Fractal Characteristics and Scaling of the Drying Front in Porous Media: A Pore Network Study

Abstract

We perform two-dimensional pore network simulations of isothermal drying in order to provide better insight on the structure of the drying patterns, particularly in the frontal region, both in the presence and absence of gravity forces. Our numerical results for the fractal dimension of the invading gaseous phase (D _p  = 1.88 ± 0.03) and the drying front perimeter (D _e  = 1.34 ± 0.06) in the absence of gravity are in very good agreement with reported experimental and theoretical values. The scaling of the drying front width, σ _f , in the presence of a front-stabilizing gravity gradient is also examined and it is found to scale with the Bond number (ratio of gravity to capillary forces) as σ _f  ∝ |B|^−0.58. The width of the finger, ξ, that develops by a front-destabilizing gravity gradient is found to scale as ξ ∝ |B|^−0.57. We also report the effects of gravity forces on the drying rates and their scaling.

Keywords:

• Drying
• Fractal
• Invasion percolation
• Pore network
• Porous medium
• Scaling