Advection-Dispersion in Fluid Media and Selected Works of Rabi Bhattacharya

In its broadest sense, understanding the dispersion of particles suspended in fluid media is a classic problem that has motivated a tremendous amount of laboratory and field experimentation as well as mathematical and physical theory for centuries. The theory traces back to celebrated work of such historically eminent scientists as Adolf Fick, Albert Einstein, Marian Smoluchowski, Jean Perrin, and Geoffrey I. Taylor, to name a few of the most prominent historic figures. The richness of the problem is reflected in the development of new mathematical, statistical, and computational tools that have resulted from continued explorations of this phenomena beyond the framework of advection-dispersion in a pure liquid. The work of Rabi Bhattacharya, in collaboration with hydrologist Vijay Gupta, stands out for the important theoretical insights provided to contemporary understanding of this phenomena in heterogeneous media over a range of space-time scales. This chapter is an attempt to provide some overview and context for the salient features of these contributions.