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We study a mesoscopic model for the flow of amorphous solids. The model isbased on the key features identified at the microscopic level, namely peri- odsof elastic deformation interspersed with localised rearrangements of parti-cles that induce long-range elastic deformation. These long-range deformationsare derived following a continuum mechanics approach, in the presence of solidboundaries, and are included in full in the model. Indeed, they mediate spatialcooperativity in the flow, whereby a localised rearrangement may lead a distantregion to yield. In particular, we simulate a channel flow and findmanifestations of spatial cooperativity that are consistent with publishedexperimental obser- vations for concentrated emulsions in microchannels. Twocategories of effects are distinguished. On the one hand, the coupling ofregions subject to different shear rates, for instance,leads to finite shearrate fluctuations in the seemingly un- sheared "plug" in the centre of thechannel. On the other hand, there is convinc- ing experimental evidence of aspecific rheology near rough walls. We discuss diverse possible physicalorigins for this effect, and we suggest that it may be associated with thebumps of particles into surface asperities as they slide along the wall.

A mesoscopic model for the rheology of soft amorphous solids, with application to mi- crochannel flows