Foam Generation Through a Single Pore with Rectangular Cross-Section: Hysteretic Behavior and Geometric Limitation of the Volume Fraction of Bubbles.

We study foam production and destabilization through a flow-focusing geometry, namely a single pore of rectangular cross-section, by coinjecting gas and liquid at constant pressure, Pg, and constant flow rate, Qw. We observe that bubble production results from a Rayleigh-Plateau destabilization of the internal gas thread that occurs at the pore neck when its width becomes comparable to the height of the rectangular-section channel. Using a simple model and numerical approach, we (i) predict the shape of the gas jet and its stability range as a function of flow parameters and device geometry, which we successfully compare with our experimental results, and (ii) demonstrate the existence of a critical local pressure drop at the pore neck that determines whether or not a stable gas flow can form. We thus show that bubble foam generation exhibits hysteretic behavior due to hydrodynamic feedback and demonstrate that there is a maximum bubble volume fraction that the generated foam cannot exceed, the value of which is fixed by the geometry. Our results suggest that the foam collapse observed in porous media when the fractional gas flow becomes too large may result from hydrodynamic feedback inhibiting foam generation and not necessarily from coalescence between bubbles, as is usually claimed.

Formation of glassy skins in drying polymer solutions: approximate analytical solutions.

We study the formation of a glassy skin at the air interface of drying polymer solutions. We introduce a simple approximation, which is valid for most diffusion problems, and which allows us to derive analytical relationships for the polymer concentration as a function of time. We show that the approximate results differ by less than 15% from those obtained by numerically solving the diffusion equation. We use the approximation to study skin formation in evaporating solutions. We focus on the influence of variations of the mutual diffusion coefficient with concentration, when the latter decreases sharply at high concentrations, as observed in the vicinity of the glass transition. We show that the skin thickness depends very strongly on the exponent characterising the decrease of the diffusion coefficient, in contrast to the polymer volume fraction at the interface, which varies only slightly with the exponent.

Drying Liquid Coatings with an Evaporation Mask: Theory and Experiments.

We report a study of the spatially varying thickness of dried films of polymer solutions resulting from a nonuniform evaporation flux. The controlled heterogeneity of the evaporation flux is imposed by placing a solid mask above the evaporating film spread on a solid substrate. At the end of drying, a depression has formed under the mask, together with overthicknesses extending from the edge of the mask and over distances that may be larger than its size. By considering the flows induced in a vertically homogeneous film, we obtain analytical solutions for the thickness profiles during drying using a linear approximation in the limits of either gravity or capillarity-driven flows. We demonstrate that gravity can play a role in the deformations of the films, even if their initial thicknesses are 1 order of magnitude smaller than the capillary length. In addition, we examine two possible reference states for the linear approximation, i.e., far from the mask in the film of decreasing thickness and increasing viscosity, or under the mask where no evaporation occurs. We further compare these results with experimental ones obtained by drying thin films of polymer solutions under a mask. Both the extent and amplitude of the thickness heterogeneities of the dry film are quantitatively predicted by the linear analysis for a reference state under the mask. Our results therefore provide new insight on the patterns resulting from evaporation masks and can be generalized to minimize thickness heterogeneities in any situation in which the evaporation flux is nonuniform.

Uptake kinetics of spontaneously emulsified microdroplets at an air-liquid interface.

Understanding the transfers occurring at the interfaces between emulsions and air is required to predict the properties of foamed emulsions, used for example as antifoaming lubricants or for oil extraction. Whereas bubbling oil-in-water emulsions have been studied in details, oil-in-oil emulsions have received less attention. We consider a phase-separating mixture of three oils being Polydimethylsiloxane (PDMS), decane and cyclopentanol. PDMS is dispersed as submicrometer-sized droplets by spontaneous emulsification. In bulk, we show that the time evolution of the emulsion is driven by undelayed coalescence of the Brownian microdroplets. At the freshly created interface of an air bubble created in the emulsion, we use tensiometry measurements to investigate the uptake kinetics of PDMS-rich microdroplets at the air-liquid interface. Specifically, we evidence two mechanisms of uptake: the advection of droplets at the interface during bubble swelling, followed by their diffusion on a longer time scale. We model the growth of the PDMS-rich layer at the interface and, finally, we establish the surface energy of a thin film of PDMS-rich phase squeezed between air and liquid as a function of its thickness.

