Singularities in droplet pinching with vanishing viscosity

A slender-jet model for the pinching of a liquid column is considered in the limit of vanishing viscosity. We find the model to develop a singularity in the gradients of the local radius and the velocity at a finite thread radius, so it does not describe breakup. However, the observed steepening of the profile corresponds to experiments and simulations with fluids at low viscosity. The singularity has similarity form, which we compute analytically. The result agrees well with numerical simulations of the model equations.Comment: 18 pages including 4 eps figures, revte

Stability of viscous long liquid filaments

We study the collapse of an axisymmetric liquid filament both analytically and by means of a numerical model. The liquid filament, also known as ligament, may either collapse stably into a single droplet or break up into multiple droplets. The dynamics of the filament are governed by the viscosity and the aspect ratio, and the initial perturbations of its surface. We find that the instability of long viscous filaments can be completely explained by the Rayleigh-Plateau instability, whereas a low viscous filament can also break up due to end pinching. We analytically derive the transition between stable collapse and breakup in the Ohnesorge number versus aspect ratio phase space. Our result is confirmed by numerical simulations based on the slender jet approximation and explains recent experimental findings by Castrejon-Pita et al., PRL 108, 074506 (2012).Comment: 7 page

Self-similar breakup of polymeric threads as described by the Oldroyd-B model

When a drop of fluid containing long, flexible polymers breaks up, it forms threads of almost constant thickness, whose size decreases exponentially in time. Using an Oldroyd-B fluid as a model, we show that the thread profile, rescaled by the thread thickness, converges to a similarity solution. Using the correspondence between viscoelastic fluids and non-linear elasticity, we derive similarity equations for the full three-dimensional axisymmetric flow field in the limit that the viscosity of the solvent fluid can be neglected. A conservation law balancing pressure and elastic energy permits to calculate the thread thickness exactly. The explicit form of the velocity and stress fields can be deduced from a solution of the similarity equations. Results are validated by detailed comparison with numerical simulations

On the physics of transient ejection from bubble bursting

The transient ejection due to a bubble bursting at the interface of a liquid with a gas environment is here described using a dynamical scaling analysis along the process. We show here that the ejection of a liquid microjet requires the backfire of a vortex ring inside the liquid to preserve physical symmetry, which involves a non-trivial scaling. We present the first single uniformly valid expression for the size and speed of ejected droplets for the whole range of the Ohnesorge and Bond numbers where droplet ejection occurs. The evolution of the flow variables, the apparent singularity for a critical Ohnesorge number, and the dispersion of data around this point are explained. Our model generalizes or displaces other recently proposed ones, impacting for instance the statistical description of sea spray.Comment: 10 pages, 3 figure

Effect of an axial electric field on the breakup of a leaky-dielectric liquid filament

Article number 092114We study experimentally and numerically the thinning of Newtonian leaky-dielectric filaments subjected to an axial electric field. We consider moderately viscous liquids with high electrical permittivity. We analyze the influence of the electric field on the formation of satellite droplets from the breakup of the filaments in the experiments. The electric force delays the free surface pinching. Two electrified filaments with the same minimum radius are thin at the same speed regardless of when the voltage is applied. The numerical simulations show that the polarization stress is responsible for the pinching delay observed in the experiments. Asymptotically close to the pinching point, the filament pinching is dominated by the diverging hydrodynamic forces. The polarization stress becomes subdominant even if this stress also diverges at this finite-time singularity. © 2021 Author(s).Ministerio de Economía, Industria y Competitividad (España) PID2019–108278RBJunta de Extremadura GR1817

Thermal rupture of a free liquid sheet

We consider a free liquid sheet, taking into account the dependence of surface tension on temperature, or concentration of some pollutant. The sheet dynamics are described within a long-wavelength description. In the presence of viscosity, local thinning of the sheet is driven by a strong temperature gradient across the pinch region, resembling a shock. As a result, for long times the sheet thins exponentially, leading to breakup. We describe the quasi one-dimensional thickness, velocity, and temperature profiles in the pinch region in terms of similarity solutions, which posses a universal structure. Our analytical description agrees quantitatively with numerical simulations