To measure rate constants while performing biomolecular interaction analysis (BIA), scientists often use resonant mirror devices such as the IAsysTM. A full mathematical model of the IAsysTM consists of a convection–diffusion equation in a closed well with a reacting surface at the bottom. The flow in the well is complex, but near the sensor, the qualitative nature of the reaction can be analyzed by reducing to stagnation point flow. The concentration of the reacting species in several cases is analyzed using singular perturbation techniques. Linear and nonlinear integral equations result from the analysis; explicit and series solutions are constructed for physically realizable cases. These solutions, which include the effects of transport on the reaction, provide improved estimates for the rate constants from raw IAsysTM binding data.