Dynamics and Stability of Capillary Surfaces: Making Micro-Switches

In common experience, the shape of a liquid/gas or liquid/liquid interface is a compromise between surface tension $\sigma$ and gravity $g$. If the shape is dominated by surface tension, the interface is called a `capillary surface'. Capillary surfaces are distinguished by a capillary length $\ell \sim (\sigma/ \rho g)^{1/2}$ that is much longer than the container scale. Accordingly, capillary surfaces play an important role for liquids on small scales on earth (e.g. micro-flows) and in low gravity environments (e.g. space shuttle). A remarkable feature of a liquid bounded by a capillary surface is that, as length-scale diminishes, the surface-area-to-volume ratio grows unbounded. Singular dynamic behavior is anticipated in view of Newton's law. We report results of our study of the instability of capillary surfaces, framed in the context of capillary switches - components exhibiting multiple stable states. The palm beetle example from nature provides motivation. Although capillarity is a rather weak force, it can be amplified by parallel action and has the advantage of less dissipation compared to other approaches to manipulating fluids on the micro-scale.