Shape Factor and Hydraulic Conductance in Noncircular Capillaries: I. One-Phase Creeping Flow
byTadeusz W. Patzek, Dmitriy B. Silin
Patzek, T. W. and Silin, D. B., “Shape Factor and Hydraulic Conductance in Noncircular Capillaries: I. One-Phase Creeping Flow,” J. Colloid and Interface Sci., 236 295-304 April 2001.
We use the Mason–Morrow shape factor, i.e., a dimensionless hydraulic radius, and corner half-angles to capture the geometry of noncircular capillaries pertinent to a physically adequate pore network description of porous media. We give analytic expressions for random corner half-angles that satisfy a given shape factor calculated from the microscopic images of pore space. We demonstrate that use of the shape factor leads to particularly simple expressions for the hydraulic conductance in single-phase flow through noncircular capillaries. In particular, we obtain the hydraulic conductances of arbitrary triangular ducts semianalytically, using conformal mapping. The conductances of equilateral triangular, rectangular, and elliptic ducts are calculated analytically.