  The established macroscopic equations of motion for two phase immiscible
displacement in porous media are known to be physically incomplete because they
do not contain the surface tension and surface areas governing capillary
phenomena. Therefore a more general system of macroscopic equations is derived
here which incorporates the spatiotemporal variation of interfacial energies.
These equations are based on the theory of mixtures in macroscopic continuum
mechanics. They include wetting phenomena through surface tensions instead of
the traditional use of capillary pressure functions. Relative permeabilities
can be identified in this approach which exhibit a complex dependence on the
state variables. A capillary pressure function can be identified in equilibrium
which shows the qualitative saturation dependence known from experiment. In
addition the new equations allow to describe the spatiotemporal changes of
residual saturations during immiscible displacement.
