Localized Elasticity Governs the Nonlinear Rheology of Colloidal Supercooled Liquids

We propose a microscopic picture for understanding the nonlinear rheology of\nsupercooled liquids with soft-repulsive potentials. Based on Brownian dynamics\nsimulations of supercooled charge-stabilized colloidal suspensions, our\nanalysis shows that the shear thinning of viscosity (eta) at large enough shear\nrates (sr), expressed as eta~sr^(-lambda), originates from the evolution of the\nlocalized elastic region (LER). An LER is a transient region composed of the\nfirst several coordination shells of a reference particle. In response to the\nexternal shear, particles within LER undergo nearly affine displacement before\nthe yielding of LER. The characteristic strain (gamma) and size (xi) of LER\nrespectively depend on the shear rate by gamma~sr^epsilon and xi~sr^(-nu).\nThree exponents, lambda, epsilon, and nu, are related by lambda=1-epsilon=4*nu.\nThis simple relation connects the nonlinear rheology to the elastic properties\nand the microscopic configurational distortion of the system. The relaxation of\nthe LER is promoted by the large-step nonaffine particle displacement along the\nextensional direction of the shear geometry with the step length of 0.4\nparticle diameter. The elastic deformation and the relaxation of the LER are\nubiquitous and succesive in the flow, which compose the fundamental process\ngoverning the bulk nonlinear viscoelasticity. We apply this model to analyze\nthe Rheo-Small Angle Neutron Scattering data of sheared charge-stabilized\ncolloidal suspensions. It is seen that our model well explains the neutron\nspectra and the rheological data.\n