The radial capillary

Abstract The radial capillary model, which describes radial penetration of a liquid between two flat plates, is developed and analyzed. This model is useful in studying the effect of the radial motion of a liquid which penetrates a thin porous medium on the kinetics of the process. A thermodynamic analysis reveals that the radial capillary has to be primed before spontaneous penetration can proceed. A differential equation for the kinetics of penetration is developed, and an approximate analytical solution is presented for the case of an infinite liquid reservoir. For this case it is found that the rate of penetration into the radial capillary is slower than that into either a cylindrical capillary or a unidirectional flat plate capillary. The rate of penetration of a drop increases as the size of the drop decreases. Two limiting cases are presented with respect to hysteresis of the contact angle which the drop makes with the outside surface of the plate: (a) no hystereis and (b) constant basal radius. It is shown that hysteresis counteracts the effect of the finite drop size for very small drops. Capillary penetration is shown to be possible for contact angles higher than 90° when the drop is sufficiently small and when hysteresis is not dominant.