CAPILLARY BEHAVIOR OF A PERFECTLY WETTING LIQUID IN IRREGULAR TRIANGULAR TUBES

Triangles provide a useful example of simple pore shapes: they have angular corners, which can retain liquid, and irregular triangles give a wide range of shapes. The exact meniscus curvature of perfectly wetting liquids draining from pores of general triangular cross section is derived. The appropriate normalized shape factor for capillary action in triangular pores is the ratio of the area of cross section, A, to the square of the perimeter length, P. The drainage penetration curvature is calculated for all possible shapes of triangular tubes. The amount of wetting phase that drains at the penetration curvature decreases as aspect ratio increases. The remaining liquid is retained in the corners of the triangular pore. Thus, after drainage, there is dual occupancy of the pore and continuity of both wetting and nonwetting phases. The decrease in liquid retained in the corners with increase in curvature of are menisci subsequent to penetration is also calculated. The relation between saturation and the square of the curvature is shown to be hyperbolic. Imbibition occurs by the progressive filling of corners. At low saturations imbibition is the exact reverse of drainage. Corner filling continues even when the meniscus curvature falls below the drainage penetration curvature, thus giving hysteresis. When the menisci in the corners meet, the liquid spontaneously redistributes. A portion of the tube length refills and the meniscus curvature jumps to the drainage penetration curvature. Spontaneous redistribution is an example of "snap-off" and may give rise to the entrapment of nonwetting phase. Both the curvature and saturation at which spontaneous filling occurs are derived as a function of shape factor. The triangular pore has much greater versatility than the commonly used cylindrical pore, and models, in a simple way, several basic features of the capillary behavior of highly complex porous materials. © 1991.