Criteria for Applying the Lucas-Washburn Law

Spontaneous imbibition happens in many natural and chemical engineering processes in which the mean advancing front usually follows Lucas-Washburn's law. However it has been found that the scaling law does not apply in many cases. There have been few criteria to determine under what conditions the Washburn law works. The effect of gravity on spontaneous imbibition in porous media was investigated both theoretically and experimentally. The mathematical model derived analytically was used to calculate the imbibition rates in porous media with different permeabilities. The results demonstrated that the effect of gravity on spontaneous imbibition was governed by the hydraulic conductivity of the porous media (permeability of the imbibition systems). The criteria for applying the Lucas-Washburn law have been proposed. The effect of gravity becomes more apparent with the increase in permeability or with the decrease in CGR number (the ratio of capillary pressure to gravity forces) and may be ignored when the CGR number is less than a specific value N(*)(cg) ≅ 3.0. The effect of gravity on imbibition in porous media can be modeled theoretically. It may not be necessary to conduct spontaneous imbibition experiments horizontally in order to exclude the effect of gravity, as has been done previously.