Flow of foam past an elliptical obstacle

Simulating the interaction between a descending super-quadric solid object and a soap film

We investigate the interaction that occurs between a light solid object and a horizontal soap film of a ‘bamboo’ foam contained in a cylindrical tube. We vary the shape of the descending object from a sphere to a cube by changing a single shape parameter. We investigate in detail how the soap film deforms and determine the forces that the film exerts on the object, depending on the radius of the cylindrical tube, and the shape, orientation and position of the object. We show that a cubic particle in a particular orientation experiences the largest drag force, and that this orientation is also the most likely outcome of dropping a cube from an arbitrary orientation through a bamboo foam.

Estimation of Reynolds number for flows around cylinders with lattice Boltzmann methods and artificial neural networks

The present work investigates the application of artificial neural networks (ANNs) to estimate the Reynolds (Re) number for flows around a cylinder. The data required to train the ANN was generated with our own implementation of a lattice Boltzmann method (LBM) code performing simulations of a two-dimensional flow around a cylinder. As results of the simulations, we obtain the velocity field (v[over ⃗]) and the vorticity (∇[over ⃗]×v[over ⃗]) of the fluid for 120 different values of Re measured at different distances from the obstacle and use them to teach the ANN to predict the Re. The results predicted by the networks show good accuracy with errors of less than 4% in all the studied cases. One of the possible applications of this method is the development of an efficient tool to characterize a blocked flowing pipe.

Flow of foam through a convergent channel

We study experimentally the flow of a foam confined as a bubble monolayer between two plates through a convergent channel. We quantify the velocity, the distribution and orientation of plastic events, and the elastic stress, using image analysis. We use two different soap solutions: a sodium dodecyl sulfate (SDS) solution, with a negligible wall friction between the bubbles and the confining plates, and a mixture containing a fatty acid, giving a large wall friction. We show that for SDS solutions, the velocity profile obeys a self-similar form which results from the superposition of plastic events, and the elastic deformation is uniform. For the other solution, the velocity field differs and the elastic deformation increases towards the exit of the channel. We discuss and quantify the role of wall friction on the velocity profile, the elastic deformation, and the rate of plastic events.

Elastoplastic flow of a foam around an obstacle

We simulate quasistatic flows of an ideal two-dimensional monodisperse foam around different obstacles, both symmetric and asymmetric, in a channel. We record both pressure and network contributions to the drag and lift forces and study them as a function of obstacle geometry. We show that the drag force increases linearly with the cross section of an obstacles. The lift on an asymmetric aerofoil-like shape is negative and increases with its arc length, mainly due to the pressure contribution.

Surfactant mixtures for control of bubble surface mobility in foam studies

A new class of surfactant mixtures is described, which is particularly suitable for studies related to foam dynamics, such as studies of foam rheology, liquid drainage from foams and foam films, and bubble coarsening and rearrangement. These mixtures contain an anionic surfactant, a zwitterionic surfactant, and fatty acids (e.g., myristic or lauric) of low concentration. Solutions of these surfactant mixtures exhibit Newtonian behavior, and their viscosity could be varied by using glycerol. Most importantly, the dynamic surface properties of these solutions, such as their surface dilatational modulus, strongly depend on the presence and on the chain-length of fatty acid(s). Illustrative results are shown to demonstrate the dependence of solution properties on the composition of the surfactant mixture, and the resulting effects on foam rheological properties, foam film drainage, and bubble Ostwald ripening. The observed high surface modulus in the presence of fatty acids is explained with the formation of a surface condensed phase of fatty acid molecules in the surfactant adsorption layer.

Theoretical model of viscous friction inside steadily sheared foams and concentrated emulsions

In a recent Letter [N. D. Denkov, Phys. Rev. Lett. 100, 138301 (2008)] we calculated theoretically the macroscopic viscous stress of steadily sheared foam or emulsion from the energy dissipated inside the transient planar films, formed between neighboring bubbles or drops in the shear flow. The model predicts that the viscous stress in these systems should be proportional to Ca 1/2, where Ca is a capillary number and n=1/2 is the power-law index. In the current paper we explain our model in detail and develop it further in several aspects: First, we extend the model to account for the effects of viscous friction in the curved meniscus regions, surrounding the planar films, on the dynamics of film formation and on the total viscous stress. Second, we consider the effects of surface forces (electrostatic, van der Waals, etc.) acting between the surfaces of the neighboring bubbles or drops and show that these forces could be important in emulsions, due to the relatively small thickness of emulsion films (often comparable to the range of action of surface forces). In contrast, the surface forces are usually negligible in steadily sheared foams, because the dynamic foam films are thicker than the extent of surface forces, except for foams containing micrometer-sized bubbles and/or at very low shear rates. Third, additional consideration is made for bubbles or drops exhibiting high surface viscosity, for which we demonstrate an additional contribution to the macroscopic viscous stress, created by the surface dissipation of energy. The new upgraded model predicts that the energy dissipation at the bubble or drop surface leads to power-law index n<1/2 , whereas the contribution of the surface forces leads to n>1/2 , which explains the rich variety of foam or emulsion behaviors observed upon steady shear. Various comparisons are made between model predictions and experimental results for both foams and emulsions, and very good agreement is found.

Simulations of two-dimensional foam rheology: localization in linear Couette flow and the interaction of settling discs

Surface Evolver simulations of flowing two-dimensional foams are described. These are used for two purposes. Firstly, to extract the location of the T 1s, the changes in bubble topology that occur during plastic flow. It is shown that in linear Couette flow the T1 s are localized in space, becoming more so as the polydispersity of the foam decreases. Secondly, the sedimentation of two circular discs through a foam under gravity is studied. If the discs are sufficiently close, they begin to interact and one moves behind the other during their descent.

Reversible plastic events in amorphous materials

For crystalline materials, the microscopic origin of plasticity is well understood in terms of the dynamics of topological defects. For amorphous materials, the underlying structural disorder prevents such a description. Therefore identifying and characterizing the microscopic plastic events in amorphous materials remains an important challenge. We show direct evidence for the coexistence of reversible and irreversible plastic events (T1 events) at the microscopic scale in both experiments and simulations of two-dimensional foam. In the simulations, we also demonstrate a link between the reversibility of T1 events and pathways in the potential energy landscape of the system.

Yield drag in a two-dimensional foam flow around a circular obstacle: effect of liquid fraction

We study the two-dimensional flow of foams around a circular obstacle within a long channel. In experiments, we confine the foam between liquid and glass surfaces. In simulations, we use a deterministic software, the Surface Evolver, for bubble details and a stochastic one, the extended Potts model, for statistics. We adopt a coherent definition of liquid fraction for all studied systems. We vary it in both experiments and simulations, and determine the yield drag of the foam, that is, the force exerted on the obstacle by the foam flowing at very low velocity. We find that the yield drag is linear over a large range of the ratio of obstacle to bubble size, and is independent of the channel width over a large range. Decreasing the liquid fraction, however, strongly increases the yield drag; we discuss and interpret this dependence.