C. Flament

Viscous fingering in a magnetic fluid. I. Radial Hele-Shaw flow

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.

Foams out of stable equilibrium: Cell elongation and side swapping

Abstract The evolution of a liquid foam usually mixes quasi-equilibrium topological and geometrical features in an intricate way. We take advantage of special properties of ferrofluid froths and of constrained area evolution simulations, to distinguish the effects of side swapping (TI processes) from other rearrangements in the froth. Cell elongation characterizes the froth and its deviation from mechanical equilibrium as robustly as the usually measured total wall length, that is surface energy.

Voltage generator using a magnetic fluid

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.

Two-Dimensional Magnetic Liquid Froth

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.