Capillary penetration between dissimilar solids

Abstract

The major purpose of this study was to develop and evaluate a mathematical model for the capillary penetration of a liquid between two dissimilar plates. Attempts have been made in the past to apply the Young-Laplace equation to this situation, but without success because of the complex curvature of the meniscus. Instead, free energy considerations were used to derive the proposed equation. The equation obtained for the capillary rise h for a liquid of surface tension [gamma]LV into a space b between two plates whose contact angles with the liquid are [theta]1 and [theta]2 was found to be: , where d is the liquid density and g is the gravitational constant.Experimental values of capillary penetration between combinations of three liquids and several solids were obtained with the use of the hyperbola method. A factorial design was employed. These data were compared with those predicted by means of the proposed equation. Regression, correlation, and analysis of variance were used to test for the degree and significance of the association between the predicted and observed values. These results and a dimensional analysis indicate that the proposed equation is satisfactory.