Diffusion Reaction Interaction for a Pair of Spheres - ETD ...

Hassan, 1985; Teixeira et al., 1994; Poughon et al., 1998; Picioreanu, 1999;
Dillon and Fauci, 2000).
1.4 Diffusive Interaction in the Two-Particle System
1.4.1 Overview of Two-Particle Model
Consider two non-overlapping reactive spheres of varying sizes with their
center to center distance d, where sphere 1 has radius a1 and sphere 2 has radius
a2,. The two spheres are surrounded by an inert bulk phase, with reactant and or
products diffusing to or from a reactive sphere with the diffusion rate D. Chapters
2- 5 all build on this simple system (Figure 1.1). Four versions of this problem
with a wide range of radial ratios, center-to-center separation distances, kinetic
strengths, kinetic types and interfacial concentrations are studied. Chapter 2
covers the mutualism-like reaction for zeroth order generation of an intermediate
product on the surface sphere 2, diffusion away from sphere 2, followed by
possible first order consumption of the intermediate product on the surface of
sphere 1. The competition problem is studied in Chapter 3 for first order surface
consumption by either of the two different spheres of bulk concentration from the
surroundings; the calculations include size variations, center-to-center separation
distances and kinetic strengths. Chapter 4 uses the bispherical coordinate system
to evaluate the mutualism-like reaction for a constant concentration source and
diffusion limited sink for a range of intersphere distances and radial ratios. The
final chapter, Chapter 5 evaluates the reliability of the surface model given an
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