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.

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Two methods of determination of the surface tension at the interface of a magnetic liquid and another fluid, in a confined two-dimensional geometry, are presented. The first is based upon a surface instability under the action of a vertical magnetic field and the second uses the deformation of a magnetic droplet in plane layer under the influence of a horizontal magnetic field. Theoretical calculations and experimental results are presented in both cases. Both determinations lead to comparable values of the surface tension Ϸ3 mN m Ϫ1 .͓S1063-651X͑96͒00205-X͔ PACS number͑s͒: 47.65.ϩa, 75.50.Mm, 68.10.Ϫm

International audienc

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Viscous fingering phenomena in a circular geometry are studied for a magnetic fluid submitted to a perpendicular magnetic field. Air is injected at the center of a Hele-Shaw cell filled with a viscous magnetic fluid. The instability of the interface between the air and the magnetic fluid is favored by the presence of a magnetic field. More precisely, the threshold of the instability is magnetic field dependent. The patterns obtained for high values of the magnetic field with a low injection rate are similar to those obtained in the absence of an external field and at high flow rates. We also give a linear analysis for the stability of radial flow under the influence of a magnetic field. This calculation provides us with an understanding of the magnetic field effect.

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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.