Session R05: Bubbles: Surfactants and Foams (5:00pm - 5:45pm CST)

Rheological behavior of a millimetric foam films assembly: Part III shear

\\Do you shear the films when you shear a foam?\\ The high viscosity of foam is usually explained by the confinement of the liquid phase in the thin films, leading to local shear rates much higher than the globally imposed one. We revisit this assumption for millimetric bubbles. In this study, we replicate a simple shear deformation in a soap film assembly. Five films are created on a frame in the shape of a StarWars X-wing, with the four external branches inclined at an angle of 120$^{\circ}$ from the horizontal central film. These branches can be independently displaced using piezo-motors. By photo-bleaching a dark spot in the central film, and measuring its shape and position, we demonstrate the absence of shear in this film, and we evidence that the dynamic strongly differs from a simple shear. It is localized close to the menisci, and involves complex exchanges of liquid and surfactants between the film and the menisci. By measuring the menisci displacements, combined with an interferometry technique, we obtain the tension of each film. This work allows us to elucidate the stress transmission in this complex assembly of surfactant monolayers, gas bubbles, and confined Newtonian phase and to propose different scenarii for foam shear, depending on the bubble size.   

Stability of marginal pinching in soap films.

The stability of soap bubbles and hence of liquid foams is a set by the film thinning, which is known to occur locally: rounds patches of thin films appear at the edges of the film before moving to the top of the film by buoyancy. This phenomenon, the marginal regeneration, has been observed for decades, but its origin hasn’t yet been established. It involves the appearance of a localized pinch between the film and the meniscus, which dynamics has been entirely characterized by assuming its invariance in the direction of the meniscus. We identify a limit in which the bulk drainage and the surface rearrangements are decoupled, the film thus evolving in a sliding-puzzle-like dynamic. In this frame, we study theoretically and numerically the stability of this straight marginal pinch, and show that it is unstable to long wavelengths. We predict a critical wavelength of fastest destabilization and a thickness ratio between the thin and thick parts of the film, both in good agreement with experimental observations.   

Probing surfactant dynamics in a sheared foam through level-set simulations

A liquid foam is a dispersion of gas bubbles in a soapy liquid matrix, routinely used in various applications for its large specific area, light weight, and insulating properties. We investigate its flow behavior, which strongly depends on the properties of the surfactants used to generate it. This is done by imposing a shear flow in the foam at the bubble scale, wherein the bubbles undergo T1 transformations, and the evolution of the surfactant distribution is followed during this process. To follow the surfactant dynamics, experimentally inaccessible, and its coupling to the flow, we simulate T1 events numerically, using a two-phase flow level-set method that has been adapted to include the surfactant transport (Titta et al., Journal of Fluid Mechanics, 2018). We perform a parametric study of this system by varying the dimensionless numbers for the surfactant dynamics, including the Biot and Péclet numbers, and the adsorption depth, and identify dissipation sources inside the sheared foam.   

Rheological behavior of a millimetric foam films assembly: Part I Elasticity

Liquid foam has been extensively used in several industrial applications for its surprising viscoelastic rheology allowing to efficiently dissipate energy. However, the origin of this behavior remains unclear due to the lack of the local constitutive laws of the liquid matrix. Here, we experimentally and theoretically investigate the dynamic of an elementary brick of foam constituted of 5 soap films. A horizontal film is connected, through two free menisci, to four peripheral films (two on each side) with controllable lengths. Deformation consists of a simultaneous stretching of peripheral films on one side and compression on the other side. Kinematic quantities (velocity and thickness) are measured during the excitation and the relaxation. Surface tension variations, induced by the deformation, result into a free menisci displacement and these two quantities have been linked allowing us to monitor local forces. We quantify the elastic constitutive law of the film by relating film extension and surface tension variation. It is shown that film exhibits a purely elastic behavior, well captured by a model based on surfactant conservation. This demonstrates that the dissipation is localized close to the menisci, and is not controlled by the interfacial viscosity of the thin films.   

Rheological behavior of a millimetric foam films assembly: Part II Viscosity

A foam, made of inviscid gas and Newtonian liquid, has an effective viscosity that may reach thousand times the viscosity of the foaming solution. Liquid phase confinement is at the origin of this spectacular viscosity enhancement. However, one puzzling question remains: how, and where, is the imposed stress transmitted to the liquid phase? \\ Using a dedicated, home made, "thin film rheometer", we measure local velocities and tensions and show that (i) a generic geometrical frustration arises from the fact that 3 films meet at each meniscus (ii) the rate of surfactant transfer, from one film to its neighbor, is controled by the tension difference between the two adjacent films, and determines the dissipation rate. \\ We develop a model based on the Stokes equation and on the surfactant diffusion/convection, and we show that Marangoni stress is strong enough to shear the films, only in a small region close to the menisci, which extension $\ell$ may be of the order of 100 micrometers for usual physicochemical properties. We thus predict the existence of a sheared regime, for bubble size $d<\ell$, in which the imposed shear is entirely transmitted to the thin films, and of a regime of film extension/compression, with localised film shearing, for $d>\ell$.   

