56 research outputs found
Self-similar impulsive capillary waves on a ligament
We study the short-time dynamics of a liquid ligament, held between two solid
cylinders, when one is impulsively accelerated along its axis. A set of
one-dimensional equations in the slender-slope approximation is used to
describe the dynamics, including surface tension and viscous effects. An exact
self-similar solution to the linearized equations is successfully compared to
experiments made with millimetric ligaments. Another non-linear self-similar
solution of the full set of equations is found numerically. Both the linear and
non-linear solutions show that the axial depth at which the liquid is affected
by the motion of the cylinder scales like . The non-linear solution
presents the peculiar feature that there exists a maximum driving velocity
above which the solution disappears, a phenomenon probably related to
the de-pinning of the contact line observed in experiments for large pulling
velocities
Quantitative analysis of the dripping and jetting regimes in co-flowing capillary jets
We study a liquid jet that breaks up into drops in an external co-flowing
liquid inside a confining microfluidic geometry. The jet breakup can occur
right after the nozzle in a phenomenon named dripping or through the generation
of a liquid jet that breaks up a long distance from the nozzle, which is called
jetting. Traditionally, these two regimes have been considered to reflect the
existence of two kinds of spatiotemporal instabilities of a fluid jet, the
dripping regime corresponding to an absolutely unstable jet and the jetting
regime to a convectively unstable jet. Here, we present quantitative
measurements of the dripping and jetting regimes, both in an unforced and a
forced state, and compare these measurements with recent theoretical studies of
spatiotemporal instability of a confined liquid jet in a co-flowing liquid. In
the unforced state, the frequency of oscillation and breakup of the liquid jet
is measured and compared to the theoretical predictions. The dominant frequency
of the jet oscillations as a function of the inner flow rate agrees
qualitatively with the theoretical predictions in the jetting regime but not in
the dripping regime. In the forced state, achieved with periodic laser heating,
the dripping regime is found to be insensitive to the perturbation and the
frequency of drop formation remains unaltered. The jetting regime, on the
contrary, amplifies the externally imposed frequency, which translates in the
formation of drops at the frequency imposed by the external forcing. In
conclusion, the dripping and jetting regimes are found to exhibit the main
features of absolutely and convectively unstable flows respectively, but the
frequency selection in the dripping regime is not ruled by the absolute
frequency predicted by the stability analysis.Comment: 10 pages, 12 figures, to appear in Physics of Fluid
On the three-dimensional temporal spectrum of stretched vortices
The three-dimensional stability problem of a stretched stationary vortex is
addressed in this letter. More specifically, we prove that the discrete part of
the temporal spectrum is only associated with two-dimensional perturbations.Comment: 4 pages, RevTeX, submitted to PR
Experimental and theoretical study of the elliptic instability in a rotating stratified flow
The combined effects of Coriolis force and buoyancy effects on the dynamics of a weakly elliptical bounded vortex are treated theoretically as well as experimentally. As predicted theoretically, stratification and rotation have antagonist contributions to the stability of an elliptical vortex. Thus if the stratification is strong enough (Nb>Omega_c, Nb and Omega_c being respectively the Brunt-Väisälä frequency and the rotation rate of the flow in a frame rotating with the elliptical deformation at angular velocity Omega_t), we have observed that only anticyclones (such that |Wa|<Omega_c with Wa=2(Omega_c+Omega_t)) are unstable, whereas the cyclones are always stable. In addition if the stratification is weak, instability areas over change. These instability thresholds found theoretically have been observed experimentally with a good accuracy and the measured growth rate are in a good agreement with those predicted by a linear stability analysis in the limit of small deformation
Magnetic field induced by elliiptical instability in a rotating tidally distorded sphere
It is usually believed that the geo-dynamo of the Earth or more generally of
other planets, is created by the convective fluid motions inside their molten
cores. An alternative to this thermal or compositional convection can however
be found in the inertial waves resonances generated by the eventual precession
of these planets or by the possible tidal distorsions of their liquid cores. We
will review in this paper some of our experimental works devoted to the
elliptical instability and present some new results when the experimental fluid
is a liquid metal. We show in particular that an imposed magnetic field is
distorted by the spin- over mode generated by the elliptical instability. In
our experiment, the field is weak (20 Gauss) and the Lorenz force is negligible
compared to the inertial forces, therefore the magnetic field does not modify
the fluid flow and the pure hydrodynamics growth rates of the instability are
recovered through magnetic measurements
Three-dimensional instability during vortex merging
4 p.The interaction of two parallel vortices of equal circulation is observed experimentally. For low Reynolds numbers (), the vortices remain two-dimensional and merge into a single one, when their time-dependent core size exceeds approximately 30\% of the vortex separation distance. At higher , a three-dimensional instability is discovered, showing the characteristics of an elliptic instability of the vortex cores. The instability rapidly generates small-scale turbulent motion, which initiates merging for smaller core sizes and produces a bigger final vortex than for laminar 2D flow
Delayed Capillary Breakup of Falling Viscous Jets
Thin jets of viscous fluid like honey falling from capillary nozzles can attain lengths exceeding 10 m before breaking up into droplets via the Rayleigh-Plateau (surface tension) instability. Using a combination of laboratory experiments and WKB analysis of the growth of shape perturbations on a jet being stretched by gravity, we determine how the jet's intact length lb depends on the flow rate Q, the viscosity η, and the surface tension coefficient γ. In the asymptotic limit of a high-viscosity jet, lb∼(gQ2η4/γ4)1/3, where g is the gravitational acceleration. The agreement between theory and experiment is good, except for very long jets.</p
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