Partially Absorbing Outer Boundary with Geminate Recombination

4 Partially Absorbing Outer Boundary with Geminate Recombination 

This section extends the outer radiation boundary condition in the previous model to include geminate reaction within the micelle. In this model a single particle diffuses with a sink at the centre and an outer radiation boundary. The required initial condition is S2(( = 0) = 1, inner boundary S2(r = a) = 0 and outer boundary condition — wS2(r = R). Solving the backward diffusion equation with these boundary conditions gives the analytical expression for the survival probability to be 

The coefficient =. Jx/D (where A, being an arbitrary constant) are the solutions of the equation 

The analytical form of the first passage time densities in the Laplace space is given by the expression 

In order to decipher whether the mean reaction time corresponds to a reaction with the surface or geminate recombination, it is necessary to calculate the probabilities of each event. Using a similar strategy as before, the steady state backward diffusion equation must be solved subject to the boundary conditions  

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Partially Absorbing Outer Boundary with No Geminate Recombination 9.3.1.2 Brownian Bridge... 

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