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We present here new experimental results about the waves at the horizontal free surface of a magnetic fluid submitted to a normal magnetic field. The waves are generated by a small modulation at frequency of the vertical field . Using a shadowgraph method, we are able to measure the wavevector k of the 2D waves for a given value of and . The dispersion relation of the surface waves is established experimentally. On the other hand, we propose a theoretical derivation of the dispersion equation which includes a more complete treatment of the magnetic term than the previous works. Finally, we conclude that a linear and inviscid analysis is sufficient to fit well the experimental data, except in the vicinity of the critical field where a surface instability occurs.

Viscous fingering phenomenon in a linear channel is studied for a magnetic fluid subjected to an external magnetic field. The competition between the hydrodynamic effects and the capillary effects leads to the formation of an interface between the air and the fluid which has a finger shape. It is the so-called Saffman–Taylor instability (STI). The influence of the magnetic effects depends on the direction of the applied field: it is possible either to enhance or to reduce the destabilizing phenomena. We study the onset of the STI and compare the experimental results with the linear analysis including the magnetic contribution. In the nonlinear regime, the measurement of the width of the finger as a function of the direction and the amplitude of the magnetic field is understood using a phenomenological approach.

We present an experimental study of a cellular system which may be formed in a two-dimensional ~2D! layer made of an immiscible mixture of a magnetic fluid and an oil. We obtain a wet or a dry 2D froth, the characteristics of which are determined by the strength of an externally applied magnetic field. The froth is formed in an equilibrium state; the topological and geometrical features of the froth are fixed by the value of the applied field. The cellular pattern of the froth is stable in time, and a coarseninglike behavior is observed on decreasing the amplitude of the field. This cellular system can be used as a model to study topological processes in the equilibrium state, contrary to soap froths which are nonequilibrium systems because gas diffusion occurs. We show that the topological characteristics are statistically reversible after a magnetic-field cycle, and we present a statistical study of the froth features as a function of the amplitude of the field. The topological correlations between neighboring cells are well described by the Aboav-Weaire law. Finally, we consider the area of an n-sided cell, and show that its growth rate ~magnetic field dependent! is, in a surprising manner, proportional to n26, similarly to the Von Neumann law. @S1063-651X~97!10009-5#

A model and numerical code are presented that describe quasi-one-dimensional compressible flows of gases with nonequilibrium of their vibrational and electronic energy modes. Chemical reaction channels are also modeled. Rate equations governing individual vibrational state populations are integrated as a function of streamwise position in a flow channel. Results are presented for flows of CO, N 2 , and NO in supersonic nozzles, and the conditions creating extreme nonequilibrium overpopulation of upper vibrational states are shown

Dynamics of the chemical reaction model introduced by Fichthorn et al (1989) is discussed along the lines of the authors previous work. They find that the steady-state reaction rate is reached as 1/t in Euclidean dimension d=1 and d=2 is the marginal dimension. The distinction made between the segregation regime and the saturation regime is recovered for the transient regime.

We define the boundary energy for a 2D homogeneous phase in the general case of 1/Rn interactions between particles. In the large-domain size-limit, this energy is proportional to the interface length only for n > 3. For n ≤ 3 a line tension can no longer be defined. For arbitrary n, we calculate the mean amplitude of the thermal fluctuations of the boundary. A crystal interface is modelized by a periodic pinning potential U, and its roughness depends on the value of U averaged over boundary fluctuations. A first-order calculation shows that the interface is rough for n > 2, and faceted for n < 2, at any temperature. In the particular case n = 2 a roughening transition should occur at a finite temperature TR that we explicitly calculate. The possible observation of this transition in some experimental situations is discussed.

We study the equilibrium energies of two-dimensional (2D) noncoarsening fluid foams, which consist of bubbles with fixed areas. The equilibrium states correspond to local minima of the total perimeter. We present a theoretical derivation of energy minima; experiments with ferrofluid foams, which can be either highly distorted, locally relaxed, or globally annealed; and Monte Carlo simulations using the extended large-Q Potts model. For a dry foam with small size variance we develop physical insight and an electrostatic analogy, which enables us to (i) find an approximate value of the global minimum perimeter, accounting for (small) area disorder, the topological distribution, and physical boundary conditions; (ii) conjecture the corresponding pattern and topology: small bubbles sort inward and large bubbles sort outward, topological charges of the same signs "repel" while charges of the opposite signs "attract;" (iii) define local and global markers to determine directly from an image how far a foam is from its ground state; (iv) conjecture that, in a local perimeter minimum at prescribed topology, the pressure distribution and thus the edge curvature are unique. Some results also apply to 3D foams.

