  In this work, we extend the model of contact angles that we have previously
developed for sessile drops on a wetted surface to the case of a meniscus in a
capillary. The underlying physics of our model describe the intermolecular
forces between the fluid and the surface of the capillary that result in the
formation of a thin, non-removable fluid layer that coats the capillary wall.
We describe the shape of the meniscus using a Young-Laplace equation and an
incompressible, two-phase, CFD calculation, both modified to take into account
intermolecular forces using the disjoining pressure model. We find that our
numerical solutions of the Young-Laplace equation and equilibrium meniscus
shapes obtained by CFD agree well with each other. Furthermore, for capillaries
that are sufficiently larger than the thickness of the non-removable film, our
numerical solutions agree well with the effective contact angle model that we
previously developed for sessile drops. Finally, we observe that it is possible
to tune the disjoining pressure model parameters so that the intermolecular
forces between the liquid and solid molecules becomes so strong compared to the
surface tension that our formula for effective contact angle gives an imaginary
solution. We analyze this situation using CFD and find that it corresponds to
dewetting, where the bulk liquid detaches from the walls of the capillary
leaving behind the non-removable thin liquid film.
