Affiliation: College of Arts and Sciences, Department of Mathematics
This dissertation is concerned with understanding how the behavior of a concentration of tracer undergoing an advection-diffusion process in Poiseuille flows depends on the pipe cross-section.
Solutions to the advection-diffusion problem are approached both for the longitudinal moments of the concentration, via exact and asymptotics analysis, and for the entire tracer concentration, via analysis and experiments. The main focus of this work is on the skewness of the distribution, which is the simplest statistic to describe longitudinal asymmetries in the tracer concentration. The results of exact and asymptotic analysis along with experiments and numerical simulations, show that the distribution’s skewness depends significantly on the cross section of the pipe.