We present experiments showing the Rayleigh-Taylor instability at the interface between a dense magnetic liquid and an immiscible less dense liquid. The liquids are confined in a Hele-Shaw cell and a magnetic field is applied perpendicular to the cell. We measure the wavelength and the growth rate at the onset of the instability as a function of the external magnetic field. The wavelength decreases as the field increases. The amplitude of the interface deformation grows exponentially with time in the early stage, and the growth rate is an increasing function of the field. These results are compared to theoretical predictions given in the framework of linear stability analysis.

International audience; We describe the concept of a voltage generator based on the use of a magnetic fluid. A cell contains two immiscible liquids: the lower liquid boils at a low temperature and the upper is a magnetic liquid magnetized by a permanent magnet. By heating the bottom of the cell the lower liquid boils, and bubbles of the gas phase cross both liquid phases; consequently a flux variation is induced in a detection coil. Finally, the gas phase condenses in a recovery device in order to be injected back at the bottom of the cell. We obtain a voltage generator with a shape signal linked to the nucleation frequency and volume of the gas bubbles. This device has been built by secondary school pupils and requires the acquisition of knowledge of magnetism, hydrodynamics and thermodynamics.

We present a new cellular structure, obtained in a pseudo two-dimensional (2D) layer of magnetic fluid (MF) submitted to a perpendicular magnetic field. This froth is analogous to 2D soap froths, because its energy contains an interfacial contribution. Nevertheless, whereas a soap froth coarsens in time to minimize the surface of its interface, the 2D MF froth can be stable in time. Indeed it also has a magnetic energy, which allows the cellular pattern to reach an equilibrium state. The properties of such a froth in its equilibrium state are thus driven by competition between the surface energy and the magnetic energy. The latter depends on the amplitude of the applied magnetic field, which is a control parameter of this system. An evolution of the structure is obtained on decreasing the amplitude of the field: the number of cells decreases so that the pattern turns into a single drop of MF in zero field. We present here a study of this coarsening with decreasing of the field. For high amplitudes of the applied field, we have observed out of equilibrium states of the 2D MF froth: the area of the cells evolves in time, depending on their number of sides. This behaviour looks like a Von Neumann one (which drives the time-evolution of 2D soap froths), but with the opposite sign: 5-sided cells grow in time, 7-sided cells shrink, whereas 6-sided cells do not evolve. In section 6, the 2D MF froths are shown to obey the Aboav and Weaire law which describes the topological interactions between cells, as all the 2D cellular structures. Finally, we present a potential application of the 2D MF froth, for the study of topology in 2D cellular patterns.

A fully coupled implicit finite volume mctbod for dculr t ing rxisymmetric viscous flows with thermal and chemical noaequilibrium is presented. The numerid approximuion of the governing equations is &rived using a d order upwind schcme of H8rta1-Yee type for the inviscid fluxes and 8 sp.ce a n t e d s c h a ~ ~ ~ for thc viscous fluxes. Numerical fluxes and soume terms are fully coupled in the implicit scep. A particular attention is paid on the physical models involved in this study. New vansport models for species diffusion and thermal coaductivities for internal mode rre introduced. Furtbcmore, lo original dissociation-vibration coupling derived from Park's apprruch and including the influence of rcaaion rates on vibrational reluation is proposed. Results are first presented for a 2D uisymmetric thermo-chemical nonequilibrium flow around a rpberecylinder. Tbe influence of physical models is discussed. Comparisons ut performed with available numerical rcsults md show r rather good agreement. ' h e stcbad appliruion deals with tbe 2D uisymmetric flow around a hyperboloid simulating a shuttle shape in r hypemthalpic nozzle flow.

The equations governing chemical and vibrational non-equilibrium nozzle flows are first presented. The resulting differential system is then discretized using a fully implicit non centered finite volume approach. The method is finally applied to two different hypersonic nozzle geometries. Results are compared with equilibrium as well as with previous space marching calculations.