115 research outputs found

### 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

### Straight contact lines on a soft, incompressible solid

International audienceThe deformation of a soft substrate by a straight contact line is calculated, and the result applied to a static rivulet between two parallel contact lines. The substrate is supposed to be incompressible (Stokes like description of elasticity), and having a non-zero surface tension, that eventually differs depending on whether its surface is dry or wet. For a single straight line separating two domains with the same substrate surface tension, the ridge profile is shown to be be very close to that of Shanahan and de Gennes, but shift from the contact line of a distance equal to the elastocapillary length built upon substrate surface tension and shear modulus. As a result, the divergence near contact line disappears and is replaced by a balance of surface tensions at the contact line (Neumann equilibrium), though the profile remains nearly logarithmic. In the rivulet case, using the previous solution as a Green function allows one to calculate analytically the geometry of the distorted substrate, and in particular its slope on each side (wet and dry) of the contact lines. These two slopes are shown to be nearly proportional to the inverse of substrate surface tensions, though the respective weight of each side (wet and dry) in the final expressions is difficult to establish because of the linear nature of standard elasticity. A simple argument combining Neumann and Young equations is however provided to overcome this limitation. The result may have surprising implications for the modelling of hysteresis on systems having both plastic and elastic properties, as initiated long ago by Extrand and Kumagai

### Dewetting with conical tail formation: how to include a line friction of microscopic origin, and possibly evaporation?

Most studies of dewetting fronts in 3D with a "corner formation", as happens behind a drop sliding down an incline are based on a generalisation of Voinov theory, with (at least implicitly) a slip length at small scale. I here first examine what happens, if instead of considering a free slip at small scale, one admits a non-zero additional line friction of microscopic origin. Concerning the selection of cone angles, I show that most features of the model are unchanged, except that the "slip length" must be replaced in the equations with an "effective" cut off that can become apparently unphysically small. I suggest that these results could explain problematical cutoffs in the hydrodynamical modelling observed recently by Winkels et al on water drops. The sole difficulty with this interpretation is the law ruling the radius of curvature of the corner tip at small scale, which remains unsatisfactory. I suggest that evaporation of the liquid should also be considered at these very small scales and propose a preliminary "toy model" to take this effect into account. The orders of magnitude are better recovered without changing the structure of the equations developed initially for "classical" wetting dynamics with silicon oil drops

### Drops sliding down an incline at large contact line velocity: What happens on the road towards rolling?

International audienceDrops sliding down an incline exhibit fascinating shapes, which indirectly provide a great deal of information about wetting dynamics. Puthenveettil, Kumar & Hopfinger (J. Fluid Mech., vol. 726, 2013, pp. 26-61) have renewed this subject by considering water and mercury drops sliding at high speed. The results raise puzzling questions: how to take into account inertia at a high-speed contact line, large contact angles, the nature of the dissipation at small scale and sliding versus rolling behaviours

### Elastic properties of cellular dissipative structure

Transition towards spatio-temporal chaos in one-dimensional interfacial
patterns often involves two degrees of freedom: drift and out-of-phase
oscillations of cells, respectively associated to parity breaking and
vacillating-breathing secondary bifurcations. In this paper, the interaction
between these two modes is investigated in the case of a single domain
propagating along a circular array of liquid jets. As observed by Michalland
and Rabaud for the printer's instability \cite{Rabaud92}, the velocity $V_g$ of
a constant width domain is linked to the angular frequency $\omega$ of
oscillations and to the spacing between columns $\lambda_0$ by the relationship
$V_g = \alpha \lambda_0 \omega$. We show by a simple geometrical argument that
$\alpha$ should be close to $1/ \pi$ instead of the initial value $\alpha =
1/2$ deduced from their analogy with phonons. This fact is in quantitative
agreement with our data, with a slight deviation increasing with flow rate

### Contact lines on soft solids with uniform surface tension: analytical solutions and double transition for increasing deformability

International audienceUsing an exact Green function method, we calculate analytically the substrate deformations near straight contact lines on a soft, linearly elastic incompressible solid, having a uniform surface tension γs. This generalized Flamant-Cerruti problem of a single contact line is regularized by introducing a finite width 2a for the contact line. We then explore the dependance of the substrate deformations upon the softness ratio ls/a, where ls = γs/(2µ) is the elastocapillary length built upon γs and on the elastic shear modulus µ. We discuss the force transmission problem from the liquid surface tension to the bulk and surface of the solid, and show that Neuman condition of surface tension balance at the contact line is only satisfied in the asymptotic limit a/ls → 0, Young condition holding in the opposite limit. We then address the problem of two parallel contact lines separated from a distance 2R, and we recover analytically the "double transition" upon the ratios ls/a and R/ls identified recently by Lubbers et al, when one increases the substrate deformability. We also establish a simple analytic law ruling the contact angle selection upon R/ls in the limit a/ls ≪ 1, that is the most common situation encountered in problems of wetting on soft materials

### 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

### Transonic liquid bells

http://www.irphe.univ-mrs.fr/~clanet/PaperFile/PHFBell.pdfThe shape of a liquid bell resulting from the overflow of a viscous liquid out of a circular dish is investigated experimentally and theoretically. The main property of this bell is its ability to sustain the presence of a ‘‘transonic point,'' where the liquid velocity equals the speed of antisymmetric—or sinuous—surface waves. Their shape and properties are thus rather different from usual ‘‘hypersonic'' water bells. We first show that the bell shape can be calculated very accurately, starting from the sonic point.We then demonstrate the extreme sensitivity of the shape of these bells to the difference of pressure across the interface, making them a perfect barometer. Finally, we discuss the oscillations of the bell which occur close to the bursting limit

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