Localized elasticity governs the nonlinear rheology of colloidal supercooled liquids

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