Scaling theory of drying in porous media

Concepts of immiscible displacements in porous media driven by mass transfe r are utilized to model drying of porous media. Visualization experiments o f drying in two-dimensional glass micromodels are conducted to identify por e-scale mechanisms. Then, a pore network approach is used to analyze the ad vancing drying front. It is shown that in a porous medium, capillarity indu ces a flow that effectively limits the extent of the front, which would oth erwise be of the percolation type, to a finite width. In conjuction with th e predictions of a macroscale stable front, obtained from a linear stabilit y analysis, the process is shown to be equivalent to invasion percolation i n a stabilizing gradient. A power-law scaling relation of the front width w ith a diffusion based capillary number is also obtained. This capillary num ber reflects the fact that drying is controlled by diffusion in contrast to external drainage. The scaling exponent predicted is compatible with the e xperimental results of Shaw [Phys Rev. Lett. 59, 1671 (1987)]. A framework for a continuum description of the upstream drying regimes is also develope d.