Stretching and slipping liquid bridges: liquid transfer in industrial printing.

Abstract

Liquid bridges with moving contact lines are found in a variety of settings, such as capillary feeders and high-speed printing processes. Despite this relevance, studies on liquid bridges often assume that the contact lines remain pinned in place during stretching. While this may be the case for some applications, contact line motion is \emph{desirable} in printing processes so that the amount of liquid transferred can be maximized. In this thesis we study several model problems to improve our understanding of how moving contact lines alter the dynamics of liquid bridges. We use the finite element method to study the stretching of a liquid bridge between either two flat plates or a flat plate and a cavity. For axisymmetric bridges we find that while the wettability of the two surfaces is a key factor in controlling liquid transfer between two flat plates, the presence of a cavity leads to fundamentally different bridge dynamics. This is due to the pinning of the contact line on the cavity wall, which leads to a decrease in the amount of liquid transferred to the flat plate. We find that the presence of inertia aids in cavity emptying by forcing the interface further into the cavity. However, this increase in emptying can be offset by an increased tendency for the production of satellite drops as the flat plate is made more wettable. To study non-axisymmetric flows we solve the Navier-Stokes equations in three dimensions. We find that when the stretching motion is asymmetric the liquid remains evenly distributed after breakup, so long as the two plates are not accelerating relative to each other. If the bridge shape is not initially cylindrical we find that the ability of the bridge to maintain its initial shape after breakup depends on the friction between the contact line and the solid. Finally, we use flow visualization to observe the stretching of liquid bridges both with and without small air bubbles. We find that while the breakup of wetting fluids between two identical surfaces is symmetric about the bridge midpoint, contact line pinning breaks this symmetry at slow stretching speeds for nonwetting fluids. We exploit this observation to force the bubbles selectively toward the least hydrophillic plate confining the bridge.