The effect of contact lines on the dynamics of drops and liquid bridges

In the first part of the thesis, the evolution of a three-dimensional liquid drop on an inclined substrate oscillating vertically is examined. The oscillations are assumed to be weak and slow, which effectively makes the inertia and viscosity of the liquid negligible. The effects of the vibration-induced inertial force and gravity are balanced by surface tension forces. Asymptotic expressions are derived for the mean velocity of the drop up to the second order, where the small parameter, , is the ratio of the vibration-induced inertia to surface tension. There is no assumption made regarding the thickness of the drop. This distinguishes this study from other theoretical studies of the problem, all of which relied on the thin-film approximation. From an experimental point of view, this approximation is highly restrictive, whereas, crucially, the conclusions of this study may be tested through a specially-designed experiment. It is shown that, if the amplitude of the substrate’s oscillations exceeds a certain threshold value, , drops climb uphill. itself depends strongly on the thickness of the drop that, in turn, depends on the drop’s equilibrium contact angle, 0. It is found that, as 0 grows, there is a dramatic decrease in ?, which means that thick drops can climb for much weaker substrate vibrations. In the second part of the thesis, the stability of a static liquid bridge rising from an infinite pool, with its top attached to a horizontal plate suspended at a certain height above the pool’s surface is studied. Two different models are examined for the bridge’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 it is further argued that, if this dependence involves a hysteresis interval, the contact line is effectively pinned to the plate. It is shown that, within the framework of Model 1, all liquid bridges are unstable. In Model 2, in turn, both stable and unstable bridges exist (the former have larger contact angles and/or larger heights H than the latter). For Model 2, the marginalstability curve in the ( ,H)-parameter space is computed.