Testing the Validity of the Averaged Approximation for the IAsys

One device used to measure rate constants is the IAsys, and the flow in such a device can be modeled as stagnation point flow. Due to the special nature of the flow, the effects of transport on a surface reaction near a stagnation point may be incorporated exactly as long as the initial concentration of bound state is uniform. However, if the bound state is nonuniform initially, a complicated integrodifferential equation arises for the evolution of the bound state. Such a form is inconvenient for data analysis. The averaged approximation replaces the nonuniform initial state with its average, thus simplifying the analysis. This approximation is correct to O(Da) as the Damköhler number Da → 0. A numerical simulation of the integrodifferential equation is performed which shows that the averaged approximation is useful even outside this regime. Keywords—Surface-volume reactions, integrodifferential equations, numerical simulation, surface plasmon resonance, IAsys. § This work was supported by the University of Delaware Research Foundation. ∗ To whom correspondence should be addressed. E-mail address: [email protected]. This work was supported by the University of Delaware Research Foundation. † Current address: Federal Sector/Defense Group, Computer Sciences Corporation, Moorestown, NJ 08057-0902. Email address: [email protected]. UD Technical Report 2002-3.2