The Force Singularity for Partially Immersed Parallel Plates
  In earlier work, we provided a general description of the forces of attraction and repulsion, encountered by two parallel vertical plates of infinite extent and of possibly differing materials, when partially immersed in an infinite liquid bath and subject to surface tension forces. In the present study, we examine some unusual details of the exotic behavior that can occur at the singular configuration separating infinite rise from infinite descent of the fluid between the plates, as the plates approach each other. In connection with this singular behavior, we present also some new estimates on meniscus height details. 
Rajat Bhatnagar and Robert Finn
math.DG math.CA physics.flu-dyn