Line Tension in a Thick Soap Film.

The thickness of freshly made soap films is usually in the micron range, and interference colors make thickness fluctuations easily visible. Circular patterns of constant thickness are commonly observed, either a thin film disc in a thicker film or the reverse. In this Letter, we evidence the line tension at the origin of these circular patterns. Using a well controlled soap film preparation, we produce a piece of thin film surrounded by a thicker film. The thickness profile, measured with a spectral camera, leads to a line tension of the order of 10^{-10} N which drives the relaxation of the thin film shape, initially very elongated, toward a circular shape. A balance between line tension and air friction leads to a quantitative prediction of the relaxation process. Such a line tension is expected to play a role in the production of marginal regeneration patches, involved in soap film drainage and stability.

Non linear elasticity of foam films made of SDS/dodecanol mixtures.

Foam film elasticity plays a significant role in film drainage and film stability and is thus expected to influence foam dynamical properties. It strongly depends on the foaming solution composition and differs from the interface elasticity measured in unconfined geometries. We use a deformable frame to deform an assembly of five films and we measure the tension and extension of each film. This provides a simple and accurate determination of the film elasticity, in the linear and non-linear regimes, for a set of SDS/dodecanol mixtures, at various concentrations. We show that the non-linear elastic behavior is well reproduced by Mysel's model coupled with a Langmuir coadsorption isotherm for a large range of chemical compositions.

Dynamical Coupling between Connected Foam Films: Interface Transfer across the Menisci.

The highly confined flow of the liquid phase, trapped between the gas bubbles, is at the origin of the large effective viscosity of the liquid foams. Despite the industrial relevance of this complex fluid, the foam viscosity remains difficult to predict because of the lack of flow characterization at the bubble scale. Using an original deformable frame, we provide the first experimental evidence of the interface transfer between a compressed film (or a stretched film) and its first neighbor, across their common meniscus. We measure this transfer velocity, which is a key boundary condition for local flows in foams. We also show the dramatic film thickness variation induced by this interface transfer, which may play an important role in the film thickness distribution of a 3D foam sample.

Marangoni stress induced by rotation frustration in a liquid foam.

The role of surface tension gradients in the apparent viscosity of liquid foams remains largely unexplained. In this article, we develop a toy-model based on a periodic array of 2D hexagonal bubbles, each bubble being separated from its neighbors by a liquid film of uniform thickness. The two interfaces of this thin liquid film are allowed to slide relatively to each other, thus shearing the liquid phase in between. We solve the dynamics under external shear of this minimal system and we show that the continuity of the surface tension around the whole bubble is the relevant condition to determine the bubble rotation rate and the energy dissipation. This result is expected to be robust in more complex situations and illustrates that thin film dynamics should be solved at the scale of the whole bubble interface when interface rheology matters.

Lamella Division in a Foam Flowing through a Two-Dimensional Porous Medium: A Model Fragmentation Process.

We flow a 2D foam through a model 2D porous medium and study experimentally and numerically how the bubble size distribution evolves along the medium. The dominant mechanism of bubble creation is a fragmentation process occurring when bubbles pinched against obstacles are split in two smaller bubbles. We infer the statistics of these individual and local fragmentation events from the experimental data and propose a fragmentation equation to relate that statistics to the evolution of the global size distribution. The predicted evolution shows very good agreement with direct experimental measurements of the bubble size distribution.

Velocity Field in a Vertical Foam Film.

The drainage of vertical foam films governs their lifetime. For a foam film supported on a rectangular solid frame, when the interface presents a low resistance to shear, the drainage dynamics involves a complex flow pattern at the film scale, leading to a drainage time proportional to the frame width. Using an original velocimetry technique, based on fluorescent foam films and photobleaching, we measure the horizontal and vertical components of the velocity in a draining film, thus providing the first quantitative experimental evidence of this flow pattern. Upward velocities up to 10 cm/s are measured close to the lateral menisci, whereas a slower velocity field is obtained in the center of the film, with comparable downwards and horizontal components. Scaling laws are proposed for all characteristic velocities, coupling gravitational effects, and capillary suction.

Blast wave attenuation in liquid foams: role of gas and evidence of an optimal bubble size.

