Diffusion and trapping in a suspension of spheres with simultaneous reaction in the continuous phase

Much progress has been made in modeling the reaction of Brownian particles with spherical traps. Previously, work has focused on the effective reaction rate of systems of particles that diffuse freely until they are trapped by spheres in the dispersion. A particularly effective and efficient method to describe the reacting system is based on first-passage time distributions, from which an effective reaction rate coefficient of the suspension can be determined. The analysis presented here addresses reaction and diffusion in systems in which particles can undergo reaction in the continuous phase as well as reaction at the sphere surface. The first-passage method is extended to allow reaction or decay of the diffusing species in the continuous phase. The diffusion path is divided into a series of first-passage regions and is considered the probability of the particle being consumed in each of these regions. This allows the determination of the total reaction rate of the suspension (continuous phase reaction plus trapping) and the relative consumption rate in each phase. The extended method is applied to a model system of concentric spheres with a known continuum solution. It is shown to be accurate for consumption of reactant in the continuous phase from approximately 0 to approximately 100%. The method then is applied to a suspension of spheres.