Meniscus behaviors and capillary pressures in capillary channels having various cross-sectional geometries

A numerical study has been conducted to simulate the liquid/gas interface (meniscus) behaviors and capillary pressures in various capillary channels using the volume of fluid (VOF) method. Calculations are performed for four channels whose cross-sectional shapes are circle, regular hexagon, square and equilateral triangle and for four solid/liquid contact angles of 30°, 60°, 120° and 150°. No calculation is needed for the contact angle of 90° because the liquid/gas interface in this case can be thought to be a plane surface. In the calculations, the liquid/gas interface in each channel is assumed to have a flat surface at the initial time, it changes towards its due shape thereafter, which is induced by the combined action of the surface tension and contact angle. After experiencing a period of damped oscillation, it stabilizes at a certain geometry. The interface dynamics and capillary pressures are compared among different channels under three categories including the equal inscribed circle radius, equal area, and equal circumscribed circle radius. The capillary pressure in the circular channel obtained from the simulation agrees well with that given by the Young–Laplace equation, supporting the reliability of the numerical model. The channels with equal inscribed circle radius yield the closest capillary pressures, while those with equal circumscribed circle radius give the most scattered capillary pressures, with those with equal area living in between. A correlation is developed to calculate the equivalent radius of a polygonal channel, which can be used to compute the capillary pressure in such a channel by combination with the Young–Laplace equation.