Transport in laminar flows: Peristalsis and Taylor dispersion

This dissertation employs analytical and numerical techniques to compute transport in two types of laminar flow problems: net transport in high-frequency peristaltically driven flows in closed rectangular channels and species transport in Poiseuille-like flows through constricted channels. We use averaging techniques to eliminate the less important transport details and compute only the more physically relevant and measurable quantities such as the net transport over time in the first problem and the streamwise mean and spread of the cross-sectionally averaged solute concentration in the second.; The high-frequency, low-amplitude, peristaltically driven flows we have examined model the fluid transport in prototype MEMS devices which operate on a peristaltic principle. We employ asymptotic analysis to compute analytically the time-averaged Eulerian and Lagrangian velocities and describe the boundary-layer structure of the flow in such devices in the limit of high frequencies, clearly indicating the dependence of the flow on these frequencies. It is determined that in the high-frequency limit, the dominant flow is confined to a thin boundary-layer near the oscillating wall where time-averaged velocities scale as the square-root of the driving frequency.; Taylor dispersion in channels with localized spatial non-uniformities such as constrictions or bulges is also examined. A one-dimensional transport equation is derived, describing the evolution of the cross-sectionally averaged solute concentration in channels with slowly varying cross sections, and this equation is solved both analytically and numerically for a variety of channel shapes. Results for channels with constrictions and bulges are compared to the well-known straight channel results, and the effect of these spatial non-uniformities is analyzed and quantified. We demonstrate that the effect of such spatial non-uniformities on Taylor dispersion can be characterized by a single number—the equivalent dispersivity $Dr$ in such regions. Results are useful for modeling the transport of drugs in stenosed arteries, as well as transport of reactants in lab-on-a-chip MEMS devices. In addition, our theoretical findings provide a framework for constructing graphs or tables containing dispersion information for different spatial non-uniformities, which in turn can be used similarly to the way friction factors are used to predict approximate solvent behavior.