53 research outputs found
Liquid jet eruption from hollow relaxation
A cavity hollowed out on a free liquid surface is relaxing, forming an
intense liquid jet. Using a model experiment where a short air pulse sculpts an
initial large crater, we depict the different stages in the gravitational
cavity collapse and in the jet formation. Prior eversion, all cavity profiles
are found to exhibit a shape similarity. Following hollow relaxation, a
universal scaling law establishing an unexpected relation between the jet
eruption velocity, the initial cavity geometry and the liquid viscosity is
evidenced experimentally. On further analysing the jet forms we demonstrate
that the stretched liquid jet also presents shape similarity. Considering that
the jet shape is a signature of the initial flow focusing, we elaborate a
simple model capturing the key features of the erupting jet velocity scaling
A pressure impulse theory for hemispherical liquid impact problems
Liquid impact problems for hemispherical fluid domain are considered. By
using the concept of pressure impulse we show that the solution of the flow
induced by the impact is reduced to the derivation of Laplace's equation in
spherical coordinates with Dirichlet and Neumann boundary conditions. The
structure of the flow at the impact moment is deduced from the spherical
harmonics representation of the solution. In particular we show that the slip
velocity has a logarithmic singularity at the contact line. The theoretical
predictions are in very good agreement both qualitatively and quantitatively
with the first time step of a numerical simulation with a Navier-Stokes solver
named Gerris.Comment: 11 pages, 14 figures, Accepted for publication in European Journal of
Mechanics - B/Fluid
Soft beams: when capillarity induces axial compression
We study the interaction of an elastic beam with a liquid drop in the case
where bending and extensional effects are both present. We use a variational
approach to derive equilibrium equations and constitutive relation for the
beam. This relation is shown to include a term due to surface energy in
addition of the classical Young's modulus term, leading to a modification of
Hooke's law. At the triple point where solid, liquid, and vapor phases meet we
find that the external force applied on the beam is parallel to the
liquid-vapor interface. Moreover, in the case where solid-vapor and
solid-liquid interface energies do not depend on the extension state of the
beam, we show that the extension in the beam is continuous at the triple point
and that the wetting angle satisfy the classical Young-Dupr\'e relation
On the physics of fizzing: How bubble bursting controls droplets ejection
Bubbles at a free surface surface usually burst in ejecting myriads of
droplets. Focusing on the bubble bursting jet, prelude for these aerosols, we
propose a simple scaling for the jet velocity and we unravel experimentally the
intricate roles of bubble shape, capillary waves, gravity and liquid
properties. We demonstrate that droplets ejection unexpectedly changes with
liquid properties. In particular, using damping action of viscosity,
self-similar collapse can be sheltered from capillary ripples and continue
closer to the singular limit, therefore producing faster and smaller
droplets.These results pave the road to the control of the bursting bubble
aerosols
Transient energy growth for the Lamb-Oseen vortex
The transient evolution of infinitesimal flow disturbances whichoptimally induce algebraic growth in the Lamb-Oseen (gaussian) vortex is studied using a direct-adjoint technique. This optimal perturbation analysis reveals that the Lamb-Oseen vortex allows for intense amplification of kinetic energy for 2D and 3D perturbations of azimuthal wavenumber . In both cases, the disturbances experiencing the most growth initially take the form of concentrated spirals at the outer periphery of the vortex which rapidly excite bending waves within the vortex core. In the limit of large wavelengths, the optimal perturbation leads to arbitrary large growths via an original scenario combining the Orr mechanism with vortex induction
On vortex rings around vortices: an optimal mechanism
Stable columnar vortices subject to hydrodynamic noise (\eg turbulence) present some recurrent behaviours like the systematic development of vortex rings at the periphery of the vortex core. This phenomenon still lacks a comprehensive explanation, partly because it is not associated to an instability \textit{stricto sensu}. The aim of the present paper is to identify the physical mechanism triggering this intrinsic feature of vortices using an optimal perturbation analysis as a tool of investigation. We found that the generation of vortex rings is linked to the intense and rapid amplification of specific disturbances in the form of azimuthal velocity streaks that eventually evolve into azimuthal vorticity rolls generated by the rotational part of the local Coriolis force. This evolution thus appears to follow a scenario opposite to the classical lift-up view, where rolls give rise to streaks
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