Christophe Josserand

Droplet Splashing on a Thin Liquid Film

We propose a theory predicting the transition between splashing and deposition for impacting drops. This theory agrees with current experimental observations and is supported by numerical simulations. It assumes that the width of the ejected liquid sheet during impact is precisely controlled by a viscous length l ν . Numerous predictions follow this theory and they compare well with recent experiments reported by Thoroddsen [J. Fluid Mech. 451, 373 (2002)].

Drop dynamics after impact on a solid wall: Theory and simulations

We study the impact of a fluid drop onto a planar solid surface at high speed so that at impact, kinetic energy dominates over surface energy and inertia dominates over viscous effects. As the drop spreads, it deforms into a thin film, whose thickness is limited by the growth of a viscous boundary layer near the solid wall. Owing to surface tension, the edge of the film retracts relative to the flow in the film and fluid collects into a toroidal rim bounding the film. Using mass and momentum conservation, we construct a model for the radius of the deposit as a function of time. At each stage, we perform detailed comparisons between theory and numerical simulations of the Navier–Stokes equation.

Numerical simulation of droplets, bubbles and waves : state of the art

This work presents current advances in the numerical simulation of twophase flows using a volume of fluid (VOF) method, balanced-force surface tension and quad/octree adaptive mesh refinement (AMR). The simulations of the atomization of a liquid sheet, the capillary retraction of a liquid sheet and two- and three-dimensional wave breaking all for air/water systems are used to show the potential of the numerical techniques. New simulations of atomization processes for air/water conditions are allowing us to investigate the processes leading to the appearance of instabilities in the primary atomization zone in real conditions. For the retracting liquid sheet, the new simulations show that two different regimes can be encountered as a function of the Ohnesorge number. For large values, a laminar flow is encountered inside the rim and a steady state is reached after a quick transient state. For small values, a turbulent flow is generated inside the rim, which is responsible for large oscillations in the rim size and neck thickness. The breaking wave case study demonstrates the orders-of-magnitude efficiency gains of the AMR method.

Jet formation in bubbles bursting at a free surface

We study numerically bubbles bursting at a free surface and the subsequent jet formation. The Navier–Stokes equations with a free surface and surface tension are solved using a marker-chain approach. Differentiation and boundary conditions near the free surface are satisfied using least-squares methods. Initial conditions involve a bubble connected to the outside atmosphere by a preexisting opening in a thin liquid layer. The evolution of the bubble is studied as a function of bubble radius. A jet forms with or without the formation of a tiny air bubble at the base of the jet. The radius of the droplet formed at the tip of the jet is found to be about one tenth of the initial bubble radius. A series of critical radii exist, for which a transition from a dynamics with or without bubbles exist. For some parameter values, the jet formation is close to a singular flow, with a conical cavity shape and a large curvature or cusp at the bottom. This is compared to similar singularities investigated in other contexts such as Faraday waves.

Inviscid coalescence of drops

We study the coalescence of two drops of an ideal fluid driven by surface tension. The velocity of approach is taken to be zero and the dynamical effect of the outer fluid (usually air) is neglected. Our approximation is expected to be valid on scales larger than

Pyramidal and toroidal water drops after impact on a solid surface

\ell_{\nu} = \rho\nu^2/\sigma

Retraction dynamics of aqueous drops upon impact on non-wetting surfaces

, which is 10 nm for water. Using a high-precision boundary integral method, we show that the walls of the thin retracting sheet of air between the drops reconnect in finite time to form a toroidal enclosure. After the initial reconnection, retraction starts again, leading to a rapid sequence of enclosures. Averaging over the discrete events, we find the minimum radius of the liquid bridge connecting the two drops to scale like

Condensation of Classical Nonlinear Waves

r_b \propto t^{1/2}

von Kármán vortex street within an impacting drop.

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Droplet impact on a dry surface: triggering the splash with a small obstacle

Superhydrophobic surfaces generate very high contact angles as a result of their microstructure. The impact of a water drop on such a surface shows unusual features, such as total rebound at low impact speed. We report experimental and numerical investigations of the impact of approximately spherical water drops. The axisymmetric free surface problem, governed by the Navier–Stokes equations, is solved numerically with a front-tracking marker-chain method on a square grid. Experimental observations at moderate velocities and capillary wavelength much less than the initial drop radius show that the drop evolves to a staircase pyramid and eventually to a torus. Our numerical simulations reproduce this effect. The maximal radius obtained in numerical simulations precisely matches the experimental value. However, the large velocity limit has not been reached experimentally or numerically. We discuss several complications that arise at large velocity: swirling motions observed in the cross-section of the toroidal drop and the appearance of a thin film in the centre of the toroidal drop. The numerical results predict the dry-out of this film for sufficiently high Reynolds and Weber numbers. When the drop rebounds, it has a top-heavy shape. In this final stage, the kinetic energy is a small fraction of its initial value.