Place: CECAM Workshop on multiscale modelling of amorphous materials: from structure to mechanical properties, Dublin, Ireland
Heterogeneous flow and shear banding are central to the rheology of complex fluids and are widely observed in many industrial and natural materials, such as foams, emulsions, pastes, or even rocks. In the simplest case, shear-banding can be captured by a non-monotonic dependence of the shear stress on shear rate . For certain complex fluids, like colloidal gels, shear banding can be associated to the competition between a structural phase transition and shear . However, in other systems such as dense hard sphere colloidal suspensions  and granular materials  flow heterogeneity is often observed without such accompanying structural changes. The rheological response of these systems is essentially determined by the competition between an inherent slow dynamics (aging) and the acceleration ("rejuvenation") caused by the external drive [5,6]. This may lead to a spatially and temporally heterogeneous flow if the system is close to the yielding threshold [7-9].
It has been recently proposed that flow localization in dense hard-sphere suspensions can be rationalized in terms of flow-concentration coupling , a well-known feedback mechanism for flow instability in complex fluids . In this picture, the coupling between local density fluctuations and local shear rate arises here through the shear-rate dependence of the non-equilibrium (osmotic) pressure and a strongly non-Newtonian shear stress. However, no test of the basic underlying assumptions, such as the presence of a correlation between shear rate and concentration fluctuations or the growth of emergent velocity fluctuations has been provided so far for colloidal hard sphere glasses. This is not surprising, as the relevant density fluctuations that trigger the initial instability are quite small and practically inaccessible to experiments. Furthermore, the available experimental time window for the observation of velocity fluctuations is limited to a few hundred percent strain thus making a temporal analysis rather difficult.
We study this issue via large scale Event Driven Molecular Dynamics (EDMD) simulations of a model glass (a polydisperse hard sphere system). It is shown that fluctuations of the local volume fraction are correlated to the fluctuations of the local shear rate. More precisely, a decrease of local density is accompanied by an increase of the local shear rate and vice versa. Furthermore, we determine both the osmotic pressure and shear stress for a wide range of shear rates and volume fractions, the latter ranging from the supercooled state to the glassy phase. It is shown that an analysis of our data within the framework of shear concentration coupling may indeed lead to the prediction of heterogeneous flow in our simulations.
Furthermore, a detailed analysis of temporal variations of shear rate is performed. For the studied range of shear rates, the time scale of these fluctuations is of the order of a few hundred percent strain. An interpretation of this finding in terms of spatial correlations in the system is proposed. This interpretation is in line with results on correlation volume, obtained from independent measures such as the four point correlation function χ4 as well and the overlap-function.
Moreover, motivated by recent experiments of P. Schall  and coworkers, we address spatial correlations of irreversible plastic rearrangements along various spatial directions. In agreement with experiments, we find isotropic correlations in the supercooled state (where thermal fluctuations dominate the system response) and significant anisotropy in the glassy state.
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 See the talk by P. Schall.