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

2
D c = 0
(5.1)
∇ ext
where D is the external Fickian diffusion coefficient and the concentration of the
reactant is c. The concentration far from the two spheres is fixed as
c ext = 0 , r 1 and ∞ → r 2 . (5.2)
The remaining boundary conditions describe zeroth order generation of a
substrate (reactant) occurring at the surface of sphere 2
∂c
∂r
D ext
2
= −σ
2 , 2 a2
r = , (5.3)
where it travels away from the source at a rate of D the substrate either escapes
or is trapped and consumed inside sphere 1. The internal diffusion chemical
reaction inside the sphere is described by
D =
2
int∇
cint
kintcint
, 1 1
r ≤ a , (5.4)
where D is the internal Fickian diffusion rate of the substrate with internal
int
concentration cint.
The reactant is consumed inside sphere 1 by a first-order
reaction with kinetic rate constant kint. The solution of equations (5.1) and (5.4)
are both valid at the sink-medium interface because the reactant is transported
106