Constant Froude number in a circular hydraulic jump and its implication on the jump radius selection

The properties of a standard hydraulic jump depend critically on a Froude number Fr defined as the ratio of the flow velocity to the gravity waves speed. In the case of a horizontal circular jump, the question of the Froude number is not well documented. Our experiments show that Fr measured just after the jump is locked on a constant value that does not depend on flow rate Q, kinematic viscosity {\nu} and surface tension {\gamma}. Combining this result to a lubrication description of the outer flow yields, under appropriate conditions, a new and simple law ruling the jump radius RJ : $R_J (ln (\frac{R_\infty}{R_J}))^{3/8} \sim Q^{5/8}\nu ^{-3/8}$, in excellent agreement with our experimental data. This unexpected RJ result asks an unsolved question to all available models.Comment: 5 pages, 3 figure

Orbits and reversals of a drop rolling inside a horizontal circular hydraulic jump

We explore the complex dynamics of a non-coalescing drop of moderate size inside a circular hydraulic jump of the same liquid formed on a horizontal disk. In this situation the drop is moving along the jump and one observes two different motions: a periodic one (it orbitates at constant speed) and an irregular one involving reversals of the orbital motion. Modeling the drop as a rigid sphere exchanging friction with liquid across a thin film of air, we recover the orbital motion and the internal rotation of the drop. This internal rotation is experimentally observed.Comment: 5 pages, 6 figure

Absolute stability of a Bénard-von Kármán vortex street in a confined geometry

International audienceWe have investigated the stability of a double vortex street, induced in a rectangular container by a tape, or a rope, moving at high speed on its free surface. Depending on the tape velocity and on the geometrical aspect ratios, three patterns of flows are observed: (1) a vortex street with recirculation of the liquid along the lateral sides of the container, (2) the same recirculation but with no stable vortex array, (3) recirculation along the bottom of the container. We have investigated the spatial structure of the vortex street and found that this system explores the phase space available inside a stability tongue predicted at the end of the 1920s by Rosenhead for point vortices in a perfect fluid. Although this very surprising result contrasts with the well-known von Kármán unique stability condition for point vortex streets in an infinite domain, this complements the theory inside a channel of finite breadth. In this paper, we present the very first experimental confirmation of this 90-year old theory

Viscoelastic liquid curtains

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Gyroscopic Instability of a Drop Trapped Inside an Inclined Circular Hydraulic Jump

International audienceA drop of moderate size deposited inside a circular hydraulic jump remains trapped at the shock front and does not coalesce with the liquid flowing across the jump. For a small inclination of the plate on which the liquid is impacting, the drop does not always stay at the lowest position and oscillates around it with a sometimes large amplitude, and a frequency that slightly decreases with flow rate. We suggest that this striking behavior is linked to a gyroscopic instability in which the drop tries to keep constant its angular momentum while sliding along the jump

La pub pour le tabac augmente sa consommation

En Suisse, les jeunes sont très exposé·e·s au marketing vantant les produits du tabac, engendrant une consommation élevée parmi ce public vulnérable. Des études montrent qu’interdire la publicité est une mesure efficace contre le tabagisme

Viscoelastic liquid curtains: Experimental results on the flow of a falling sheet of polymer solution

International audienceWe experimentally investigate the extensional flow of a sheet-or curtain-of viscoelastic liquid falling freely from a slot at constant flow rate under gravity. Extruded liquids are aqueous solutions of flexible polyethylene oxide (PEO) and of semi-rigid partially hydrolysed polyacrylamide (HPAM) with low shear viscosities. Velocimetry measurements reveal that the mean velocity field U(z), z being the distance from the slot exit, does not reduce to a free-fall. More precisely, we show that the liquid falls initially with sub-gravitational accelerations up to a distance from the slot which scales as gτ 2 f il , where g is gravity and τ f il is the extensional relaxation time of the liquid, beyond which the local acceleration reaches the asymptotic free-fall value g. The length of the sub-gravitational part of the curtain is shown to be much larger than the equivalent viscous length ((4η/ρ) 2 /g) 1/3 for Newtonian liquids of density ρ and dynamic viscosity η, which is usually small compared to the length of the curtain. The elastic length gτ 2 f il can indeed be surprisingly large when adding high molecular weight polymer molecules to a low-viscosity Newtonian solvent. By analogy with Newtonian curtains, we show that the velocity field U(z) rescales on a master curve. Besides, we show that the flow is only weakly affected by the history of polymer deformations in the die upstream of the curtain. Furthermore, investigations of the curtain stability reveal that polymer addition reduces the minimum flow rate required to maintain a continuous sheet of liquid

Rotations d'une goutte dans un ressaut hydraulique circulaire

International audienceUne goutte dont la taille est de l'ordre de la longueur capillaire dans un ressaut circulaire peutêtre piégée le long du front. Elle ne coalesce pas avec le bain du même liquide. Dans le cas d'un ressaut formé sur une plaque horizontale, la goutte peut adopter deux comportements distincts : l'un périodique (la goutte orbite dans le ressaut), l'autre apériodique. Nous mettons enévidence expérimentalement la rotation propre de la goutte (duè a l'entraînement via le film d'air qui sépare la goutte et le ressaut) ; c'est un paramètre clé de cette dynamique. Nous caractérisons cette rotation propre et nous montrons, en particulier, que la loi de fréquence n'est pas cellè a laquelle on pourrait s'attendre avec un modèle simple de sphère dure entraînée par le liquideà travers un film d'air en cisaillement simple. Abstract. A drop of moderate size deposited inside a circular hydraulic jump remains trapped at the shock front and does not coalesce with the liquid flowing across the jump. For a horizontal plate on which the liquid is impacting, the drop exhibits two different motions : a periodic one (the drop orbitates around the jump) and an aperiodic one. We experimentally show that a key parameter is the internal rotation of the drop (across the air layer which separates the drop and the jump). We characterize this internal rotation, particularly, we show that the frequency law is not the one we can deduce from a simple model of rigid sphere driven by the liquid through a sheared air layer