Interfacial Mass Transfer In Microfluidic Systems: Existence And Persistence Of The Modified Graetz Behavior
In the works contained in this dissertation, we study interfacial mass transfer to stationary, moving, and diffusive interfaces in steady, laminar flows in microfluidic systems. These processes operate in the low Reynolds number, high Peclet number regime, where, for uniaxial flows, the absence of turbulence leads to poorly mixed bulk flows and a thick region depleted of solute (called the concentration boundary layer) near the reactive interface. The classic solutions for mass transfer to the walls of a pipe in uniaxial flow, due to Graetz and Leveque, present an entrance region where the reactive flux drops quickly as the boundary layer thickness increases and an asymptotic region where the boundary layer has grown to the full thickness of the pipe and the shape of the concentration profile becomes self-similar. We present a generalization of the classic solutions to the case of three-dimensional flow, called the modified Graetz behavior: the transverse flow sweeps depleted fluid away from the reactive interface, keeping the boundary layer thin and maintaining high gradients of concentration and therefore high rates of mass transfer. Casting the problem in terms of the Sherwood number (a non-dimensionalized mass transfer coefficient), we distill the full convection-diffusion problem in a mathematically tractable form that leads to predicted correlations in uniaxial and three-dimensional flows. The local Sherwood number and the shape of the concentration profile in the cross section allow for the investigation of the role of Lagrangian chaos in maintaining this modified Graetz behavior at arbitrarily large axial distance and Peclet number: chaos ensures that fluid swept away from the reactive surface is homogenized with the bulk before it returns to the reactive surface. We approach the problem by three methods: numerically - building the flux profile, concentration field, and local Sherwood number from particle trajectories; theoretically - generalizing the classic Graetz result to three-dimensional flow and moving interfaces; and experimentally, with studies of an electrochemical potential cell to extract the average Sherwood number from measurements of the total current. Our numerical and experimental results support the theoretical predictions and inform the design of efficient microfluidic reactors.
dissertation or thesis