2007
DOI: 10.1093/imamat/hxm043
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Surface-tension-driven flow in a slender cone

Abstract: After a droplet has broken away from a slender thread or jet of liquid, the tip of the thread or jet recoils rapidly. At the moment of break-off, the tip of the thread/jet is observed to have the shape of a cone close to the bifurcation point. In this paper, we study the evolution of an ideal fluid which is initially conical, where the only force acting on the fluid is due to surface tension. We find an asymptotic solution to the problem in terms of the aspect ratio of the cone which is assumed to be small. Us… Show more

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Cited by 4 publications
(3 citation statements)
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“…A two-dimensional planar version of these dynamics has been considered using potential flow theory [17] and leads to an exponent of 2=3, irrespective of eq . In fact, a number of theoretical studies in planar as well as axisymmetric geometries predict power-law exponents of 2=3 for situations involving self-similar generation of capillary waves [17][18][19]. We postulate a different extension of these ideas to our experiments, which leads to a power law for the spreading radius with the exponent depending continuously on eq .…”
Section: Fig 2 Evidence Of Inertial Wetting (A)mentioning
confidence: 74%
“…A two-dimensional planar version of these dynamics has been considered using potential flow theory [17] and leads to an exponent of 2=3, irrespective of eq . In fact, a number of theoretical studies in planar as well as axisymmetric geometries predict power-law exponents of 2=3 for situations involving self-similar generation of capillary waves [17][18][19]. We postulate a different extension of these ideas to our experiments, which leads to a power law for the spreading radius with the exponent depending continuously on eq .…”
Section: Fig 2 Evidence Of Inertial Wetting (A)mentioning
confidence: 74%
“…Obviously, p = 0 for a stationary array of all identical blobs when δ = 0 and for δ = 0, a longitudinal flow sets-in (Sierou & Lister 2004;Brasz, Bemy & Bird 2018) which interferes with the capillary instability (Decent & King 2008). The dynamics of a blob radius h(t) in the assembly, now incorporating the influence of the adjacent blobs, is thus given byḧ…”
Section: Rough Ligaments: Rearrangements Versus Instability Time Scalesmentioning
confidence: 99%
“…Even though the resolution of our computations is not enough to describe these stages in detail, figure 5() suggests that the analysis of the last cited references could hold also during the detachment of an electrified ligament. The first stages following pinch-off in the absence of electric forces have been analysed by Keller, King & Ting (1995) and Decent & King (2008), among others. However, the strong electric stress at the tip in figure 5() (which could be an artefact due to the numerical truncation of the surface) makes this analysis less certain for an electrified meniscus.…”
Section: Numerical Procedures and Resultsmentioning
confidence: 99%