Analytical solutions of drying in porous media for gravity-stabilized fronts

A. G. Yiotis, D. Salin, E. S. Tajer, and Y. C. Yortsos
Phys. Rev. E 85, 046308 – Published 19 April 2012

Abstract

We develop a mathematical model for the drying of porous media in the presence of gravity. The model incorporates effects of corner flow through macroscopic liquid films that form in the cavities of pore walls, mass transfer by diffusion in the dry regions of the medium, external mass transfer over the surface, and the effect of gravity. We consider two different cases: when gravity opposes liquid flow in the corner films and leads to a stable percolation drying front, and when it acts in the opposite direction. In this part, we develop analytical results when the problem can be cast as an equivalent continuum and described as a one-dimensional (1D) problem. This is always the case when gravity acts against drying by opposing corner flow, or when it enhances drying by increasing corner film flow but it is sufficiently small. We obtain results for all relevant variables, including drying rates, extent of the macroscopic film region, and the demarkation of the two different regimes of constant rate period and falling rate period, respectively. The effects of dimensionless variables, such as the bond number, the capillary number, and the Sherwood number for external mass transfer are investigated. When gravity acts to enhance drying, a 1D solution is still possible if an appropriately defined Rayleigh number is above a critical threshold. We derive a linear stability analysis of a model problem under this condition that verifies front stability. Further analysis of this problem, when the Rayleigh number is below critical, requires a pore-network simulator which will be the focus of future work.

  • Figure
  • Figure
  • Figure
  • Figure
  • Figure
  • Figure
  • Figure
5 More
  • Received 17 June 2011

DOI:https://doi.org/10.1103/PhysRevE.85.046308

©2012 American Physical Society

Authors & Affiliations

A. G. Yiotis and D. Salin

  • Laboratoire FAST, Université Pierre & Marie Curie, Université d'Orsay Paris-Sud, CNRS, Orsay 91405, France

E. S. Tajer and Y. C. Yortsos

  • Mork Family Department of Chemical Engineering and Materials Science, University of Southern California, Los Angeles, California 90089-1450, USA

Article Text (Subscription Required)

Click to Expand

References (Subscription Required)

Click to Expand
Issue

Vol. 85, Iss. 4 — April 2012

Reuse & Permissions
Access Options
Author publication services for translation and copyediting assistance advertisement

Authorization Required


×
×

Images

×

Sign up to receive regular email alerts from Physical Review E

Log In

Cancel
×

Search


Article Lookup

Paste a citation or DOI

Enter a citation
×