Mass transfer to reactive boundaries from steady three-dimensional flows in microchannels

This paper presents a numerical study of the effect of transverse secondary flows on mass transfer to reactive boundaries in microchannels. The geometry considered is relevant to surface catalyzed reactions, fuel cells, biochemical sensors, and other microreactor applications. The 3D flows that we consider approximate flows that are experimentally achievable through topographical patterning of one wall of a microchannel, as in the Staggered Herringbone Mixer (SHM) and similar geometries. We simulate a mass transfer process using passive tracers to model reactive solute molecules in a Stokes flow (Reynolds number, Re=0) over a range of Peclet number, 10(2)<= Pe <= 10(5), with instantaneous kinetics at the reactive boundary. Our simulation allows for the evaluation of the local Sherwood number produced by a uniaxial Poiseuille flow and several chaotic and nonchaotic 3D flows. In chaotic flows, the local Sherwood number evolves in a simple manner that shares features with the classic Graetz solution for transfer from a uniaxial pipe flow: an entrance region with cube-root scaling in the Graetz number and a constant asymptotic value. This "Modified Graetz" behavior also differs in important ways from the standard case: the entrance length is Pe independent and the asymptotic rate of transfer is Pe dependent and potentially much greater than in the uniaxial case. We develop a theoretical model of the transfer process; the predictions of this model compare well with simulation results. We use our results to develop a correlation for the mass transfer in laminar channel flows, to elucidate the importance of chaos in defining transfer in these flows, and to provide design rules for microreactors with a single reactive wall. (c) 2006 American Institute of Physics.