Breaking of Emulsions with Chemical Additives: Using Surrogate Fluids to Develop a Novel Theoretical Framework and Its Application to Water-in-Crude Oil Emulsions.

We investigate the role of adding a water-soluble surfactant (Tween 20) that acts as a demulsifier on the stability of water-in-dodecane emulsions stabilized with Span 80. Performing bottle test experiments, we monitor the emulsion separation process. Initially, water droplets sediment fast (∼10 min) until they become closely packed and form the so-called dense packed layer (DPL). The presence of the DPL, a long-lived metastable high-water-fraction (70-90%) emulsion separating bulk oil and water layers, slows down significantly the kinetics (∼105 min) of water separation. Once the DPL is formed, the ratio of the volume of separated water to the total water amount is called as water separation efficiency. We assume that the emulsion stability is reached when the coverage of the emulsifier surfactant exceeds 80% and use the ideal solution approximation. From that, we rationalize the water separation efficiency and the minimum demulsifier concentration required to maximize it, in terms of the mean droplet size, the surfactant concentrations, the total water volume fraction, and the adsorption strength of the water-soluble surfactant. Model predictions and experimental findings are in excellent agreement. We further test the validity and robustness of our theoretical model, by applying it successfully to data found in the literature on water-in-crude oil emulsion systems. Ultimately, our results prove that the efficiency of a demulsifier agent to break a W/O emulsion strongly correlates to its adsorption strength at the W/O interface, providing a novel contribution to the selection guidelines of chemical demulsifiers.

Effect of a Surfactant Mixture on Coalescence Occurring in Concentrated Emulsions: The Hole Nucleation Theory Revisited.

By conducting both a bottle test and isolate drop-drop experiments, we determine the coalescence rates of water droplets within water-in-oil emulsions stabilized by a large amount of Span 80 in the presence of Tween 20, a surfactant that acts as a demulsifier. Using a microscopic model based on a theory of hole nucleation, we establish an analytical formula that quantitatively predicts the coalescence frequency per unit area of droplets whose interfaces are fully covered by surfactant molecules. Despite its simplicity and the strong assumptions made for its derivation, this formula captures our experimental findings on Span 80-stabilized emulsions as well as other results, found in the literature, remarkably well on a wide range of water-in-crude oil systems.

Spinodal stratification in micellar films between oil and silica.

We report on the thinning mechanisms of supported films of surfactant (nTAB) solutions above the critical micellar concentration. The films are formed by pressing an oil drop immersed in an aqueous surfactant solution on a silica surface. Depending on the length of the carbon chain of the surfactant and its concentration, two modes of destabilization of the stratified films are observed. The first one proceeds by heterogeneous nucleation, characterized by the lateral expansion of the domain of lower thickness as evidenced long ago in suspended micellar films. In addition, the simultaneous stepwise thinning of several domains, called spinodal stratification, is observed here in supported films. We measure the time evolution of the thickness of the films, and we discuss the selection mechanism of each destabilization mode.

Dramatic Slowing Down of Oil/Water/Silica Contact Line Dynamics Driven by Cationic Surfactant Adsorption on the Solid.

