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Almost frictionless skating on ice relies on a thin layer of melted water insulating mechanically the blade of the skate from ice. Using the basic equations of fluid mechanics and Stefan law, we derive a set of two coupled equations for the thickness of the film and the length of contact, a length scale which cannot be taken as its value at rest. The analytical study of these equations allows to define a small a-dimensional parameter depending on the longitudinal coordinate which can be neglected everywhere except close to the contact points at the front and the end of the blade, where a boundary layer solution is given. This solution provides without any calculation the order of magnitude of the film thickness, and its dependence with respect to external parameters like the velocity and mass of the skater and the radius of profile and bite angle of the blade, in good agreement with the numerical study. Moreover this solution also shows that a lubricating water layer of macroscopic thickness always exists for standard values of ice skating data, contrary to what happens in the case of cavitation of droplets due to thermal heating (Leidenfrost effect). [ABSTRACT FROM AUTHOR]

This is a discussion of the present understanding of transition to turbulence in parallel flows, based upon the idea that it arises from a subcritical instability. The result is a coupled set of equations, one amplitude equation in the direction of translational invariance of the geometry coupled with the standard Reynolds equation for the average transfer of momentum. It helps to understand a basic feature of the transition in parallel flows, namely that turbulence manifests itself in localised domains growing at a constant speed depending on the Reynolds number. [ABSTRACT FROM AUTHOR]

Lubrication equations based on diffuse interface theory are applied to description of slow motion and interaction of droplets on solid support. For the case of quasistationary motion of a weakly nonwetting fluid, we derive integral relations reducing the problem to computation of ratios of applicable “thermodynamic forces” to a dissipative integral characterizing an individual droplet. This allows us to describe the droplet motion without computing explicitly the distortion of their shape. Explicit computations are carried out for a droplet sliding on an inclined plane, and for an ensemble of droplets interacting through the precursor layer. © 2004 American Institute of Physics. [ABSTRACT FROM AUTHOR]

In a dilute Bose gas the interaction between the normal gas and the condensate can be studied both at equilibrium and for its relevance to superfluid mechanics. In this article, one reviews first the thermodynamics of the interacting Bose gas in the low density limit and in the low temperature–finite density case. This is extended to thermodynamics with a velocity difference between the two components, normal and superfluid. It is argued that, if the initial value of the momentum related to this velocity difference is larger than the one given by thermodynamic stability, a new condensate should form in a finite time with a velocity close to the that of the normal gas. In the dilute case this occurrence of a new condensate is reminiscent of the condensation in the isotropic case at high enough density. To cite this article: Y. Pomeau, C. R. Physique 5 (2004). [Copyright &y& Elsevier]

We consider the motion of a small droplet sliding under gravity down an inclined plane. Experimentally [see T. Podgorski, Thèse, Université Paris 6 (October 2000); T. Podgorski et al., Phys. Rev. Lett. 87, 036102 (2001)] it has been observed that such a droplet will develop an angular point in the contact line at its rear if its velocity is sufficiently high (i.e., if the plane is inclined sufficiently steeply to the horizontal). The angular point first appears at some critical, or threshold speed, U[sub c], and the angular discontinuity observed increases monotonically from zero at U=U[sub c]. We seek to describe this phenomenon using a simple mathematical model based on lubrication theory. In the subcritical regime we find an exact solution to our model: a drop of circular perimeter sliding steadily down the inclined plane. This allows us to predict the formation of a nonanalyticity in the contact line at a well-defined critical droplet speed. For speeds just beyond this, we construct a local solution valid near the singular point, for which the angle in the contact line predicted by our theory agrees with the experimental results. We also construct a local solution in the fully developed critical regime, for sliding speeds well above critical, which is suggestive of a further bifurcation, also observed in the experiments [T. Podgorski, Thèse, Université Paris 6 (October 2000)]. [ABSTRACT FROM AUTHOR]

Shows that a droplet of nonwetting viscous liquid moves on an inclined plane by rolling along it. Scaling law for the uniform sped of such a droplet; Analysis of the flow in the contact region; Classical stress singularity at the contact line.

Stable localized wave packets in two-dimensional incompressible Poiseuille flow are characterized by direct simulation of the Navier–Stokes equations. These asymmetric wave packets depend only on the Reynolds number when the channel periodicity length is sufficiently large. They are created through a saddle-node bifurcation at Re ∼2330, well below the critical Reynolds number for finite-amplitude Tollmien–Schlichting waves. Pairs of wave packets are found to interact repulsively, and no evidence for locking has been observed. Finally, an amplitude-equation model is suggested which incorporates the spatial asymmetry of the localized solutions. [ABSTRACT FROM AUTHOR]

Under the effect of surface tension, a blob of liquid adopts a spherical shape when immersed in another fluid. We demonstrate experimentally that soft, centimeter-size elastic solids can exhibit a similar behavior: when immersed into a liquid, a gel having a low elastic modulus undergoes large, reversible deformations. We analyze three fundamental types of deformations of a slender elastic solid driven by surface stress, depending on the shape of its cross section: a circular elastic cylinder shortens in the longitudinal direction and stretches transversally; the sharp edges of a square based prism get rounded off as its cross sections tend to become circular; and a slender, triangular based prism bends. These experimental results are compared to analysis and nonlinear simulations of neo-Hookean solids deformed by surface tension and are found to be in good agreement with each other. [ABSTRACT FROM AUTHOR]