Hamid Kellay

Two-dimensional turbulence: a review of some recent experiments

A review of recent experiments in two-dimensional turbulence is presented. Work on flowing soap films and on thin layers of fluid driven electromagnetically is covered. Theoretical notions of turbulence in two and three dimensions are introduced.

Properties of surfactant monolayers in relation to microemulsion phase behaviour

Abstract The relationship between the properties of surfactant monolayers at oil-water interfaces and the phase behaviour in bulk of mixtures of oil + water + surfactant is discussed. Such monolayer properties include the spontaneous curvature, c o the interfacial tension, I γ, the elasticity K (or rigidity) associated with the mean curvature, and the elasticity K associated with the Gaussian curvature. The model system chosen for investigation is the anionic surfactant AOT + aqueous NaCl + n-alkane at 20°C. In such systems, inversion of microemulsion type from oil-in-water (o/w) to water-in-oil (w/o) is possible with increasing electrolyte concentration. The tension, γ, passes through an ultralow minimum value at conditions corresponding to the formation of three phases. Using small angle neutron scattering, we have determined the structure of surfactant-rich third phases (c o ~ 0) formed with the different alkanes. Lamellar phases consisting of surfactant monolayers separated alternately by oil and water appear with short alkanes, whereas L 3 and bicontinuous phases form in systems containing longer alkanes. The bending elasticity K has been measured for planar monolayers at the oil-water interface by ellipsometry. K is independent of salt concentration but depends markedly on alkane chain length N, falling from ~ 1 k B T for N B T for N = 14. This is discussed in terms of the differing extents of oil penetration into the surfactant chains. Higher rigidities favouring lamellar phases and lower rigidities favouring bicontinuous microemulsions are in line with the theoretical predictions of de Gennes and Taupin. Estimates of the constant K have been obtained in droplet microemulsions (w/o) from a knowledge of their size, K and γ. The sign of the constant is in agreement with the geometry of the phases formed in three phase systems. Finally, the ideas and concepts developed in the oil-water systems described above are used to explain the wetting behaviour by alkanes of AOT monolayers at the air-water surface.

Effects of Alkane Chain Length on the Bending Elasticity Constant K of AOT Monolayers at the Planar Oil-Water Interface

In systems containing AOT + aqueous NaCl + normal alkane, the change of the microemulsion type from oil-in-water to water-in-oil through a surfactant-rich phase can be effected by increasing the aqueous phase salt concentration. We have investigated the multiphase behaviour (in Winsor systems) for a range of alkanes. The low oil-water interfacial tensions enable us to measure the bending elasticity constant K of the monolayer by ellipsometry. Values of K are independent of salt concentration but decrease with increasing alkane chain length. This is discussed in terms of the differing extents of oil penetration into the surfactant chain region and its consequences on the structure of the third phase.

Measurement of the slip length of water flow on graphite surface

We present measurements of the hydrodynamic damping of an atomic force microscopy cantilever-tip immersed in water and approaching a mica surface or a graphite surface. Water completely wets the mica surface while it partially wets the graphite surface with a contact angle of 74°. The measurements show that the damping is higher on mica than on graphite giving a slip length of about 8nm on this latter surface.

The Microcantilever: A Versatile Tool for Measuring the Rheological Properties of Complex Fluids

Silicon microcantilevers can be used to measure the rheological properties of complex fluids. In this paper two different methods will be presented. In the first method the microcantilever is used to measure the hydrodynamic force exerted by a confined fluid on a sphere that is attached to the microcantilever. In the second method the measurement of the microcantilever’s dynamic spectrum is used to extract the hydrodynamic force exerted by the surrounding fluid on the microcantilever. The originality of the proposed methods lies in the fact that not only may the viscosity of the fluid be measured but also the fluid’s viscoelasticity, i.e., both viscous and elastic properties, which are key parameters in the case of complex fluids. In both methods the use of analytical equations permits the fluid’s complex shear modulus to be extracted and expressed as a function of shear stress and/or frequency.

Velocity fluctuations in a turbulent soap film: The third moment in two dimensions

Quasi-two-dimensional decaying turbulence is studied in a flowing soap film by measuring the moments of the probability density function P(δv(r)) for the longitudinal velocity differences δv(r) on a scale r. As in three-dimensional (3-D) turbulence, P becomes non-Gaussian with decreasing r. The third moment S3(r)≡〈(δv(r))3〉 is small and negative at small scales, but becomes positive at larger scales. The exact calculation of S3(r) for 2-D homogeneous isotropic turbulence relates this change in sign to the development of the velocity correlation function as the turbulence decays.

Viscous fingering in complex fluids

Viscous fingers form when in a thin linear channel a fluid pushes a more viscous fluid. The instability of the interface results from a competition between viscous and capillary forces. We show here by acting on the viscosity or the surface tension by means of surfactants or polymers that the instability can be modified drastically. For the two different systems, unlike in the classical system, the width of the finger can go through a minimum and increases with increasing velocity before settling at a plateau value larger than half the channel width. A numerical resolution of the relevant hydrodynamic equations reveals that these large deviations from the classical result can be interpreted in terms of a velocity dependent dynamic interfacial tension for the surfactant system and viscosity for the polymer solution.

Passive appendages generate drift through symmetry breaking

Plants and animals use plumes, barbs, tails, feathers, hairs and fins to aid locomotion. Many of these appendages are not actively controlled, instead they have to interact passively with the surrounding fluid to generate motion. Here, we use theory, experiments and numerical simulations to show that an object with a protrusion in a separated flow drifts sideways by exploiting a symmetry-breaking instability similar to the instability of an inverted pendulum. Our model explains why the straight position of an appendage in a fluid flow is unstable and how it stabilizes either to the left or right of the incoming flow direction. It is plausible that organisms with appendages in a separated flow use this newly discovered mechanism for locomotion; examples include the drift of plumed seeds without wind and the passive reorientation of motile animals.

Speed of sound from shock fronts in granular flows

We show, in two different experiments on stationary flow past an obstacle, that several features such as Mach cones and shock wave detachment usually observed in supersonic molecular fluids under extreme conditions are also observed for granular fluids. By pursuing this analogy, we measure the speed of sound in these experiments and find it in agreement with predictions from granular kinetic theories. Surprisingly, and in spite of this agreement, measured velocity distributions are far from being Gaussian and display algebraic tails.

The granular jump

When a fluid jet hits a solid surface, a hydraulic jumps occurs. This jump sharply delimits a thin film of liquid from a thicker film. We show here that a granular jet impinging on a solid surface also gives rise to several features reminiscent of the hydraulic jump and we refer to this situation as the granular jump. We describe, in detail, this phenomenon and show that if many of its features can be understood in analogy with the hydraulic jump, others are directly related to the granular nature of the medium and, in particular, the small-scale dynamics of the jump.