Manipulating transport properties of passive tracers in channels via cross section

Traditionally, theory developed for dispersion of passive tracers has focused on predicting the effect of anomalous diffusion which occurs as the result of laminar flow. This theory has had success matching with both experiment and numerical simulation. However, precise control of tracer distribution is more challenging. Our prior work has established similar agreements between theory, simulation, and experiment in predicting a tracer distribution's skewness. In particular, we developed asymptotic theory which predicts the sign differences seen in skewness depending on cross section -- and this showed agreement with experiment. However, these studies relied mainly on idealized cross-sectional shapes, and left an open question about questions of optimality and channel design for specific purposes. Here, I will present a computational framework to extend this work past idealized cross sections and explore questions in shape optimization towards precise control of the tracer distribution.