Although many experimental studies over the years have shown strong (inverse) correlation between excess viscosity and excess volume of a binary mixture, there does not seem to exist any microscopic theoretical study of such behavior. In this work, we introduce and study two new models of binary mixture with the aim of removing this lacuna. Our models consist of a mixture of two molecular species (1 and 2) with the same diameter and mass but varying solute-solvent Lennard-Jones interactions. In model I, the two different species are strongly attractive, while in model II, the attraction is weaker than that between the pure components. That is, model I encourages structure formation, while the reverse is true for model II. Extensive constant pressure-constant temperature (NPT) molecular dynamics (MD) simulations have been carried out which show that these models can indeed reproduce the strong inverse correlation between the calculated excess volume and excess viscosity. The two models show opposite trends in the composition dependence. Another interesting result is the observation of a re-entrant behavior in the excess volume dependence of total viscosity of the mixture-the same re-entrance is also observed in the dependence of excess viscosity on excess volume. In addition, we derive the first two terms in the virial expansion for the composition dependence, for the infinite frequency shear modulus, G(infinity). These terms can explain the composition dependence at low composition in terms of partial radial distribution functions and interaction potentials, The calculated self-diffusion coefficients have nonmonotonic behavior and show considerable deviations from Stokes-Einstein relation.