Elastic modulus of a colloidal suspension of rigid spheres at rest

TL;DR

This paper derives a new expression for the elastic modulus of a resting colloidal suspension modeled as a solid, highlighting differences from classical fluid-based estimates and applicability to yield stress systems.

Contribution

It introduces a novel solid-based modeling approach to estimate the elastic modulus of colloidal suspensions at rest, contrasting with traditional fluid-based methods.

Findings

Derived a new elastic modulus expression for colloidal suspensions at rest.

Showed the conditions under which solid and fluid models yield different moduli.

Proposed a hypothesis to reconcile high-frequency modulus estimates with classical fluid approaches.

Abstract

By modeling a colloidal suspension at rest as a solid, a new expression for the linear elastic modulus is obtained. This estimate is valid for a yield stress colloidal suspension submitted to a small strain. Interestingly, it is also possible to construct an hypothesis allowing one to recover the high-frequency modulus classically found by means of a classical ?fluid approach'. However, in most of the situations, the moduli obtained by the two approaches are different.