Estimation of adsorption rate coefficients based on the Smoluchowski equation

Abstract

In this paper we show how the Smoluchowski equation can be used to determine the coefficients in the interfacial flux constitutive equation given by − n γκ· D γ ∇c Aγ=k 1c Aγ−k −1c As. Here c As is the surface concentration (particles/cm 2) at the γ– κ interface and c Aγ is the volume concentration (particles/cm 3) in the γ-phase. This form of the flux relation represents the simplest linear expression for the one-sided fluxes to and from a solid surface. Values of k 1 and k −1= k 1 K eq −1 are determined on the basis of numerical solutions of both the Smoluchowski equation and the classical diffusion equation coupled to a jump condition. This approach allows for subsequent averaging or upscaling without the complications associated with the Smoluchowski equation. Results are presented for two forms of the particle–surface interaction potential. In addition to the direct numerical solution of the Smoluchowski equation, numerical results are also obtained for the case of local adsorption equilibrium.