Cooperativity flows and shear-bandings: a statistical field theory approach.
Cooperativity effects have been proposed to explain the non-local rheology in the dynamics of soft jammed systems. Based on the analysis of the free-energy model proposed by L. Bocquet, A. Colin and A. Ajdari, Phys. Rev. Lett., 2009, 103, 036001, we show that cooperativity effects resulting from the non-local nature of the fluidity (inverse viscosity) are intimately related to the emergence of shear-banding configurations. This connection materializes through the onset of inhomogeneous compact solutions (compactons), wherein the fluidity is confined to finite-support subregions of the flow and strictly zero elsewhere. The compacton coexistence with regions of zero fluidity ("non-flowing vacuum") is shown to be stabilized by the presence of mechanical noise, which ultimately shapes up the equilibrium distribution of the fluidity field, the latter acting as an order parameter for the flow-noflow transitions occurring in the material.
Department of Physics and INFN, University of "Tor Vergata", Via della Ricerca Scientifica 1, 00133 Rome, Italy. sbragaglia@roma2.infn.it.
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Benzi
Department of Physics and INFN, University of "Tor Vergata", Via della Ricerca Scientifica 1, 00133 Rome, Italy. sbragaglia@roma2.infn.it.
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Sbragaglia
Istituto per le Applicazioni del Calcolo CNR, Via dei Taurini 19, 00185 Rome, Italy.
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Bernaschi
Istituto per le Applicazioni del Calcolo CNR, Via dei Taurini 19, 00185 Rome, Italy.
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Succi
Istituto per le Applicazioni del Calcolo CNR, Via dei Taurini 19, 00185 Rome, Italy and Department of Physics and Department of Mathematics and Computer Science and J. M. Burgerscentrum, Eindhoven University of Technology, 5600 MB, Eindhoven, Netherlands.
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Toschi