We report on the contact line dynamics of a triple-phase system silica/oil/water. When oil advances onto silica within a water film squeezed between oil and silica, a rim forms in water and recedes at constant velocity. We evidence a sharp (three orders of magnitude) decrease of the contact line velocity upon the addition of cationic surfactants above a threshold concentration, which is slightly smaller than the critical micellar concentration. We show that, with or without surfactant, and within the range of small capillary numbers investigated, the contact line dynamics can be described by a friction term that does not reduce to pure hydrodynamical effects. In addition, we derive a model that successfully accounts for the selected contact line velocity of the rim. We further demonstrate the strong increase of the friction coefficient with surfactant bulk concentration results from the strongly nonlinear adsorption isotherm of surfactants on silica. From the variations of the friction coefficient and spreading parameter with surface concentration, we suggest a picture in which the part of the adsorbed surfactants that are strongly bound to the silica interface is trapped under the oil droplet and is responsible for the large increase in line friction.

Coalescence in concentrated emulsions: theoretical predictions and comparison with experimental bottle test behaviour.

Fusion between emulsion drops, also called coalescence, may be undesirable for storage or sought after depending on the desired application. In this latter case, a complete separation of the two liquids composing the emulsion is required. The same objective may be applicable to foams. We have performed bottle test experiments on a model system of water in oil (w/o) emulsion stabilized by high amounts of hydrophobic surfactant Span 80. We observe two regimes for emulsion separation: the first regime, which is fast and includes sedimentation of the water droplets, and the second regime, which exhibits a very dense and stable emulsion zone. We predict the initial thickness of the dense zone as a simple function of surfactant concentration and mean droplet size. From the assumption that the coalescence rate depends only on the area of the thin film between two contacted droplets, we quantitatively model the separation kinetics of the dense emulsion zone. Our results give rise to a simple method that allows measuring the coalescence frequency per unit area, only by monitoring bottle test experiments.

Rouse 2D Diffusion of Polymer Chains in Low Density Precursor Films of Polybutadiene Melts.

We took advantage of pseudopartial wetting to promote the spreading of precursor films whose surface density smoothly decays to zero away from a sessile droplet. By following the spreading dynamics of semidilute precursor films of polybutadiene melts on silicon wafers, we measure molecular diffusion coefficients for different molar masses and temperatures. For homopolymers, chains follow a thermally activated 2D Rouse diffusion mechanism, with an activation energy revealing polymer segment interactions with the surface. This Rouse model is generalized to chains with specific terminal groups.

Combining Ellipsometry and AFM To Probe Subnanometric Precursor Film Dynamics of Polystyrene Melts.

We investigate the evolution over time of the space profiles of precursor films spreading away from a droplet of polymer in the poorly explored pseudo-partial wetting case. We use polystyrene melt droplets on oxidized silicon wafers. Interestingly, the film thicknesses measured by ellispometric microscopy are found in the 0.01 to 1 nm range. These thicknesses were validated by atomic force microscopy measurements performed on the textured film obtained after quenching at room temperature. From this, an effective thickness is obtained and compares well to the thicknesses measured by ellipsometry, validating the use of an optical method in this range of thickness. Ellipsometric microscopy provides a height resolution below the ångström with lateral resolution, image size, and framerate well adapted to spreading precursor films. From this, we demonstrate that precursor films of polystyrene consist of polymer chains with a surface density decreasing to zero away from the droplet. We further find that the polymer chains follow a simple diffusive law with the diffusion coefficient independent of density. This demonstrates that polystyrene chains spread independently in precursor films in pseudo-partial wetting condition. This behavior differs significantly from the case of chains spreading in total wetting for which the diffusion coefficient was found in the literature to depend on surface density or thickness.

Geometrical control of dissipation during the spreading of liquids on soft solids.

Gel layers bound to a rigid substrate are used in cell culture to control differentiation and migration and to lower the friction and tailor the wetting of solids. Their thickness, often considered a negligible parameter, affects cell mechanosensing or the shape of sessile droplets. Here, we show that the adjustment of coating thickness provides control over energy dissipation during the spreading of flowing matter on a gel layer. We combine experiments and theory to provide an analytical description of both the statics and the dynamics of the contact line between the gel, the liquid, and the surrounding atmosphere. We extract from this analysis a hitherto-unknown scaling law that predicts the dynamic contact angle between the three phases as a function of the properties of the coating and the velocity of the contact line. Finally, we show that droplets moving on vertical substrates coated with gel layers having linear thickness gradients drift toward regions of higher energy dissipation. Thus, thickness control opens the opportunity to design a priori the path followed by large droplets moving on gel-coated substrates. Our study shows that thickness is another parameter, besides surface energy and substrate mechanics, to tune the dynamics of liquid spreading and wetting on a compliant coating, with potential applications in dew collection and free-surface flow control.

