Antoine Sellier

Viscous effects in the absolute–convective instability of the Batchelor vortex

The effects of viscosity on the instability properties of the Batchelor vortex are investigated. The characteristics of spatially amplified branches are first documented in the convectively unstable regime for different values of the swirl parameter q and the co-flow parameter a at several Reynolds numbers Re. The absolute-convective instability transition curves, determined by the Briggs Bers zero-group velocity criterion, are delineated in the (a,q)-parameter plane as a function of Re. The azimuthal wavenumber m of the critical transitional mode is found to depend on the magnitude of the swirl q and on the jet (a > -0.5) or wake (a < -0.5) nature of the axial flow. At large Reynolds numbers, the inviscid results of Olendraru et al. are recovered. As the Reynolds number decreases, the pocket of absolute instability in the (a,q)-plane is found to shrink gradually. At Re = 667, the critical transitional modes for swirling jets are m = -2 or m = -3 and absolute instability prevails at moderate swirl values even in the absence of counterflow. For higher swirl levels, the bending mode m = -1 becomes critical

A UNIFIED UNSTEADY LIFTING-LINE THEORY

A lifting-line theory is developed for wings of large aspect ratio oscillating in an inviscid fluid. The theory is unified in the sense that the wing may be curved or inclined to the flow, and the asymptotic expansion is uniformly valid with respect to the frequency. The method is based on the integral equation formulation of the problem. The technique, pioneered by Kida & Miyai (1978), consists of asymptotically solving the Fredholm equation of the first kind which links the unknown pressure jump and the normal velocity imposed on the wing. Use of the finite-part integral theory introduced by Hadamard (1932) and of a technique developed in Guermond (1987, 1988, 1990) yields an asymptotic expansion of the surface integral in terms of the inverse of the aspect ratio. At each approximation order, the problem reduces to a classical two-dimensional integral equation, whose unknown is the pressure jump, and whose right-hand side depends only on the previous approximation orders of the solution. The first finite-span correction is explicitly calculated. An extensive numerical study is carried out, and comparisons with published results are made.

Migration of an insulating particle under the action of uniform ambient electric and magnetic fields. Part 1. General theory

The behaviour of an insulating particle suspended in a liquid metal and subject to the influence of locally uniform electric and magnetic fields (E, B) is considered. The electric field drives a current J which is perturbed by the presence of the particle, and the resulting Lorentz force drives a flow. It is assumed that both the Reynolds number and the Hartmann number based on particle size are small. If the particle is fixed, it experiences a force and couple that are each bilinear in J and B; if it is freely suspended, then it moves with translational velocity U and angular velocity Q each similarly bilinear in J and B. The general form of these bilinear relationships is determined, with particular attention to three types of particle symmetry: (i) isotropy; (ii) axisymmetry; and (iii) orthotropy

Low-Reynolds-number gravity-driven migration and deformation of bubbles near a free surface

We investigate numerically the axisymmetric migration of bubbles toward a free surface, using a boundary-integral technique. Our careful numerical implementation allows to study the bubble(s) deformation and film drainage; it is benchmarked against several tests. The rise of one bubble toward a free surface is studied and the computed bubble shape compared with the results of Princen [J. Colloid Interface Sci. 18, 178 (1963)]. The liquid film between the bubble and the free surface is found to drain exponentially in time in full agreement with the experimental work of Debregeas et al. [Science 279, 1704 (1998)]. Our numerical results also cast some light on the role played by the deformation of the fluid interfaces and it turns out that for weakly deformed interfaces (high surface tension or a tiny bubble) the film drainage is faster than for a large fluid deformation. By introducing one or two additional bubble(s) below the first one, we examine to which extent the previous trends are affected by bubble-...

Migration of an insulating particle under the action of uniform ambient electric and magnetic fields. Part 2. Boundary formulation and ellipsoidal particles

This paper examines the low-Reynolds-number migration of an insulating and rigid particle that is freely suspended in a viscous liquid metal and subject to uniform ambient electric and magnetic fields

Instabilities and Vortex Breakdown in Swirling Jets and Wakes

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On the capillary motion of arbitrary clusters of spherical bubbles. Part 1. General theory

and

On the low-Reynolds-number flow about two rotating circular cylinders

\hbox{\bf\itshape B}.

Migration d'une particule ellipsoı̈dale conductrice sous l'action d'un champ électromagnétique uniforme

Under the same physical assumptions as Part 1, a whole boundary formulation of the problem is established. It allows the determination of the particle rigid-body motion without calculating the modified electric field and the flow induced by the Lorentz body force in the fluid domain. The advocated boundary approach, well-adapted for future numerical implementation, makes it possible to obtain an analytical expression for the translational velocity of any ellipsoidal particle (the simplest case of non-spherical orthotropic particles). The behaviour of a spheroid is carefully investigated and discussed both without and with gravity. The migration of this simple non-spherical particle is found to depend on both its nature (prolate or oblate) and the ambient uniform fields

Slow viscous gravity-driven interaction between a bubble and a free surface with unequal surface tensions

\hbox{\bf\itshape E}