LAMINAR-FLOW OF A WETTING LIQUID ALONG THE CORNERS OF A PREDOMINANTLY GAS-OCCUPIED NONCIRCULAR PORE

The problem of low Reynolds number wetting liquid flow in a noncircular capillary occupied predominantly by a nonwetting gas phase is separated into individual corner flow problems and solved numerically. The solution is presented in terms of a dimensionless flow resistance, beta , which is tabulated as a function of corner geometry (half angle and degree of roundedness), surface shear viscosity, and contact angle. The effect of corner geometry and contact angle is to change the cross-sectional area available for flow, while the surface shear viscosity affects the boundary condition at the gas-liquid interface. The dimensionless flow resistance is shown to increase with increasing half angle, degree of roundedness, surface shear viscosity, and contact angle. Finally, it is demonstrated that the error resulting from the use of the hydraulic-diameter approximation for the corner flow problem is on the order of 50% or higher.