Propagation of capillary waves and ejection of small droplets in rapid droplet spreading

• Published in: Journal of fluid mechanics Vol. 697; pp. 92 - 114
• Main Authors: Ding, H., Li, E. Q., Zhang, F. H., Sui, Y., Spelt, P. D. M., Thoroddsen, S. T.
• Format: Journal Article
• Language: English
• Published: Cambridge, UK Cambridge University Press 25.04.2012; Cambridge University Press (CUP)
• Subjects: Applied fluid mechanics; Capillarity; Capillary waves; Coalescence; Computer simulation; Deviation; Droplets; Drops and bubbles; Ejection; Engineering Sciences; Exact sciences and technology; Fluid dynamics; Fluid mechanics; Fluids mechanics; Fundamental areas of phenomenology (including applications); Hydrodynamics, hydraulics, hydrostatics; Mechanics; Nonhomogeneous flows; Numerical analysis; Physics; Self-similarity; Spreading; Surface tension; Wave power; Wave propagation; capillary waves; drops; contact lines; Capillary waves; Wave propagation; Spreading; Digital simulation; Impact phenomena; Hydrodynamics; Droplets; Liquid layer; Experimental study; Ejection
• ISSN: 0022-1120; 1469-7645
• DOI: 10.1017/jfm.2012.49

A new regime of droplet ejection following the slow deposition of drops onto a near-complete wetting solid substrate is identified in experiments and direct numerical simulations; a coalescence cascade subsequent to pinch-off is also observed for the first time. Results of numerical simulations indicate that the propagation of capillary waves that lead to pinch-off is closely related to the self-similar behaviour observed in the inviscid recoil of droplets, and that motions of the crests and troughs of capillary waves along the interface do not depend on the wettability and surface tension (or Ohnesorge number). The simulations also show that a self-similar theory for universal pinch-off can be used for the time evolution of the pinching neck. However, although good agreement is also found with the double-cone shape of the pinching neck for droplet ejection in drop deposition on a pool of the same liquid, substantial deviations are observed in such a comparison for droplet ejection in rapid drop spreading (including the newly identified regime). This deviation is shown to result from interference by the solid substrate, a rapid downwards acceleration of the top of the drop surface and the rapid spreading process. The experiments also confirm non-monotonic spreading behaviour observed previously only in numerical simulations, and suggest substantial inertial effects on the relation between an apparent contact angle and the dimensionless contact-line speed.