We perform direct numerical simulations of drainage by solving Navier-
Stokes equations in the pore space and employing the Volume Of Fluid
(VOF) method
to track the evolution of the fluid-fluid interface. After demonstrating
that the method
is able to deal with large viscosity contrasts and to model the transition
from stable
flow to viscous fingering, we focus on the definition of macroscopic
capillary pressure.
When the fluids are at rest, the difference between inlet and outlet
pressures and the difference between the intrinsic phase average
pressure coincide with the capillary pressure.
However, when the fluids are in motion these quantities are dominated
by viscous forces.
In this case, only a definition based on the variation of the interfacial
energy provides an
accurate measure of the macroscopic capillary pressure and allows
separating the viscous
from the capillary pressure components.