Foaming of Transient Polymer Hydrogels.

Foams made with polymer hydrogels can be used in a variety of applications, such as scaffolds for biomedical applications or decontamination processes. However, from a practical point of view, it is difficult to introduce bubbles into viscous or viscoelastic fluids and to produce large volumes of hydrogel foams. In the present article, we investigate the foaming process of poly(vinyl alcohol) (PVA)/borax transient hydrogels, where PVA chains reversibly bind to borax molecules. In a previous article, we showed that foams obtained with PVA/borax mixtures are highly stable because of both high interfacial and bulk viscosities and can be used to quickly absorb liquids, which make them suitable for detergency or decontamination processes. To produce these foams, we use a two-step foaming process which consists in first shearing a PVA solution to obtain a PVA foam and second adding borax to the PVA foam under continuous shearing. The obtained PVA/borax foams are stable for weeks. In this study, we observe a shear-induced collapse of the foams for formulations containing a low borax/PVA ratio, whereas they remain stable under shear for high PVA/borax ratios. Using scaling arguments, we find that the shear-induced collapse of the foams and bubbles is obtained below a critical ratio, N E/N B = 15, of the number of entanglements per chain, N E, and the number of borax per chain, N B. Rheology measurements show that the samples present a shear-thickening behavior that increases with the borax concentration. We suggest that during the foaming process when the shearing rate is of the order of 100 s-1, the viscosity of these samples diverges, leading to a viscous to fragile transition. To mimic the fast stretching of the PVA/borax thin films during the foaming process, we study the stretching of individual PVA/borax catenoid-shaped thin films at high stretching rates. We observe that the films containing low PVA/borax ratios do not minimize their surface area unlike what is theoretically expected for standard surfactant films. Moreover, the films tend to be unstable and fracture because the PVA/borax network does not have time to rearrange and relax stresses for high stretching rates.

Shear thinning in non-Brownian suspensions.

We study the flow of suspensions of non-Brownian particles dispersed into a Newtonian solvent. Combining capillary rheometry and conventional rheometry, we evidence a succession of two shear thinning regimes separated by a shear thickening one. Through X-ray radiography measurements, we show that during each of those regimes, the flow remains homogeneous and does not involve particle migration. Using a quartz-tuning fork based atomic force microscope, we measure the repulsive force profile and the microscopic friction coefficient µ between two particles immersed into the solvent, as a function of normal load. Coupling measurements from those three techniques, we propose that (1) the first shear-thinning regime at low shear rates occurs for a lubricated rheology and can be interpreted as a decrease of the effective volume fraction under increasing particle pressures, due to short-ranged repulsive forces and (2) the second shear thinning regime after the shear-thickening transition occurs for a frictional rheology and can be interpreted as stemming from a decrease of the microscopic friction coefficient at large normal load.

Growth and relaxation of a ridge on a soft poroelastic substrate.

Elastocapillarity describes the deformations of soft materials by surface tensions and is involved in a broad range of applications, from microelectromechanical devices to cell patterning on soft surfaces. Although the vast majority of elastocapillarity experiments are performed on soft gels, because of their tunable mechanical properties, the theoretical interpretation of these data has been so far undertaken solely within the framework of linear elasticity, neglecting the porous nature of gels. We investigate in this work the deformation of a thick poroelastic layer with surface tension subjected to an arbitrary distribution of time-dependent axisymmetric surface forces. Following the derivation of a general analytical solution, we then focus on the specific problem of a liquid drop sitting on a soft poroelastic substrate. We investigate how the deformation and the solvent concentration field evolve in time for various droplet sizes. In particular, we show that the ridge height beneath the triple line grows logarithmically in time as the liquid migrates toward the ridge. We then study the relaxation of the ridge following the removal of the drop and show that the drop leaves long-lived footprints after removal which may affect surface and wetting properties of gel layers and also the motion of living cells on soft materials. Preliminary experiments performed with water droplets on soft PDMS gel layers are in excellent agreement with the theoretical predictions.

