Florence Elias

Two-dimensional flow of foam around an obstacle: force measurements.

A Stokes experiment for foams is proposed. It consists of a two-dimensional flow of a foam, confined between a water subphase and a top plate, around a fixed circular obstacle. We present systematic measurements of the drag exerted by the flowing foam on the obstacle versus various separately controlled parameters: flow rate, bubble volume, bulk viscosity, obstacle size, shape, and boundary conditions. We separate the drag into two contributions: an elastic one (yield drag) at vanishing flow rate and a fluid one (viscous coefficient) increasing with flow rate. We quantify the influence of each control parameter on the drag. The results exhibit in particular a power-law dependence of the drag as a function of the bulk viscosity and the flow rate with two different exponents. Moreover, we show that the drag decreases with bubble size and increases proportionally to the obstacle size. We quantify the effect of shape through a dimensional drag coefficient, and we show that the effect of boundary conditions is small.

Bubble size control and measurement in the generation of ferrofluid foams

Ordered ferrofluid foams in tubes or channels offer promising possibilities for transporting and processing small gas (or liquid) samples. For this purpose, monodisperse bubbles can be produced, with fine control of their volume over at least three orders of magnitude, by the application of a variable magnetic field gradient during bubble generation. Electrical resistance measurements can be used to count bubbles, determine their volume, and identify the foam structure they form in the tube or channel.

Juggling with bubbles in cylindrical ferrofluid foams

Monodisperse foams in long cylinders exhibit ordered spiral structures. We have made ferrofluid foams of this kind and find that they can be manipulated in a variety of ways by an external magnetic field. Effects include morphological changes, twisting of structures and size control in the bubble formation process. This offers a promising technique for the efficient transport, switching and combining of samples in fluidic networks, possibly on the microfluidic scale.

Ageing of natural rubber under stress

Abstract.We report a dynamical-mechanical study of stress relaxation at small deformation in a natural (polyisoprene) rubber well above its glass transition temperature . We find that an almost complete relaxation of stress takes place over very long relaxation periods, even though the elastic network is retained. The relaxation rate and the long-time equilibrium modulus are sensitive functions of temperature which do not follow time-temperature superposition. Many characteristic features of non-ergodic ageing response are apparent at both short and very long times. We interpret the observed behaviour in terms of the nature of rubber cross-links, capable of isomerisation under stress, and relate the results to recent models of slow glassy rheology.

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.

A technique for measuring velocity and attenuation of ultrasound in liquid foams

We describe an experimental setup specifically designed for measuring the ultrasonic transmission through liquid foams, over a broad range of frequencies (60-600kHz). The question of determining the ultrasonic properties of the foam (density, phase velocity and attenuation) from the transmission measurements is addressed. An inversion method is proposed, tested on synthetic data, and applied to a liquid foam at different times during the coarsening. The ultrasonic velocity and attenuation are found to be very sensitive to the foam bubble sizes, suggesting that a spectroscopy technique could be developed for liquid foams.

Two-dimensional shear modulus of a Langmuir foam

– We deform a two-dimensional (2D) foam, created in a Langmuir monolayer, by applying a mechanical perturbation, and simultaneously image it by Brewster angle microscopy. We determine the foam stress tensor (through a determination of the 2D gas-liquid line tension, 2.35 ± 0.4 pJ·m) and the statistical strain tensor, by analyzing the images of the deformed structure. We deduce the 2D shear modulus of the foam, μ = 38±3 nN·m. The foam effective rigidity is predicted to be 35 ± 3 nN · m, which agrees with the value 37.5 ± 0.8 nN · m obtained in an independent mechanical measurement. Introduction. – A liquid foam, made of polyhedral gas bubbles separated by thin liquid walls forming a connected network [1], is a mixture of two fluids. It has nevertheless a solidlike elasticity, characterised by a shear modulus ̅, proportional to the surface tension of the walls [2, 3]. In fact, shearing a foam modifies the total length of the walls, thus the foam energy. The value of ̅ can be determined in numerical simulations [4, 5, 6]; however, it is still an open problem to predict analytically its value for a real foam, which has a finite fluid fraction and an inherent disorder due to its distribution of bubble sizes. Here, we compare two experimental measurements of ̅. First, by global mechanical measurements on the scale of the whole foam, described in terms of elasticity of continuous media. Second, and simultaneously, by detailed imaging of the diphasic foam structure, on the local level of a few bubbles: this suggests to use two-dimensional (2D) foams. In the literature, 2D soap froths have been sheared in Couette geometry, either as bubble rafts [7, 8, 9] or confined in Hele-Shaw cells between two parallel plates of glass [10]. We investigate the elasticity of a real 2D system: a “Langmuir foam” [11]. A monomolecular layer of amphiphilic molecules deposited at the surface of water (“Langmuir monolayer”) exhibits a first order transition between a 2D gas phase and a denser 2D liquid (also called (∗) Author for correspondence at graner@ujf-grenoble.fr. Fax: (+33) 4 76 63 54 95.

A simple technique for the automation of bubble size measurements

Abstract An increasing number of research topics and applications ask for a precise measurement of the size distribution of small bubbles in a liquid—and hence for reliable and automated image analysis. However, due to the strong mismatch between the refractive index of a liquid and a gas, bubbles deform strongly the path of light rays, rendering automated bubble size analysis a challenging task. We show here how this challenge can be met using the fact that bubbles act like inverted, spherical lenses with a curvature which is the inverse of the bubble radius. The imaging properties of each bubble can then be used to accurately determine the radius of the bubble upon imaging an object which can be filtered easily by a computer. When bubbles are large enough to be deformed under the influence of gravity, it is more appropriate to measure their size after squeezing them between two narrowly spaced glass plates. We therefore show here, how the analysis can be extended to this case; and how both approaches can be combined to measure the size distributions of strongly polydisperse foams containing simultaneously small (several 10s of micrometres) and large bubbles (several 100s of micrometres).

Acoustic characterisation of liquid foams with an impedance tube

Acoustic measurements provide convenient non-invasive means for the characterisation of materials. We show here for the first time how a commercial impedance tube can be used to provide accurate measurements of the velocity and attenuation of acoustic waves in liquid foams, as well as their effective “acoustic” density, over the 0.5-6kHz frequency range. We demonstrate this using two types of liquid foams: a commercial shaving foam and “home-made” foams with well-controlled physico-chemical and structural properties. The sound velocity in the latter foams is found to be independent of the bubble size distribution and is very well described by Wood’s law. This implies that the impedance technique may be a convenient way to measure in situ the density of liquid foams. Important questions remain concerning the acoustic attenuation, which is found to be influenced in a currently unpredictible manner by the physico-chemical composition and the bubble size distribution of the characterised foams. We confirm differences in sound velocities in the two types of foams (having the same structural properties) which suggests that the physico-chemical composition of liquid foams has a non-negligible effect on their acoustic properties.Graphical abstract

Visualization of sound waves using regularly spaced soap films

We describe a novel demonstration experiment for the visualization and measurement of standing sound waves in a tube. The tube is filled with equally spaced soap films whose thickness varies in response to the amplitude of the sound wave. The thickness variations are made visible based on optical interference. The distance between two antinodes is easily measured using a ruler and the determined wavelengths of the modes of the standing wave are in excellent agreement with the theory.