Local mass transport in two-dimensional cavities in laminar shear flow

The local mass-transfer rate was investigated along the bottom wall of two-dimensional cavities of nominally rectangular shape, 100 μm wide, and aspect ratio (depth/width) 0.5. Experimental measurements were made by an electrochemical limiting current technique based on reduction of K₃Fe(CN)₆ at gold ultramicroelectrodes, each 10 μm wide and spaced 1 μm apart. Experiments were carried out in the presence of laminar fluid flow in the range between Stokes flow and turbulent flow (0.068<Re<2400). Numerical computations of two-dimensional, laminar, convective diffusion were carried out with use of (a) a research grade finite-difference code (ERMES) and (b) a commercial grade finite-element program (FIDAP). In addition, ERMES was implemented for numerical computations of two-dimensional, multispecies transport by convection, diffusion, and migration under laminar flow. The simulations carried out for both rectangular (ERMES) and undercut (FIDAP) cavity shapes indicated that the hydrodynamic profiles consisted of a major recirculating vortex in the cavity and a pair of relatively small eddies inside the two corners at all flow rates studied. The simulations indicated that above an aspect ratio of 0.33 the hydrodynamic flow pattern for a rectangular cavity changed from a major single eddy to isolated corner eddies. In the convective regime, experimental and theoretical results agreed in average mass-transport rates to the surface and in the local flux distributions but differed in predicting the location of the maximum.