Rheological constitutive equation for a model of soft glassy materials

Abstract

We solve exactly and describe in detail a simplified scalar model for the low frequency shear rheology of foams, emulsions, slurries, etc. [P. Sollich, F. Lequeux, P. Hébraud, M.E. Cates, Phys. Rev. Lett. 78, 2020Lett. 78, (1997]. The model attributes similarities in the rheology of such "soft glassy materials" to the shared features of structural disorder and metastability. By focusing on the dynamics of mesoscopic elements, it retains a generic character. Interactions are represented by a mean-field noise temperature x, with a glass transition occurring at x = 1 (in appropriate units). The exact solution of the model takes the form of a constitutive equation relating stress to strain history, from which all rheological properties can be derived. For the linear response, we find that both the storage modulus G ′ and the loss modulus G ′′ vary with frequency as ω x−1 for 1 < x < 2, becoming flat near the glass transition. In the glass phase, aging of the moduli is predicted. The steady shear flow curves show power law fluid behavior for x < 2, with a nonzero yield stress in the glass phase; the Cox-Merz rule does not hold in this non-Newtonian regime. Single and double step strains further probe the nonlinear behavior of the model, which is not well represented by the BKZ relation. Finally, we consider measurements of G ′ and G ′′ at finite strain amplitude γ. Near the glass transition, G ′′ exhibits a maximum as γ is increased in a strain sweep. Its value can be strongly overestimated due to nonlinear effects, which can be present even when the stress response is very nearly harmonic. The largest strain γc at which measurements still probe the linear response is predicted to be roughly frequency-independent.PACS numbers: 83.70.Hq, 05.40+j.

Internal dynamics and activated processes in soft-glassy materials

“…Taken all together, these points lend further credit to several results and conjectures presented in the so-glassy literature, particularly to the central idea of effective noise-induced activated escape from free energy random traps. 20,21 However, we wish to highlight that the concept of an effective noise in so glasses was invoked to explain the linear response in the rheological properties. In contrast, the work on SR presented here belongs to the nonlinear regime of nite amplitude oscillations, the amplitude being a nite fraction of the yield strain g Y .…”

“…We also posit that such a level of noise is regulated by the polydispersity of the dispersed phase, which gives rise to a random distribution of free-energy barriers within the diphasic system. The idea of an activated escape from freeenergy barriers due to effective noise is not new and it has been vigorously pursued within the so-called SGR (So-Glassy Rheology) model proposed years back by Sollich et al 10,[20][21][22][23] The SGR builds on Bouchaud's trap model, 24 based on the assumption that temperature alone is unable to achieve complete structural relaxation. Hence, an effective temperature is introduced in the system as the relevant source for plastic rearrangements to occur.…”

Direct evidence of plastic events and dynamic heterogeneities in soft-glasses

“…Some of these systems, referred as simple yield stress fluids (including nonadhesive emulsions and microgels), were shown to flow via a sequence of reversible elastic deformations and local irreversible plastic rearrangements, associated with a microscopic yield stress. These physical ingredients lie at the core of mesoscopic models for soft-glassy dynamics [2][3][4][5][6][7][8][9][10]. A challenging question concerns the emergence of features that are non-homogeneous in space (like, for example, shear bandings), where the global rheology is unable to properly capture the complex space-time behavior of the system.…”

Slow dynamics, aging, and glassy rheology in soft and living matter

“…In the specific case of disordered soft materials that can flow in response to macroscopic strains, metastability can result in anomalous rheology that is understood in terms of the soft glassy rheology (SGR) theory proposed by Sollich et al [29,30]. For those systems whose thermal energy is not sufficient to achieve complete structural relaxation, SGR predicts identical power law frequency dependences of the low-frequency elastic and viscous moduli and identifies the exponent of this power law with a mean field noise temperature.…”