Liquid foams are excellent systems to mitigate pressure waves such as acoustic or blast waves. The understanding of the underlying dissipation mechanisms however still remains an active matter of debate. In this paper, we investigate the attenuation of a weak blast wave by a liquid foam. The wave is produced with a shock tube and impacts a foam, with a cylindrical geometry. We measure the wave attenuation and velocity in the foam as a function of bubble size, liquid fraction, and the nature of the gas. We show that the attenuation depends on the nature of the gas and we experimentally evidence a maximum of dissipation for a given bubble size. All features are qualitatively captured by a model based on thermal dissipation in the gas.

Investigating the role of a poorly soluble surfactant in a thermally driven 2D microfoam.

Foam drainage dynamics is known to be strongly affected by the nature of the surfactants stabilising the liquid/gas interface. In the present work, we consider a 2D microfoam stabilized by both soluble (sodium dodecylsulfate) and poorly soluble (dodecanol) surfactants. The drainage dynamics is driven by a thermocapillary Marangoni stress at the liquid/gas interface [V. Miralles et al., Phys. Rev. Lett., 2014, 112, 238302] and the presence of dodecanol at the interface induces interface stress acting against the applied thermocapillary stress, which slows down the drainage dynamics. We define a damping parameter that we measure as a function of the geometrical characteristics of the foam. We compare it with predictions based on the interface rheological properties of the solution.

Soluble surfactant spreading: How the amphiphilicity sets the Marangoni hydrodynamics.

Amphiphiles are molecules combining hydrophilic and hydrophobic parts. The way they arrange in bulk and at interfaces is related to the balance between these two parts, and can be quantified by introducing the critical micellar concentration (cmc). Amphiphiles (also named "surfactants") are also at the origin of dynamical effects: local gradients of interfacial concentrations create the so-called Marangoni flows. Here we study the coupling between the molecule amphiphilicity and these Marangoni flows. We investigate in detail a spreading configuration, where a local excess of surfactants is locally sustained, and follow how these surfactants spread at the interface and diffuse in bulk. We have measured the features of this flow (maximal distance and maximal speed), for different types of surfactant, and as a function of all experimentally available parameters, as well as for two different configurations. In parallel, we propose a detailed hydrodynamical model. For all the measured quantities, we have found a good agreement between the data and the model, evidencing that we have captured the key mechanisms under these spreading experiments. In particular, the cmc turns out to be-as for the static picture of a surfactant-a key element even under dynamical conditions, allowing us to connect the molecule amphiphilicity to its ability to create Marangoni flows.

Droplets in Microchannels: Dynamical Properties of the Lubrication Film.

We study the motion of droplets in a confined, micrometric geometry, by focusing on the lubrication film between a droplet and a wall. When capillary forces dominate, the lubrication film thickness evolves nonlinearly with the capillary number due to the viscous dissipation between the meniscus and the wall. However, this film may become thin enough (tens of nanometers) that intermolecular forces come into play and affect classical scalings. Our experiments yield highly resolved topographies of the shape of the interface and allow us to bring new insights into droplet dynamics in microfluidics. We report the novel characterization of two dynamical regimes as the capillary number increases: (i) at low capillary numbers, the film thickness is constant and set by the disjoining pressure, while (ii) above a critical capillary number, the interface behavior is well described by a viscous scenario. At a high surfactant concentration, structural effects lead to the formation of patterns on the interface, which can be used to trace the interface velocity, that yield direct confirmation of the boundary condition in the viscous regime.

Influence of the elastic deformation of a foam on its mobility in channels of linearly varying width.

We study foam flow in an elementary model porous medium consisting of a convergent and a divergent channel positioned side by side and possessing a fixed joint porosity. Configurations of converging or diverging channels are ubiquitous at the pore scale in porous media, as all channels linking pores possess a converging and diverging part. The resulting flow kinematics imposes asymmetric bubble deformations in the two channels, which modulate foam-wall friction and strongly impact the flux distribution. We measure, as well as quantitatively predict, the ratio of the fluxes in the two channels as a function of the channel widths by modeling pressure drops of both viscous and capillary origins. This study reveals the crucial importance of boundary-induced bubble deformation on the mobility of a flowing foam, resulting in particular in flow irreversibility.

Extension of a suspended soap film: a homogeneous dilatation followed by new film extraction.

Liquid foams are widely used in industry for their high effective viscosity, whose local origin is still unclear. This Letter presents new results on the extension of a suspended soap film, in a configuration mimicking the elementary deformation occurring during foam shearing. We evidence a surprising two-step evolution: the film first extends homogeneously, then its extension stops, and a new thicker film is extracted from the meniscus. The second step is independent of the nature of the surfactant solution, whereas the initial extension is only observed for surfactant solutions with negligible dilatational moduli. We predict this complex behavior using a model based on Frankel's theory and on interface rigidification induced by confinement.

