammed solids, into the EMT, we offer new insights into the viscoelastic behavior of these materials. The theory not only explains the observed viscoelastic properties but also links the anomalous viscous loss to the marginal stability inherent in amorphous systems. This research lays the groundwork for a microscopic theory that effectively describes the impact of damping on soft jammed solids and their characteristic viscoelastic behaviors.