Dynamics of a surfactant-laden bubble bursting through an interface

When a bubble is resting close to a liquid-gas interface, its rupture gives rise to the formation of a central jet. This jet breaks up into small droplets, which could transport biological material, toxins, salts, surfactants or dissolved gases. We perform fully three-dimensional direct numerical simulations of the phenomena using a hybrid interface-tracking/level-set method accounting for surfactant-induced Marangoni stresses, sorption kinetics, and diffusive effects. We have selected an initial bubble shape corresponding to a large Laplace number and a vanishingly small Bond number to neglect gravity, and isolate the effects of surfactant on the flow. According to the foregoing results, the presence of surfactants leads to a reduction in the number of ejected droplets through Marangoni-flow, driving motion from high to low interfacial surfactant concentration regions, and not via lowering of the mean surface tension. A parametric study regarding the strength of surfactant and solubility is also performed.   

Dynamical fracture: a continuum derivation of the velocity gap

In dynamical fracture mechanics, the existence of a velocity gap has been debated - a minimum speed necessary for propagation, requiring driving above the Griffith point. A monolayer of aqueous foam has provided a model system exhibiting fracture under sudden applied pressure by rupturing successive liquid films. Using fluid dynamics principles such as film instability and viscous resistance, this process is mapped to brittle fracture. In line with experiments, the model finds a velocity gap and a critical driving pressure above the Griffith limit. We show that these features are also observed in a one-dimensional continuum model of the foam, from which we obtain explicit scaling predictions of the velocity gap and the critical driving pressure in terms of the model parameters. The model reveals the competition of dissipation processes in the thin films and the Plateau borders as the cause of the velocity gap phenomenon, confirming concepts advanced in the fracture mechanics of solids.   

Formation, growth and coalescence of nanoscopic mesas in stratifying foam films

Ultrathin micellar foam films exhibit stratification due to confinement-induced structuring and layering of micelles. Stratification proceeds by the formation and growth of thinner domains at the expense of surrounding thicker film, and flows and instabilities drive the formation of nanoscopic terraces, ridges and mesas within a film. The detailed mechanisms underlying stratification are still under debate, and are resolved in this contribution by addressing long-standing experimental and theoretical challenges. Thickness variations in stratifying films are visualized and analyzed using interferometry, digital imaging and optical microscopy (IDIOM) protocols, with unprecedented high spatial (thickness \textless 100 nm, lateral \textasciitilde 500 nm) and temporal resolution (\textless 1 ms). Using IDIOM protocols we developed recently, we characterize the shape and the growth dynamics of mesas that flank the expanding domains in micellar thin films, and we track their evolution, as well as coalescence dynamics.   

Drainage of protein foams and foam films

Many food,cosmetic and pharmaceutical foams contain proteins that influence both the interfacial and bulk properties of formulations. In this study, we characterize the drainage of protein-based foams as well as single foam films, and contrast their behavior with micellar foams formed with small molecular surfactants above the critical micelle concentration. Micellar foam films undergo drainage via stratification manifested as step-wise thinning in the plots of average film thickness over time. Stratification in micellar foam films is accompanied by formation of coexisting thick-thin regions visualized in reflected light microscopy as exhibiting distinct grey regions as intensity is correlated with thin film interference. We critically examine the drainage of protein foam films to determine how and when stratification can be observed, and evaluate the connection between drainage of single foam films and bulk foams.   

Stratification in micellar foam films as a probe for intermicellar interactions

Sodium Naphthenate (NaN) found in crude oils can act as surfactants and influence the stability, lifetime and rheology of petroleum foams and emulsions. Here, we show that foam films formed by aqueous micellar solutions of NaN exhibit step-wise thinning or stratification, due to the influence of non-DLVO forces, including supramolecular oscillatory structural forces. We utilize Interferometry, Digital, Imaging, Optical Microscopy protocols, previously developed by our group, to investigate the drainage and stratification in micellar foam films (\textless 100 nm) with high spatial (thickness \textless 10 nm) and temporal resolution (\textless 1 ms). We determine how the NaN concentration influences the nanoscopic topography, stratification kinetics and step size of foam films, and contrast the results with behavior observed with stratifying foams made with sodium dodecyl sulfate (SDS) solutions. We span a relatively wide concentration range, such that micelle shape and size vary, as is revealed by complementary small angle x-ray scattering experiments.