Element Diffusion and Other Mixing in White Dwarf Stars

White dwarf stars reveal signatures of material accreted from their surroundings. Making quantitative inferences about the processes that supply this material requires theoretical models of white dwarf surface structure. In this dissertation, I examine methods for building evolutionary white dwarf models that include element diffusion, convection, and thermohaline instability. Each of these mixing processes that occur at white dwarf surfaces has important implications for observable signatures of accreted material. Models that account for all types of surface mixing allow for inferences about accretion rates and composition of bodies that supply the material. The picture that emerges from models presented in this work is one of planetary systems supplying rocky debris at higher rates and from larger mass reservoirs than previously thought