Water film squeezed between oil and solid: drainage towards stabilization by disjoining pressure.

The spontaneous drainage of aqueous solutions of salt squeezed between an oil drop and a glass surface is studied experimentally. The thickness profile of the film is measured in space and time by reflection interference microscopy. As the film thins down, three regimes are identified: a capillary dominated regime, a mixed capillary and disjoining pressure regime, and a disjoining pressure dominated regime. These regimes are modeled within the lubrication approximation, and the role of the disjoining pressure is precisely investigated in the limit of thicknesses smaller than the range of electrostatic interactions. We derive simple analytical laws describing the drainage dynamics, thus providing tools to uncouple the effect of the film geometry from the effects of the disjoining or capillary pressures.

Optical control of surface forces and instabilities in foam films using photosurfactants.

Molecular interactions in thin liquid films, such as the disjoining pressure, are involved in interfacial phenomena such as emulsion and foam stabilization. In this article we show that through light stimulation we can control remotely the disjoining pressure in a thin liquid film stabilized by a photosurfactant. We stabilize a horizontal thin liquid film using a cationic photosurfactant, AzoTAB, bearing an azobenzene moiety on the hydrophobic tail which can switch from a trans to a cis conformation upon light stimulation. As the film is illuminated at specific wavelengths the AzoTAB molecules switch continuously their conformation and consequently their interface affinity. The main consequence of stimulating the film with light is increasing the ratio of cis in the film. This provokes a desorption flux, and an increase in the concentration of free surfactants, as the CMC of the cis isomer is higher than that of the trans isomer. Therefore the electrostatic repulsion between the surfactant layers that stabilize the film decreases, inducing an instability in the film thickness. For films with a thickness between 20 nm and 60 nm, we observe the formation of spherical caps up to 100 µm wide, whose shape is controlled by the competition between surface tension and disjoining pressure. The motion of these caps in the film is restrained by the surface viscosity of the surfactant layers. In addition, for thicknesses below 40 nm and depending on light intensity, we can observe flat stratified islands up to 100 µm wide, with thickness steps corresponding to the size of a surfactant micelle. We suggest that this second instability is due to the oscillation of the disjoining pressure isotherm under light.

Understanding the role of molar mass and stirring in polymer dissolution.

When a dry soluble polymer is put in contact with a large quantity of solvent, it swells and forms a transient gel, and eventually, yields a dilute solution of polymers. Everyday lab experience shows that when the molar mass is large, namely tens of times larger than entanglement mass, this dissolution process is slow and difficult and may require stirring. Here, in agreement with previous results, we found that the time needed to turn a dry grain into a dilute solution is not limited by water diffusion in the glassy or semi-crystalline dry polymer, but rather by the life-time of the transient gel made of entangled chains. In addition, we shed new light on the dissolution process by demonstrating that, in contrast to theoretical predictions, the gel life-time is not governed by reptation. We show instead that swelling is simply controlled by the osmotic pressure and the gel permeability until the overlap concentration is reached within the gel. At this stage, the gel turns into a dilute solution in which polymers are dispersed by natural convection. The observed dependence of the dissolution process on the molar mass therefore originates from the molar mass dependent overlap concentration. Under stirring, or forced convection, the polymer gel disappears at a higher critical concentration that depends on the shear rate. We suggest a description of the experimental data which uses the rheological flow curves of the solutions of the considered polymer. Inversely, dissolution times of polymer powders under stirring can be inferred from classical rheological measurements of the polymer solutions at varied concentrations.