# A Note on the Solute Dispersion in a Porous Medium

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## Abstract

In this paper, we study the solute transport through a semi-infinite channel filled with a fluid saturated sparsely packed porous medium. A small perturbation of magnitude \(\varepsilon \) is applied on the channel’s walls on which the solute particles undergo a first-order chemical reaction. The effective model for solute concentration in the small-Péclet-number regime is derived using asymptotic analysis with respect to the small parameter \(\varepsilon \). The obtained mathematical model clearly indicates the effects of porous medium, chemical reaction and boundary distortion. In particular, the effect of porous medium parameter on the dispersion coefficient is discussed.

## Keywords

Solute dispersion Porous medium Chemical reaction Small boundary perturbation Asymptotic analysis## Notes

### Acknowledgements

The author has been supported by the *Croatian Science Foundation* (Project 3955: *Mathematical modeling and numerical simulations of processes in thin or porous domains*). The author would like to thank the referees for their helpful comments and suggestions that helped to improve the paper.

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