Scaling behavior of the self diffusion coefficients: dependence on the mass ratio of a binary mixture

We calculate the self diffusion coefficients $D_S$ for the species $s=1,2$ of a mixture, and show that a general scaling relation $D_2{\sim}D_1^a$ with a non universal exponent $a$ holds. The generalized diffusion coefficients, dependent on the mass ratio $\kappa=m_2/m_1$ of the constituent particles of the mixture, are computed using a proper formulation of the self-consistent mode coupling theory(MCT). The present model for the dense mixture includes nonlocal and nonlinear effects within the adiabatic approximation of fast decay of momentum fluctuations compared to the density fluctuations. The dependence of the slow dynamics near the characteristic ergodicity-nonergodicity (ENE) transition of the MCT on $\kappa$ is also studied and a reentrant behavior of of $D_1$ with respect to $D_2$, in agreement with simulations is obtained.