On the asymmetrical dependence of the threshold pressure of infiltration on the wettability of the porous solid by the infiltrating liquid

A general equation has been derived for the threshold pressure of infiltration of liquids into porous solids. From this equation all the known equations for the threshold pressure can be obtained, using different assumptions on the morphology of the porous solid and on the way how the liquid infiltrates the solid. Particularly, the Young-Laplace equation, the Carman-equation, and the modification of the Carman equation, suggested by White and later by Mortensen and Cornie have been reproduced as particular cases of the general equation. A new particular solution of this general equation is also suggested, taking into account that the original solid/gas interface inside the porous body is not fully replaced by the solid/liquid interface during infiltration, especially for the case of non-wetting liquids. The new, general equation consists of three semi-empirical parameters, which should be found experimentally for a given type of morphology of the porous solid and for the given ratio of the surface tension to the density of the infiltrating liquid metal. The new equation provides a value of the threshold contact angle to be between 65.5° and 90°, depending on the morphology of the porous solid. Consequently, the threshold pressure appears to be an asymmetrical function of the contact angle. Based on the new equation, the practical constancy of the threshold pressure is predicted in the interval of the contact angles between 120° and 180°.