Self-similar recoil of inviscid drops

Abstract

After capillary pinchoff of a fluid thread or drop, the newly created drop tips recoil due to the large local curvature. Similarity solutions for the postpinchoff recoil of an axisymmetric inviscid fluid of density 1 and surface tension ␥ immersed in a surrounding fluid of density 2 are obtained over a range of the density ratio Dϭ 2 / 1 . The far-field shape of the two new drops and the far-field dipole potentials are prescribed from known prepinching solutions ͓D. Leppinen and J. R. Lister, Phys. Fluids 15, 568 ͑2003͔͒ and the positions and self-similar shape of the two recoiling tips are calculated. The momentum of the prepinching flow makes a significant difference to the recoiling shapes. Capillary waves are observed, in agreement with previous two-dimensional studies and analytical calculations, and the wave frequency is found to increase with D. The recoil of a single axisymmetric drop ͑with a conical far-field shape͒ under surface tension is also studied as a function of D and the far-field cone angle 0 . Capillary waves are again observed, and the results for small values of 0 are shown to agree well with previous asymptotic predictions. The related problem of violent jet emission, following the formation of a near-conical structure with very high curvature at its tip, is also discussed and its similarity with the recoiling cone problem investigated.

Surface-tension-driven flow in a slender cone

“…Since the aspect ratio of the cone is observed to be small in experiments (Peregrine et al, 1990;Kowalewski, 1996), this limit is particularly relevant. More recently, Sierou & Lister (2004) have numerically considered the inviscid bifurcation problem over a wide range of aspect ratios, and produce results which agree very well with our asymptotic results presented here in the regime where both the asymptotics and numerics are valid. Sierou & Lister (2004) also confirm the self-similar nature of the flow and investigate this in detail.…”

“…However, these papers have been SURFACE-TENSION-DRIVEN FLOW IN A SLENDER CONE 3 of 32 reviewed elsewhere recently (e.g. by Leppinen et al, 2003;Sierou et al, 2004;Billingham & King, 2005), and so further review here seems unnecessary.…”

Revision of Bubble Bursting: Universal Scaling Laws of Top Jet Drop Size and Speed

“…Contrarily to the physical mechanism presented in [1], which attributes to viscosity the origin of the jet generated after the bursting of a bubble resting on a free interface, in [3] we reveal that such jet emerges as a consequence of a purely inertial mechanism, triggered by the presence of the fastest capillary wave which, once generated during the rim retraction process, propagates towards the apex of the air cavity [4], breaking the self similarity of the inertio-capillary collapse of the void [5][6][7][8]. However, viscosity plays a role in the selection of FIG.…”

“…Thus, it is hypothesized in [1] that viscosity sets in motion a region of width comparable to the initial radius of the bubble with a velocity comparable with the capillary velocity V c , a fact which is in contradiction with the well known results by [2], where it is shown that the width of the region where vorticity produced by viscous effects to comply with the shear-free condition at the interface is concentrated in a boundary layer region of width much smaller than R 0 . Indeed, the numerical results in figure 1 illustrate that the thickness of the boundary layer formed in the high curvature region located at the base of the ejected jet, which depends on the Ohnesorge number, is far smaller than R 0 .Contrarily to the physical mechanism presented in [1], which attributes to viscosity the origin of the jet generated after the bursting of a bubble resting on a free interface, in [3] we reveal that such jet emerges as a consequence of a purely inertial mechanism, triggered by the presence of the fastest capillary wave which, once generated during the rim retraction process, propagates towards the apex of the air cavity [4], breaking the self similarity of the inertio-capillary collapse of the void [5][6][7][8]. However, viscosity plays a role in the selection of FIG.…”

Interfacial dynamics and pinch-off singularities for axially symmetric Darcy flow

“…Once pinch-off has occurred, the two newly formed satellite bubbles will rapidly recoil due to the large local curvature at each of the tips. While many studies concerned with the pinch-off of viscous or inviscid fluids have focused on the behaviour of the interface ap- proaching pinch-off, fewer studies consider the behaviour of post break-up [58][59][60]. As a starting point, we expect the argument in Sec.…”