Shape of a recoiling liquid filament

Conto, Francesco Paolo; Marin, Juan F.; Antkowiak, Arnaud; Castrejon-Pita, J. Rafael; Gordillo, Leonardo


We study the capillary retraction of a Newtonian semi-infinite liquid filament through analytical methods. We derive a long-time asymptotic-state expansion for the filament profile using a one-dimensional free-surface slender cylindrical flow model based on the three-dimensional axisymmetric Navier-Stokes equations. The analysis identifies three distinct length and time scale regions in the retraction domain: a steady filament section, a growing spherical blob, and an intermediate matching zone. We show that liquid filaments naturally develop travelling capillary waves along their surface and a neck behind the blob. We analytically prove that the wavelength of the capillary waves is approximately 3.63 times the filament's radius at the inviscid limit. Additionally, the waves' asymptotic wavelength, decay length, and the minimum neck size are analysed in terms of the Ohnesorge number. Finally, our findings are compared with previous results from the literature and numerical simulations in Basilisk obtaining a good agreement. This analysis provides a full picture of the recoiling process going beyond the classic result of the velocity of retraction found by Taylor and Culick.

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Título según WOS: Shape of a recoiling liquid filament
Título según SCOPUS: Shape of a recoiling liquid filament
Título de la Revista: SCIENTIFIC REPORTS
Volumen: 9
Número: 1
Fecha de publicación: 2019
Idioma: English