  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.
