Constitutive relations for colloidal gel

TL;DR

This paper critiques traditional continuum theories for colloidal gels, highlighting their limitations, and proposes improved constitutive relations validated by extensive numerical simulations.

Contribution

It introduces new constitutive relations for colloidal gels that better account for their amorphous, stressed state, surpassing traditional stress-free assumptions.

Findings

Traditional theories fail to capture gel heterogeneity.

Proposed relations align well with simulation data.

Validated across diverse gel parameters.

Abstract

The theoretical treatment of depletion gels with central interactions often involves expanding the free energy around a stress-free reference state to derive a constitutive relation between global stress and strain. The premise upon which the previous continuum theories are based, i.e., the stress-free reference state and the affine deformation, both of which do not hold in the context of amorphous gel materials. Gels never reach a true global minimum in the potential energy landscape and contain local regions of significant compressive and tensile stress, interspersed with zero-stress regions. Hence, expansion of free energy around a stressed reference state will produce scalar terms in harmonic expansion, the effects of which are qualitatively different from the terms appearing in the expansion around an unstressed reference state. In this study, we demonstrate the limitations of traditional continuum theories and propose simple constitutive relations that better capture the mechanical response of gel materials. The robustness of the proposed relations is established through large-scale numerical simulations of depletion and frictional gels across a vast parameter space.