Breaking symmetry in liquid bridges: the effect of pinning and aspect ratio on capillary forces
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Date
2014-02-06
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Johns Hopkins University
Abstract
Capillary bridges between solid substrates are critical to a myriad of natural and industrial processes, such as oil recovery from porous rocks, or the packaging of micro-circuitry components. Generally, the surfaces of these solids are not uniform, and contain physical or chemical heterogeneities that result in asymmetric bridge morphologies (due to the partial pinning of the solid-liquid-vapor interface). While such pinning can greatly affect the forces and morphologies of the liquid, many studies that investigate capillary bridges assume the solid surfaces to be ideal, and the subsequent bridge profiles to be highly symmetric. This thesis details our investigations of how breaking symmetry (through changing of the pinning condition or the shape of the substrates) results in quantitative changes to the properties of the capillary bridges such as the morphology, forces and torques.
First, we explored the importance of the pinning condition by studying capillary bridges in a narrow rectangular slit pore, which is one of the simplest ways to break symmetry. We employed experiments, numerical simulations, and theory to highlight the importance of pinning on the bridge morphology and associated capillary forces. Experiments showed that as the height of the slit pore is increased past the width of the strip the mean curvature of the capillary bridge changes sign from negative to positive (concave to convex). This counterintuitive observation was confirmed by using Surface Evolver simulations. Interestingly, the force the capillary bridge exerts on the pore itself always remains attractive due to the dominance of the vertical projection of the surface tension force at the pinning boundary. It was also found that the mean curvature was independent of the liquid volume in the pore, as long as the bridge did not extend to the end of the strip. We developed a simple theory to show that the change in mean curvature can be described as a competition between the confinement of the liquid bridge and the wetting of the strip.
Next, we studied the role of substrate shape on the restoring forces and torques of capillary based self-alignment systems, such as “flip-chip” micro-circuit packaging. To do this we varied systematically the aspect ratio of rectangular substrates under conditions where the fluid was pinned on all sides. We found that increasing the aspect ratio of the substrates (even when holding the substrate area, and liquid volume constant) resulted in higher total restoring forces and torques under both lateral and rotational perturbations. It is also shown that the rotational restoring force is of order the shift restoring force, and should generally be considered in alignment analysis. Finally, parameters from experimental flip-chip devices were used in our simulations to show how current capillary self-alignment schemes can benefit from using rectangular substrate shapes with aspect ratio greater than one.
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Surface Evolver, wetting, capillary forces, liquid bridges,