Sample delivery is a crucial aspect of point-of-care applications where sample volumes need to be low and assay times short, while providing high analytical and clinical sensitivity. In this paper, we explore the influence of the factors surrounding sample delivery on analyte capture in an immunoassay-based sensor array manifold of porous beads resting in individual wells. We model using computational fluid dynamics and a flow-through device containing beads sensitized specifically to C-reactive protein (CRP) to explore the effects of volume of sample, rate of sample delivery, and use of recirculation vs. unilateral delivery on the effectiveness of the capture of CRP on and within the porous bead sensor. Rate of sample delivery lends to the development of a time-dependent, shrinking depletion region around the bead exterior. Our findings reveal that at significantly high rates of delivery, unique to porous bead substrates, capture at the rim of the bead is reaction-limited, while capture in the interior of the bead is transport-limited. While the fluorescence signal results from the aggregate of captured material throughout the bead, multiple kinetic regimes exist within the bead. Further, under constant pressure conditions dictated by the array architecture, we reveal the existence of an optimal flow rate that generates the highest signal, under point-of-care constraints of limited-volume and limited-time. When high sensitivity is needed, recirculation can be implemented to overcome the analyte capture limitations due to volume and time constraints. Computational simulations agree with experimental results performed under similar conditions.