66 research outputs found
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
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