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 ρ1 and surface tension γ immersed in a surrounding fluid of density ρ2 are obtained over a range of the density ratio D=ρ2/ρ1. 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 (2003)] 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 shape) under surface tension is also studied as a function of D and the far-field cone angle θ0. Capillary waves are again observed, and the results for small values of θ0 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.