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This paper addresses the problem of detecting minute concentrations (nano to pico-molar) of analyte in a fluid flow chamber using an array of surface-based sensors. It is shown that in the mass-transport influenced case, when the rate of transport of analyte is comparable to or smaller than the intrinsic reaction rates at the sensor surface, substantial improvements in the response rate can be obtained from an array of spaced small sensor surfaces relative to a single large surface. Advection-diffusion-reaction models are developed to predict the response of such sensor arrays, which are compared to individual sensor surfaces of the same total area. Formulas are derived for quantifying the improvement in performance and optimal size of the sensors in the array. The results of the model are compared with experimental data obtained for an ion-channel switch biosensor and a surface plasmon resonance biosensor.