Shape Dynamics of Bouncing Droplets

Generalization of Young-Laplace, Kelvin, and Gibbs-Thomson equations for arbitrarily curved surfaces

The Young-Laplace, Kelvin, and Gibbs-Thomson equations form a cornerstone of colloidal and surface sciences and have found successful applications in many subfields of physics, chemistry, and biology. The Gibbs-Thomson effect, for example, predicts that small crystals are in equilibrium with their liquid melt at a lower temperature than large crystals and the positive interfacial energy increases the energy required to form small particles with a high curvature interface. In cases of liquids contained within porous media (confined geometry), the effect indicates decreasing the freezing/melting temperatures and the increment of the temperature is inversely proportional to the pore size. These phenomena can be reformulated for Gaussian maps of macromolecules and can be asked the following question: can one use the equations for predicting the melting temperature and shape of polymer chains in confined geometries? The answer is no, mainly because macromolecules form highly curved surfaces (Gaussian maps), and the equations hold only for simple geometries (sphere, plane, or cylinder). Here, we present general Young-Laplace, Kelvin, and Gibbs-Thomson equations for arbitrarily curved surfaces and apply them to predict temperature distribution on a few protein surfaces. Also, after increased interest toward liquid/liquid phase separation in biology, we derive generic Ostwald ripening and show that for shape-changing condensates, instead of a monotonic growing mechanism, a variety of processes are possible. Due to the generality of equations, we clarify that at appropriate internal/external pressure conditions systems, bounded by surfaces, may adopt any shape and thermal stability is strongly influenced by the geometries of confined spaces.

Activating Bubble's Escape, Coalescence, and Departure under an Electric Field Effect

In this paper, we present the results of applying an electric field to activate bubbles' escape, coalescence, and departure. A simple electrowetting-on-dielectric device was utilized in this bubble dynamics study. When a copper electrode wire inserted into deionized water was positioned on one side of single or multiple bubbles, the bubble tended to continuously escape from its initial position as the voltage was turned on. Contact angle imbalance at different sides of the bubble was observed, which further promoted the bubble's escape. An analysis model with an electromechanical framework was developed to study the charging time difference on two sides of the bubble, which generated a wettability gradient and capillary force to propel it away from the electrode. Sine, ramp, and square alternating current waveforms with 60 V amplitude and 2 Hz frequency were tested for comparison. It was shown that all waveforms promoted the bubble's escape; the square wave shape manifested the farthest escape capability, followed by sine and ramp waves. An upper view of several bubbles aligning in triangle, square, pentagon, and hexagon shapes demonstrated that the bubbles tended to move outward when the electrode is placed at the geometric centers. Experiments with an electrode on one side and several bubbles positioned in a line were conducted. In these cases, the bubbles closer to the electrode reacted faster than those farther from the electrode, resulting in coalescence. Once the bubble size became larger, it departed either by overcoming the disjoining pressure in a thin film of water or via the buoyancy force in a thick film of water. Controlling bubble dynamics by the electric field, including escape, coalescence, and departure provides an active and reversible approach to move bubbles or increase departure frequency in many fluid mechanics and heat transfer studies.