Eur. Phys. J. Plus (2014) 129: 221
https://doi.org/10.1140/epjp/i2014-14221-1

Regular Article

Effect of temperature wave on diffusive transport of weakly soluble substances in liquid-saturated porous media

¹ Institute of Continuous Media Mechanics, UB RAS, 614013, Perm, Russia
² Department of Mathematics, University of Leicester, LE1 7RH, Leicester, UK
³ Department of Theoretical Physics, Perm State University, 614990, Perm, Russia

^* e-mail: Denis.Goldobin@gmail.com

Received: 3 June 2014
Revised: 22 August 2014
Accepted: 9 September 2014
Published online: 14 October 2014

Abstract

We study the effect of surface temperature oscillations on diffusive transport of solutes of weakly soluble 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.