Arrays of probe molecules integrated into a microfluidic cell are utilized as analytical tools to screen the binding interactions of the displayed probes against a target molecule. These assay platforms are useful in enzyme or antibody discovery, clinical diagnostics, and biosensing, as their ultraminiaturized design allows for high sensitivity and reduced consumption of reagents and target. We study here a platform in which the probes are first grafted to microbeads which are then arrayed in the microfluidic cell by capture in a trapping course. We examine a course which consists of V-shaped, half-open enclosures, and study theoretically and experimentally target mass transfer to the surface probes. Target binding is a two step process of diffusion across streamlines which convect the target over the microbead surface, and kinetic conjugation to the surface probes. Finite element simulations are obtained to calculate the target surface concentration as a function of time. For slow convection, large diffusive gradients build around the microbead and the trap, decreasing the overall binding rate. For rapid convection, thin diffusion boundary layers develop along the microbead surface and within the trap, increasing the binding rate to the idealized limit of untrapped microbeads in a channel. Experiments are undertaken using the binding of a target, fluorescently labeled NeutrAvidin, to its binding partner biotin, on the microbead surface. With the simulations as a guide, we identify convective flow rates which minimize diffusion barriers so that the transport rate is only kinetically determined and measure the rate constant.