  The problem of two-phase flow in straight capillaries of polygonal cross
section displays many of the dynamic characteristics of rapid interfacial
motions associated with pore-scale displacements in porous media. Fluid inertia
is known to be important in these displacements but is usually ignored in
network models commonly used to predict macroscopic flow properties. This study
presents a numerical model for two-phase flow which describes the spatial and
temporal evolution of the interface between the fluids. The model is based on
an averaged Navier-Stokes equation and is shown to be successful in predicting
the complex dynamics of both capillary rise in round capillaries and imbibition
along the corners of polygonal capillaries. The model can form the basis for
more realistic network models which capture the effect of capillary, viscous
and inertial forces on pore-scale interfacial dynamics and consequent
macroscopic flow properties.
