Laminar Forced Convection Mass Transfer to Ordered and Disordered Single Layer Arrays of Micro-Spheres

We study laminar forced convection mass transfer to single layer arrays of equidistantly and non-equidistantly spaced micro-spheres. We report average Sherwood numbers as a function of geometry and flow conditions, for open frontal area fractions between 0.04 and 0.95, Schmidt numbers between 0.7 and 10, and Reynolds numbers (based on micro-sphere diameter and the free stream velocity) between 0.1 and 100. For equidistantly spaced arrays of micro-spheres we propose a general analytical expression for the average Sherwood number as a function of the Reynolds number, Schmidt number and the open frontal area fraction, as well as asymptotic scaling rules for small and large Reynolds. For all studied Schmidt numbers, equidistant arrays exhibit decreasing average Sherwood numbers for decreasing open frontal area fractions at low Reynolds numbers. For high Reynolds numbers, the Sherwood number approaches that of a single spheres in cross-flow, independent of the open frontal area fraction. For equal open frontal area fractions, the Sherwood number in non-equidistant arrays is lower than in equidistant arrays for intermediate Reynolds numbers. For very low and high Reynolds numbers, non-uniformity does not influence mass transfer.