How does a soft glassy material flow: finite size effects, non local rheology, and flow cooperativity

In this paper, we investigate the rheological behavior of jammed emulsions in microchannels on the basis of microvelocimetry techniques. We demonstrate that velocity profiles in this confined geometry cannot be accounted for by the bulk - Herschel- Bulkley - rheological flow curve measured independently in a rheometer. A strong dependence of the flow behavior on the confinement, pressure drop and surface roughness is evidenced, which cannot be described by classical rheological descriptions. We show that these behaviors can be rationalized on the basis of a non local rheological model, introducing the notion of local fluidity as a key rheological quantity. The model reproduces the experimental velocity profiles for any confinements and any surface nature. The non-locality is quantified by a length, zeta, characterizing the flow cooperativity of jammed emulsions, and typically of the order of several emulsion droplet diameters. We study the influence of volume fraction, droplet diameter, and emulsions polydispersity on this length.