A model for aging under deformation field, residual stresses and strains in soft glassy materials

Abstract

A model is proposed that considers aging and rejuvenation in a soft glassy material as, respectively, a decrease and an increase in free energy. The aging term is weighted by an inverse of characteristic relaxation time suggesting that greater mobility of the constituents induces faster aging in a material. A dependence of relaxation time on free energy is proposed, which under quiescent conditions leads to a power law dependence of relaxation time on waiting time as observed experimentally. The model considers two cases, namely, a constant modulus when aging is entropy controlled and a time dependent modulus. In the former and the latter cases the model has, respectively, two and three experimentally measurable parameters that are physically meaningful. Overall, the model predicts how the material undergoes aging and approaches a rejuvenated state under the application of a deformation field. In particular, the model proposes distinctions between various kinds of rheological effects for different combinations of parameters. Interestingly, when the relaxation time evolution is stronger than linear, the model predicts various features observed in soft glassy materials such as thixotropic and constant yield stress, thixotropic shear banding, and the presence of residual stress and strain.

Signatures of physical aging and thixotropy in aqueous dispersion of Carbopol

“…Furthermore, a structural kinetic model based on free energy minimization 79 also predicts all the rheological characteristic features of the Carbopol dispersion for m =1 while most rheological characteristic features of the Carbopol dispersion have been reported for n =1. 80 The fact that many predictions of the SGR theory 52,78 and the structural kinetic model 79,80 work well for the Carbopol dispersion renders insight into mechanistic aspects of aging in the same.…”

Power-law creep and residual stresses in a carbopol gel

“…Andrade-like creep and/or residual stresses are commonly predicted from various non-ergodic models for glassy behaviour, including the "Soft Glassy Rheology" (SGR) model derived from local probabilistic descriptions [39], the "Shear Transformation Zone" (STZ) theory [14,37], MCT [4,40] and more phenomenological approaches [30,57]. There, the progressive slowing down of the shear rate observed under creep is attributed to aging, i.e.…”

Distinguishing thixotropy from viscoelasticity

“…We also study the viscoelastic aging constitutive equation proposed by Joshi [50]. Physical aging is known to decrease flowability of a material -also represented as fluidity ( ) -while application of deformation field is known to enhance the same.…”

“…Both these systems have been universally accepted as viscoelastic (non-thixotropic) in the literature [29,[47][48][49]. We also consider two model time dependent systems, namely aqueous clay dispersion and viscoelastic aging model proposed by Joshi [50]. According to Larson and coworkers [29,51], both these systems do not qualify to be called thixotropic over much of the timescale of interest, as they do not reach equilibrium and show physical aging/rejuvenation dynamics.…”