I'm trying to understand capillary flow in a tube. I've found this website that explains some aspects of it, the system is illustrated here, So the (black) non-wetting fluid resides to the left and the (white) wetting fluid is to the right. Say that we are looking at a pore in a piece of chalk/rock and that the outlet (to the right) is a big reservoir of wetting fluid, whereas the inlet to the left is merely the end of the pore. Given this setup, I can't quite figure out how the inlet pressure pL relates to the outlet pressure pR. They can't be equal since the capillary forces must introduce a pressure gradient which "pushes" the non-wetting phase out, given that the solid boundary is wetting. Given this, I would anticipate that pR<pL. Is this reasoning correct?