A small-gap effective-temperature model of transient shear band formation during flow

Abstract

Recent Couette-cell shear experiments of carbopol gels have revealed the formation of a transient shear band before reaching the steady state, which is characterized by homogeneous flow.This shear band is observed in the small-gap limit where the shear stress is spatially uniform. An effective-temperature model of the transient shear banding and solid-fluid transition is developed for the small-gap limit. The small-gap model demonstrates the ability of a continuum-constitutive law that is based solely on microstructural rearrangements of the gel to account for this transient behavior, and identifies that it proceeds via two distinct processes. A shear band nucleates and gradually broadens via disordering at the interface of the band. Simultaneously, spatially homogeneous fluidization is induced outside of the shear band where the disorder of the gel grows uniformly. Experimental data are used to determine the physical parameters of the theory, and direct, quantitative comparison is made to measurements of the structural evolution of the gel, its fluidization time, and its mechanical response under plastic flow.Yield stress fluids (YSFs) are ubiquitous in everyday life, and their special properties have merited intense research [1][2][3][4][5][6][7][8][9]. Examples include gels, clay suspensions, foams, concentrated emulsions, and colloids. These seemingly distinct substances exhibit a similar mechanical response when subjected to shear deformation: Below a critical (yield) stress these materials remain elastic, behaving as solids, but above this critical stress they are able to deform and flow as viscous liquids. This characteristic ability makes them extremely sought-after for many applications [10]. In the presence of an applied shear protocol a YSF can exhibit a distinctive mode of deformation known as shear banding, where a region of highly localized strain that is far greater than that of the surrounding material appears. The region, or band, is often long or continuous in the direction of shear and of some finite width perpendicular to the shear. This form of shear localization has been shown to be a common occurrence in the rheology of complex fluids as well as glassy materials in general [11].YSFs are often categorized by the degree of thixotropy they present. Thixotropic YSFs have memory and aging effects that lead to a history dependence, marked e.g. by flow curves that are significantly different when the applied shear rate is ramped up compared to the ramp down. In contrast, nonthixotropic or "simple" YSFs have no apparent history dependence over the timescales of observation. They also tend to have predominantly repulsive interactions between their constituent mesoscopic substructures [12]. More important is the fact that thixotropic YSFs, regardless of the particular material, easily form shear bands.Some known as viscosity-bifurcating YSFs, display shear banding in the steady state, a phenomenon which as been observed in a number of complex fluids including polymers [13][14][15][16] and wormlike mi...

Triggers and signatures of shear banding in steady and time-dependent flows

“…A model foam displayed it in [76,77]. Linear stability analysis and nonlinear simulations predict it in the Rolie-poly model of polymers [17][18][19]24], the soft glassy rheology (SGR) and fluidity models of soft glasses [16,20,78], shear transformation zone (STZ) model of amorphous elastoplastic solids [21,22,79], a mesoscopic model of plasticity [23], and a model of polymer glasses [33].…”

Shear band broadening in simulated glasses

“…Strain localization, also known as shear banding, is a deformation mechanism present in a variety of amorphous systems including gels [1], granular media [2] and metallic glasses [3].…”

Transient inhomogeneous flow patterns in supercooled liquids under shear

“…Presently, most theories on transient shear banding o↵er one of the following three explanations of the phenomenon: an instability of the dynamical equations, a time dependent flow curve being non-monotonic on an intermediate time-scale and an mechanical instability associated with a stress overshoot frequently occurring in the stress-strain curve. 19,20 Extensive research has been carried out both numerically and theoretically on the timedependent formation of shear bands in the transient regime and their possible extension to steady state within the framework of the so-called shear transformation zone model employing e↵ective-temperature thermodynamics [21][22][23][24] , within the fluidity model 25 , in an alternative mesoscopic approach by Jagla 26,27 and within the phenomenological soft-glassy rheology model [28][29][30] . We note that a general criterion for the occurrence of transient shear banding has been proposed by Moorcroft and Fielding 31 , where the authors predict that the onset of shear banding occurs shortly before the stress overshoot, with a correction term depending on the form of the stress-strain curve.…”