Effect of axial diffusion on impurity adsorption in a circular tube

Abstract

Circular tubes can be used to irreversibly adsorb impurities from a dilute solution of the impurity and a non-adsorbing fluid. An analysis of the unsteady adsorption process over the region \(z = - \infty \) to \(z = \infty \) can be carried out with or without axial diffusion. The transport equation in the presence of axial diffusion can be solved using the complex Fourier transform and the Green's function method. In the absence of axial diffusion, the transport equation can be solved using the Laplace transform method. Previously reported studies over the region \(0\le z\le L\) limited the contribution of axial diffusion. Analytical solutions of the pertinent differential equations are used to determine the impurity concentration everywhere in the circular tube.

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