ORIGINAL RESEARCH article
Front. Phys.
Sec. Interdisciplinary Physics
Volume 13 - 2025 | doi: 10.3389/fphy.2025.1610082
Heat and super-diffusive melting fronts in unsaturated porous media
Provisionally accepted
- 1Department of Physics, Faculty of Mathematics and Natural Sciences, University of Oslo, Oslo, Oslo, Norway
- 2department chemistry, Department of Physics, Faculty of Natural Sciences, Norwegian University of Science and Technology, Trondheim, Sør-Trøndelag, Norway
- 3Department of Physics, Faculty of Natural Sciences, Norwegian University of Science and Technology, Trondheim, Sør-Trøndelag, Norway
Select one of your emails
You have multiple emails registered with Frontiers:
Notify me on publication
Please enter your email address:
If you already have an account, please login
You don't have a Frontiers account ? You can register here
When water is present in a medium with pore sizes in a range around 10nm the corresponding freezing point depression will cause long range broadening of a melting front. Describing the freezing-point depression by the Gibbs-Thomson equation and the pore size distribution by a power law, we derive a non-linear diffusion equation for the fraction of melted water. This equation yields super-diffusive spreading of the melting front with a diffusion exponent which is given by the spatial dimension and the exponent describing the pore size distribution. We derive this solution analytically from energy conservation in the limit where all the energy is consumed by the melting and explore the validity of this approximation numerically. Finally, we explore a geological application of the theory to the case of one-dimensional sub-surface melting fronts in granular or soil systems. These fronts, which are produced by heating of the surface, spread at a super-diffusive rate and affect the subsurface to significantly larger depths than would a system without the effects of freezing point depression.
Keywords: Gibbs-Thomson equation, Pore size distribution, Non-linear diffusion equation, super-diffusive spreading, Melting front, Diffusion exponent, Spatial dimension, Energy conservation
Received: 11 Apr 2025; Accepted: 19 Aug 2025.
Copyright: © 2025 Flekkøy, Hansen and Eiser. This is an open-access article distributed under the terms of the Creative Commons Attribution License (CC BY). The use, distribution or reproduction in other forums is permitted, provided the original author(s) or licensor are credited and that the original publication in this journal is cited, in accordance with accepted academic practice. No use, distribution or reproduction is permitted which does not comply with these terms.
* Correspondence: Eirik Grude Flekkøy, Department of Physics, Faculty of Mathematics and Natural Sciences, University of Oslo, Oslo, 0371, Oslo, Norway
Disclaimer: All claims expressed in this article are solely those of the authors and do not necessarily represent those of their affiliated organizations, or those of the publisher, the editors and the reviewers. Any product that may be evaluated in this article or claim that may be made by its manufacturer is not guaranteed or endorsed by the publisher.