The stability of a static liquid column pulled out of an infinite pool

We study the stability of a static liquid column rising from an infinite pool, with its top attached to a horizontal plate suspended at a certain height above the pool's surface. Two different models are employed for the column's contact line. Model 1 assumes that the contact angle always equals Young's equilibrium value. Model 2 assumes a functional dependence between the contact angle and the velocity of the contact line, and we argue that, if this dependence involves a hysteresis interval, linear perturbations cannot move the contact line. It is shown that, within the framework of Model 1, all liquid columns are unstable. In Model 2, both stable and unstable columns exist (the former have larger contact angles theta and/or larger heights H). For Model 2, the marginal stability curve on the (theta, H)-plane is computed. The mathematical results obtained imply that, if the plate to which a stable liquid column is attached is slowly lifted up, the column's contact line remains pinned while the contact angle is decreasing. Once it reaches the lower boundary of the hysteresis interval, the column breaks down. © 2013 AIP Publishing LLC.