Effect of Temperature Wave on Diffusive Transport of Weakly-Soluble Substances in Liquid-Saturated Porous Media

TL;DR

This paper investigates how surface temperature oscillations influence the diffusive transport of weakly-soluble substances in liquid-saturated porous media, revealing significant effects on substance release and redistribution through analytical and numerical methods.

Contribution

It provides an analytical model for the impact of temperature waves on diffusive fluxes in porous media with immobilized non-dissolved phases, validated by numerical simulations.

Findings

Temperature waves significantly affect solute flux and substance release.

Analytical theory aligns well with numerical calculations.

Non-dissolved phase redistribution is driven by temperature-induced diffusion fluxes.

Abstract

We study the effect of surface temperature oscillations on diffusive transport of solutes of weaklysoluble substances through liquid-saturated porous media. Temperature wave induced by these oscillations and decaying deep in the porous massif creates the solubility wave along with the corresponding solute diffusion flux wave. When the non-dissolved fraction is immobilized in pores---for gases the bubbles can be immobilized by the surface tension force, for solids (e.g., limestone, gas-hydrates) the immobilization of non-dissolved phase is obvious---the only remaining mechanisms of mass transport are related to solute flux through liquid in pores. We evaluate analytically the generated time-average mass flux for the case of medium everywhere littered with non-dissolved phase and reveal the significant effect of the temperature wave on the substance release from the massif and non-dissolved mass redistribution within the massif. Analytical theory is validated with numerical calculations.