Many cellular reactions involve a reactant in solution binding to or dissociating from a reactant confined to a surface. This is true as well for a BIAcore^TM, an optical biosensor that is widely used to study the interaction of biomolecules. In the flow cell of this instrument, one of the reactants is immobilized on a flat sensor surface while the other reactant flows past the surface. Both diffusion and convection play important roles in bringing the reactants into contact. Usually BIAcore^TM binding data are analyzed using well known expressions that are valid only in the reaction-limited case when the Damköhler number Da is small. Asymptotic and singular perturbation techniques are used to analyze dissociation of the bound state when Da is small and O(1). Linear and nonlinear integral equations result from the analysis; explicit and asymptotic solutions are constructed for physically realizable cases. In addition, effective rate constants are derived that illustrate the effects of transport on the measured rate constants. All these expressions provide a direct way to estimate the rate constants from BIAcore^TM binding data.