Equilibrium height of a liquid in a gap between corrugated walls under spontaneous capillary penetration.

A simple and general method is presented to calculate the equilibrium surface of a liquid that penetrates spontaneously, due to capillarity, in the gap between two vertical corrugated plates. Several properties of the equilibrium solution are discussed and the results are backed by a qualitative experiment.

Natural convection in tilted cylindrical cavities embedded in rocks.

This paper presents a theoretical investigation of the low Rayleigh number conjugate natural convection in a slender tilted cylindrical cavity which is embedded in a solid that is subject to a uniform vertical temperature gradient. Two cases have been analyzed; a fluid-filled cavity and a cavity filled with a fluid-saturated porous medium. The temperature of the solid and the velocity, temperature, and pressure in the cavity have been determined by analytically solving the coupled problems within and around the cavity. The effect of the ratio of the thermal conductivity of the material in the cavity to the thermal conductivity of the solid on the structure of the convection flow is discussed. The theoretical results for convection in the fluid-filled cavity are shown to be in good agreement with experimental PIV measurements.