A central element in many processes in physics, chemistry and biology is a reaction between a species immobilized on a surface and a partner that is able to diffuse in solution. However, integrated rate laws for this class of chemical processes have so far only been found in certain special cases. Here, we present a model for the time dependence of an irreversible reaction between particles in a solution of finite volume and a surface. The resulting analytical expression allows quantitative analysis of the transient kinetics of the reaction between soluble particles and a surface. We apply this approach to the analysis of quartz crystal microbalance experiments of protein aggregation under conditions where both reaction and diffusion define the overall kinetics. Furthermore, we use the model to determine absolute mass sensitivity coefficients for soft and rough surfaces, a situation where conventional approaches to determine the mass sensitivity a priori fail.
Keywords: Cottrell equation; Sauerbrey equation; amyloid fibers; depletion; mass sensitivity; quartz crystal microbalance (QCM); surface.