Smoluchowski equation with a sink term: Analytical solutions for the rate constant and their numerical test (original) (raw)

The Journal of Chemical Physics, 1998

Abstract

Smoluchowski equation with a sink term is widely used as a model of a rate process in a slowly relaxing environment. Two approximate solutions for the rate constant obtained for a steeply growing sink are tested numerically using an exponential sink. Both analytical solutions are in a good agreement with the numerical results over a wide range of the problem parameters (environment relaxation rate). They show how the rate constant Γ decreases when the viscosity η of the environment increases. If the dependence is approximated by the fractional power law, Γ∝η−α, the exponent α is always less than unity and depends on η. It tends to zero for fast relaxation of the environment (small η) and increases when the relaxation slows down (η grows).

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