Dimensional Analysis of Horizontal Infiltration Affected by Surface Tension and Viscosity of a Liquid

The behavior of water in porous media under variable gravities should be known for establishing agriculture in space. The effects of surface tension and viscosity may be emphasized under microgravity, where the weight is canceled and the density term can be ignored. In this article, the effects of changes in surface tension and viscosity were evaluated on horizontal infiltration, which is not influenced by gravity. A new equation with two dimensionless parameters was derived by performing dimensional analysis for horizontal water movement in porous media. A new term, the S-N number, is proposed as the ratio of surface tension and viscosity. Horizontal infiltration experiments with various concentrations of aqueous ethanol solutions were performed, and infiltration rates were measured. Horizontal infiltration rates were assessed with the newly proposed S-N number and the with the fluid mobility factor (defined as the ratio of density to viscosity). The S-N number and infiltration rates were linearly correlated with r = 0.95; thus, the S-N number could be an alternative indicator to the fluid mobility factor for the relative mobility of infiltrating liquids. For higher ethanol concentrations, a sharp wetting front collapsed and blurred due to decreases in the surface tension of ethanol solutions. The proposed S-N number is valid under any gravitational condition and so can be used to estimate mobility even under variable gravity.