89 research outputs found
Impact on floating membranes
When impacted by a rigid object, a thin elastic membrane with negligible
bending rigidity floating on a liquid pool deforms. Two axisymmetric waves
radiating from the impact point propagate. In the first place, a longitudinal
wave front -- associated with in-plane deformation of the membrane and
traveling at constant speed -- separates an outward stress free domain with a
stretched but flat domain. Then, in the stretched domain a dispersive
transverse wave travels at a wave speed that depends on the local stretching
rate. We study the dynamics of this fluid-body system and we show that the wave
dynamics is similar to the capillary waves that propagate at a liquid-gas
interface but with a surface tension coefficient that depends on impact speed.
We emphasize the role of the stretching in the membrane in the wave dynamics
but also in the development of a buckling instability that give rise to radial
wrinkles
Rayleigh-B\'enard convection with a melting boundary
We study the evolution of a melting front between the solid and liquid phases
of a pure incompressible material where fluid motions are driven by unstable
temperature gradients. In a plane layer geometry, this can be seen as classical
Rayleigh-B\'enard convection where the upper solid boundary is allowed to melt
due to the heat flux brought by the fluid underneath. This free-boundary
problem is studied numerically in two dimensions using a phase-field approach,
classically used to study the melting and solidification of alloys, which we
dynamically couple with the Navier-Stokes equations in the Boussinesq
approximation. The advantage of this approach is that it requires only moderate
modifications of classical numerical methods. We focus on the case where the
solid is initially nearly isothermal, so that the evolution of the topography
is related to the inhomogeneous heat flux from thermal convection, and does not
depend on the conduction problem in the solid. From a very thin stable layer of
fluid, convection cells appears as the depth -- and therefore the effective
Rayleigh number of the layer increases. The continuous melting of the solid
leads to dynamical transitions between different convection cell sizes and
topography amplitudes. The Nusselt number can be larger than its value for a
planar upper boundary, due to the feedback of the topography on the flow, which
can stabilize large-scale laminar convection cells.Comment: 36 pages, 16 figure
Curvature singularity and film-skating during drop impact
We study the influence of the surrounding gas in the dynamics of drop impact
on a smooth surface. We use an axisymmetric 3D model for which both the gas and
the liquid are incompressible; lubrication regime applies for the gas film
dynamics and the liquid viscosity is neglected. In the absence of surface
tension a finite time singularity whose properties are analysed is formed and
the liquid touches the solid on a circle. When surface tension is taken into
account, a thin jet emerges from the zone of impact, skating above a thin gas
layer. The thickness of the air film underneath this jet is always smaller than
the mean free path in the gas suggesting that the liquid film eventually wets
the surface. We finally suggest an aerodynamical instability mechanism for the
splash.Comment: 5 figure
Rarefied gas correction for the bubble entrapment singularity in drop impacts
We study the non-continuous correction in the dynamics of drop impact on a
solid substrate. Close to impact, a thin film of gas is formed beneath the drop
so that the local Knudsen number is of order one. We consider the first
correction to the dynamics which consists of allowing slip of the gas along the
substrate and the interface. We focus on the singular dynamics of entrapment
that can be seen when surface tension and liquid viscosity can be neglected.
There we show that different dynamical regimes are present that tend to lower
the singularity strength. We finally suggest how these effects might be
connected to the influence of the gas pressure in the impact dynamics observed
in recent experiments
The Explicit-Implicit-Null method:Removing the numerical instability of PDEs
International audienceno abstrac
Bistability in Rayleigh-B\'enard convection with a melting boundary
A pure and incompressible material is confined between two plates such that
it is heated from below and cooled from above. When its melting temperature is
comprised between these two imposed temperatures, an interface separating
liquid and solid phases appears. Depending on the initial conditions, freezing
or melting occurs until the interface eventually converges towards a stationary
state. This evolution is studied numerically in a two-dimensional configuration
using a phase-field method coupled with the Navier-Stokes equations. Varying
the control parameters of the model, we exhibit two types of equilibria:
diffusive and convective. In the latter case, Rayleigh-B\'enard convection in
the liquid phase shapes the solid-liquid front, and a macroscopic topography is
observed. A simple way of predicting these equilibrium positions is discussed
and then compared with the numerical simulations. In some parameter regimes, we
show that multiple equilibria can coexist depending on the initial conditions.
We also demonstrate that, in this bi-stable regime, transitioning from the
diffusive to the convective equilibrium is inherently a nonlinear mechanism
involving finite-amplitude perturbations
Asymptotic behaviour of the Rayleigh--Taylor instability
We investigate long time numerical simulations of the inviscid
Rayleigh-Taylor instability at Atwood number one using a boundary integral
method. We are able to attain the asymptotic behavior for the spikes predicted
by Clavin & Williams\cite{clavin} for which we give a simplified demonstration.
In particular we observe that the spike's curvature evolves like while
the overshoot in acceleration shows a good agreement with the suggested
law. Moreover, we obtain consistent results for the prefactor coefficients of
the asymptotic laws. Eventually we exhibit the self-similar behavior of the
interface profile near the spike.Comment: 4 pages, 6 figure
Two dimensional Leidenfrost Droplets in a Hele Shaw Cell
We experimentally and theoretically investigate the behavior of Leidenfrost
droplets inserted in a Hele-Shaw cell. As a result of the confinement from the
two surfaces, the droplet has the shape of a flattened disc and is thermally
isolated from the surface by the two evaporating vapor layers. An analysis of
the evaporation rate using simple scaling arguments is in agreement with the
experimental results. Using the lubrication approximation we numerically
determine the shape of the droplets as a function of its radius. We furthermore
find that the droplet width tends to zero at its center when the radius reaches
a critical value. This prediction is corroborated experimentally by the direct
observation of the sudden transition from a flattened disc into an expending
torus. Below this critical size, the droplets are also displaying capillary
azimuthal oscillating modes reminiscent of a hydrodynamic instability
Instabilité de Rayleigh–Taylor d’un film mince visqueux
Cette étude numérique concerne le
développement de l'instabilité de Rayleigh-Taylor d'un film mince aux temps longs. Nous
présenterons une étude de stabilité linéaire générale, ainsi que les différents régimes
observés aux temps longs, en fonction des paramètres sans dimensions du problème
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