Critical Angle for Electrically Driven Coalescence of Two Conical Droplets
Entry by Leon Furchtgott, APP 225 Fall 2010.
J. C. Bird, W. D. Ristenpart, A. Belmonte, and H. A. Stone, "Critical Angle for Electrically Driven Coalescence of Two Conical Droplets," Physical Review Letters 103 (16) (2009)
The authors use a combination of experimental and numerical methods to explore the coalescence behavior of two oppositely-charged conical droplets. They find that coalescence behavior depends on the cone angle: two drops coalesce when the slopes of the cones are small but recoil when the slopes exceed a critical value. They estimate and measure a critical cone angle of 30.8 degrees.
Two drops of the same liquid are expected to coalesce when they come into contact because the combined drop minimizes the surface energy. When drops fail to coalesce, it is often because of phenomena that prevent contact such as surfactant or colloidal coatings or dynamic processes such as evaporation or vibration that maintain a layer of immiscible fluid between drops. This paper is concerned with the case of two oppositely charged drops placed in large electric fields that fail to coalesce even when the two drops come directly into contact.
Electric fields cause liquid droplets to develop conical structures oriented in the direction of the field. These are known as Taylor cones and result from a balance of charge-induced pressure from the applied electric field and capillary pressure resisting interfacial deformation. The balance of the two effects is quantified by a dimensionless number <math>\Epsilon_c</math>. For sufficiently high values of <math>\Epsilon_c</math>, two drops develop conical tips and converge.
The question that this paper addresses is the previously unstudied behavior of the drop pairs after contact. They show that for sufficiently high fields, water droplets deform into steep cones and fail to coalesce. The rest of the paper documents this experimentally and gives explanations for this behavior.