Shape Factor Correlations of Hydraulic Conductance in Noncircular Capillaries: II. Two-Phase Creeping Flow

Abstract

In Part I of this paper, we introduced the Mason–Morrow shape factor and the corner half-angles to capture the part of geometry of angular capillaries essential in pore network calculations of single- and two-phase flow in drainage and imbibition. We then used this shape factor to obtain simple expressions for the hydraulic conductance in single-phase flow through triangular, rectangular, and oval capillaries. In Part II, we study two-phase fluid flow along angular capillaries. The nonwetting fluid occupies the central part of the capillary, whereas the wetting liquid fills the corners. First, we verify the numerical solution obtained by Ransohoff–Radke for concave corner menisci by using a high-resolution finite element method with zero and infinite surface shear viscosity. We present new numerical results for corner flow domains bounded by convex menisci, i.e., for pinned contact lines and forced imbibition. We also present numerical solutions for two-phase flow with momentum transfer across the interface. We introduce a dimensionless hydraulic conductance of wetting fluid in the corners and correlate it with the corner filament shape factor, corner half-angle, and contact angle. By appropriate scaling, we obtain an accurate universal curve for flow conductance in the corners of an arbitrary angular capillary and for arbitrary contact angles. We give error estimates of the Ransohoff–Radke flow resistance factors, of the Zhou et al. analytical expressions for the resistance factors, and of our universal curves for the hydraulic conductance with no-slip and perfect-slip boundary conditions at the interface. Our expressions for the hydraulic conductance in corner flow of wetting liquid not only are valid for both concave and convex fluid interfaces but also are more accurate than any other published correlation.