Singularities and Similarity Solutions in Capillary Breakup

Lister, Joseph; Brenner, Michael P.; Day, Richard F.; Hinch, E. J.; Stone, Howard A.

doi:10.1007/978-94-011-4736-1_23

Cited by 1 publication

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“…Very close in time and space to the point where a fluid thread or drop breaks into two drops, there is no externally imposed lengthscale and the evolution of the free-surface shape is self-similar and independent of initial conditions. Various dynamical regimes in the absence of surfactant have been analysed, as reviewed by Lister et al (1997), and the corresponding similarity solutions derived. In particular, we note that, in the presence of a non-zero external viscosity, however small, the eventual asymptotic balance is between internal and external viscous stresses and surface tension, with inertia being negligible (Lister & Stone 1998).…”

Section: Scaling Analysis Near Breakupmentioning

confidence: 99%

The effect of surfactant on the stability of a liquid thread

2002

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The surface-tension-driven motion of a surfactant-coated liquid thread in inviscid surroundings is investigated using linear stability theory as well as one-dimensional nonlinear approximations to the governing Navier–Stokes equations. Examination of analytic limits of the linear dispersion relationship demonstrates that surfactant acts as a distinct mechanism for long-wavelength cut-off, instead of inertia, if the surfactant effects exceed a critical value, β = ½, where β is a dimensionless surface-tension gradient. Two different long-wavelength regimes can be identified, depending on the degree of tangential stress, with β = 1 characterizing a transition from extensionally dominated inertial flow to shear-dominated viscous flow. One-dimensional nonlinear models are formulated which capture the changes in behaviour with variation of β by inclusion of the necessary high-order terms. Scaling close to breakup shows that surfactant is swept away from the pinching region and then has little effect.

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Section: Scaling Analysis Near Breakupmentioning

confidence: 99%