SOLUTION OF THE DEBYE-SMOLUCHOWSKI EQUATION FOR THE RATE OF REACTION OF IONS IN DILUTE-SOLUTION

Reactions of isolated ion pairs in solution have been modelled using the Debye-Smoluchowski equation for diffusion and conduction. An activation step was incorporated using a partially reflecting boundary condition. The method of matched expansions and the Abelian theorem of Laplace transforms was used to give an approximate solution of the Debye-Smoluchowski equation. Numerical integrations based on the finite-difference method confirmed these approximate analytic formulas. © 1979 American Institute of Physics.