  We consider a one-dimensional problem modeling two-phase flow in
heterogeneous porous media made of two homogeneous subdomains, with
discontinuous capillarity at the interface between them. We suppose that the
capillary forces vanish inside the domains, but not on the interface. Under the
assumption that the gravity forces and the capillary forces are oriented in
opposite directions, we show that the limit, for vanishing diffusion, is not in
general the optimal entropy solution of the hyperbolic scalar conservation law
as in the first paper of the series \cite{NPCX}. A non-classical shock can
occur at the interface, modeling oil-trapping.
