Spatial cooperativity in soft glassy flows

Abstract

Amorphous glassy materials of diverse nature-concentrated emulsions, granular materials, pastes, molecular glasses-display complex flow properties, intermediate between solid and liquid, which are at the root of their use in many applications. A general feature of such systems, well documented yet not really understood, is the strongly nonlinear nature of the flow rule relating stresses and strain rates. Here we use a microfluidic velocimetry technique to characterize the flow of thin layers of concentrated emulsions, confined in gaps of different thicknesses by surfaces of different roughnesses. We find evidence for finite-size effects in the flow behaviour and the absence of an intrinsic local flow rule. In contrast to the classical nonlinearities of the rheological behaviour of amorphous materials, we show that a rather simple non-local flow rule can account for all the velocity profiles. This non-locality of the dynamics is quantified by a length, characteristic of cooperativity within the flow at these scales, that is unobservable in the liquid state (lower emulsion concentrations) and that increases with concentration in the jammed state. Beyond its practical importance for applications involving thin layers (for example, coatings), these non-locality and cooperativity effects have parallels in the behaviour of other glassy, jammed and granular systems, suggesting a possible fundamental universality.

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

“…This is however not the case: the normalized profiles collapse on the same master curve independent of the applied shear, and emphasize that the shear rate is greater at the wall than in the center of the channel. This non-local effect has been discussed in terms of plastic rearrangements of the flow [10,11,13,14]. It is therefore of great interest to provide direct dynamic evidence of such plastic events.…”

“…A step towards this goal has been taken in recent works [8,11,14], where the rate of plastic events is connected to the "fluidity" field, defined as the ratio between the shear rate and the stress, f =γ σ . By using a kinetic model for the elasto-plastic dynamics of the stress distribution function, the local fluidity is shown to obey (in the steady state) the following equation…”

“…without the perturbing effects of the boundaries. The fluidity model has been tested with considerable success both in experiments [11,14,18] and in molecular dynamics simulations [10]. Under the hypothesis of low cooperativity, the model predicts proportionality between the fluidity and the rate of plastic events [10,18].…”

“…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. One needs to properly bridge between local and global rheology of the soft-glasses, an issue that has been recently addressed in several papers [11][12][13]. In [8,11,13,14] it was suggested that such a bridge can be established by introducing a cooperativity scale which determines correlations (non-local effects) in the flow rheology.…”

“…The peculiar features of plastic events are investigated below and above the yield stress threshold. Above the yield stress, the "fluidity" model recently introduced by Goyon et al [10,11,14,18] captures the essential features of the flow: fluidity changes near the boundaries on a scale ξ which is close to the stress correlation scale and to the characteristic scale of plastic events. Near the yield stress, however, the cooperativity scale can not be estimated with enough accuracy, whereas the stress correlation scale shows a clear increase.…”