Dynamic Transition in a Two-Component Fluid in the Supercooled State

A mode-coupling model has been proposed to study the dynamics of a dense binary fluid. The present model includes a correct set of slow variables, which are consistent with the corresponding conservation laws. From the equations of fluctuating hydrodynamics for slow variables, a coupled set of nonlinear equations for various time-dependent correlations of density fluctuations are obtained. In the long-time limit, a self-consistent solution of these equations shows a dynamic transition, which occurs at a much higher density than predicted by the other existing models for the same systems. Our model brings the theoretical prediction for dynamic transition in better agreement with the simulation results for these systems. We have considered a hard sphere binary mixture to make a direct comparison of our results with the predictions of models studied in earlier works.