Dewetting of a fluid between parallel plane surface with nonconstant forcing

We examine the effect of applying a nonconstant force to the radial squeezing and de-wetting of a thin film of viscous Newtonian fluid between parallel plane walls. We explore the problem theoretically for gap spacings much smaller than the typical capillary length for air-liquid systems ($<$ O(1) $mm$). In our model, we parameterize force using a single variable $F$ which is proportional to a constant force $F_0$ and the height of the gap spacing $h$ to some integer power $n \in \mathcal{Z}^+.$ Since there is no known analytic solution for $n>0$, we analyze the solution of the dewetting problem numerically. Analysis reveals the formation of a singularity, leading to capillary adhesion, as the gap spacing approaches a critical value that depends on $F_0$, $n$ and a variable $C$ that is analogous to a spring constant.