Coarsening foams robustly reach a self-similar growth regime.

Dry liquid foams coarsen like other diphasic systems governed by interfacial energy: gas slowly diffuses across liquid films, resulting in large bubbles growing at the expense of smaller ones which eventually shrink and disappear. A foam scatters light very effectively, preventing direct optical observation of bubble sizes and shapes in large foams. Using high speed x-ray tomography, we have produced 4D movies (i.e., 3D + time) of up to 30,000 bubbles. After a transient regime, the successive images look alike, except that the average bubble size increases as the square root of time: This scaling state is the long sought self-similar growth regime. The bubble size and face-number distributions in this regime are compared with experimental distributions for grains in crystals and with numerical simulations of foams.

Thermocapillary actuation by optimized resistor pattern: bubbles and droplets displacing, switching and trapping.

We report a novel method for bubble or droplet displacement, capture and switching within a bifurcation channel for applications in digital microfluidics based on the Marangoni effect, i.e. the appearance of thermocapillary tangential interface stresses stemming from local surface tension variations. The specificity of the reported actuation is that heating is provided by an optimized resistor pattern (B. Selva, J. Marchalot and M.-C. Jullien, An optimized resistor pattern for temperature gradient control in microfluidics, J. Micromech. Microeng., 2009, 19, 065002) leading to a constant temperature gradient along a microfluidic cavity. In this context, bubbles or droplets to be actuated entail a surface force originating from the thermal Marangoni effect. This actuator has been characterized (B. Selva, I. Cantat, and M.-C. Jullien, Migration of a bubble towards a higher surface tension under the effect of thermocapillary stress, preprint, 2009) and it was found that the bubble/droplet (called further element) is driven toward a high surface tension region, i.e. toward cold region, and the element velocity increases while decreasing the cavity thickness. Taking advantage of these properties three applications are presented: (1) element displacement, (2) element switching, detailed in a given range of working, in which elements are redirected towards a specific evacuation, (3) a system able to trap, and consequently stop on demand, the elements on an alveolus structure while the continuous phase is still flowing. The strength of this method lies in its simplicity: single layer system, in situ heating leading to a high level of integration, low power consumption (P < 0.4 W), low applied voltage (about 10 V), and finally this system is able to manipulate elements within a flow velocity up to 1 cm s(-1).

Experimental growth law for bubbles in a moderately "wet" 3D liquid foam.

We used x-ray tomography to characterize the geometry of all bubbles in a liquid foam of average liquid fraction phi(l) approximately 17% and to follow their evolution, measuring the normalized growth rate G=V(-1/3) dV/dt for 7000 bubbles. While G does not depend only on the number of faces of a bubble, its average over f-faced bubbles scales as G(f) approximately f - f(0) for large f's at all times. We discuss the dispersion of G and the influence of V and phi(l) on G.

In situ investigations on organic foam films using neutron and synchrotron radiation.

We report on small-angle neutron scattering (SANS) and X-ray scattering (SAXS) investigations of foam films stabilized by sodium dodecyl sulfate. Previous measurements on dry foams (Axelos, M. A. V.; Boue, B. Langmuir 2003, 19, 6598) have shown the presence of spikes in the two-dimensional scattering data which suggest that the incident beam is reflected on some film surfaces. The latter interpretation is confirmed by new neutron studies performed on ordered ("bamboo") foams which allow selection of single films. In the first case, we show that the spikes of the scattered intensity can be obtained by reflection on two parts of the foam, namely, the films and the Plateau borders. With synchrotron radiation, first observations of distinct interference fringes have allowed an accurate determination of the film thickness. A comparison with X-ray and neutron data is made, opening a general discussion about the capabilities of small-angle scattering techniques for studying the microscopic properties of foam films.

Stability of soap films: hysteresis and nucleation of black films.

We study the stability of soap films of a nonionic surfactant under different applied capillary pressures on the film. Depending on the pressure, either a thick common black film (CBF), or a micro-scopically thin Newton black film (NBF) is formed as a (metastable) equilibrium state, with a first-order (discontinuous) transition between the two. Studying the dynamics of the CBF-NBF transition, it is found that under certain conditions a hysteresis for the transition is observed: for a given range of pressures, either of the two states may be observed. We quantify the nucleation process that is at the basis of these observations both experimentally and theoretically.