Dynamics and stability of two-potential flows in the porous media.

The experimental and numerical results of the capillary-force-driven climb of wetting liquid in porous media, which is opposed by the gravity force, are analyzed with respect to the emergence of a multiphase flow front and flow stability of the climbing liquid. Two dynamic characteristics are used: (i) the multiphase flow front thickness as a function of time, and (ii) the capillary number as a function of Bond number, where both numbers are calculated from the harmonic average of pores radii. Throughout the climb, the influence of capillary, gravity, and viscous force variations on the flow behavior is investigated for different porous media. For a specific porous medium, a unique flow front power law function of time is observed for the capillary flow climbs with or without gravity force. Distinct dynamic flow front power law functions are found for different porous media. However, for capillary climb in different porous media, one is able to predict a unique behavior for the wetting height (the interface between wetted and dry regions of porous medium) using the capillary and Bond number. It is found that these two numbers correlate as a unique exponential function, even for porous media whose permeabilities vary for two orders of magnitude. For climbs without the gravity force (capillary spreads), the initial climb dynamics follows this exponential law, but for later flow times and when a significant flow front is developed, one observes a constant value of the capillary number. Using this approach to describe the capillary climb, only the capillary versus Bond number correlation is needed, which is completely measureable from the experiments.