Two dimensional foam rheology with viscous drag

We formulate and apply a continuum model that incorporates elasticity, yield stress, plasticity and viscous drag. It is motivated by the two-dimensional foam rheology experiments of Debregeas et al. [G. Debregeas, H. Tabuteau, and J.-M. di Meglio, Phys. Rev. Lett. 87, 178305 (2001)] and Wang et al [Y. Wang, K. Krishan, and M. Dennin, Phys. Rev. E 73, 031401 (2006)], and is successful in exhibiting their principal features an exponentially decaying velocity profile and strain localisation. Transient effects are also identified.Comment: accepted version (to appear in PRL). Some parts of the paper have been rewritten (mainly introduction and final discussion

Mechanical probing of liquid foam aging

We present experimental results on the Stokes experiment performed in a 3D dry liquid foam. The system is used as a rheometric tool : from the force exerted on a 1cm glass bead, plunged at controlled velocity in the foam in a quasi static regime, local foam properties are probed around the sphere. With this original and simple technique, we show the possibility of measuring the foam shear modulus, the gravity drainage rate and the evolution of the bubble size during coarsening

Bubble kinetics in a steady-state column of aqueous foam

We measure the liquid content, the bubble speeds, and the distribution of bubble sizes, in a vertical column of aqueous foam maintained in steady-state by continuous bubbling of gas into a surfactant solution. Nearly round bubbles accumulate at the solution/foam interface, and subsequently rise with constant speed. Upon moving up the column, they become larger due to gas diffusion and more polyhedral due to drainage. The size distribution is monodisperse near the bottom and polydisperse near the top, but there is an unexpected range of intermediate heights where it is bidisperse with small bubbles decorating the junctions between larger bubbles. We explain the evolution in both bidisperse and polydisperse regimes, using Laplace pressure differences and taking the liquid fraction profile as a given.Comment: 7 pages, 3 figure

The structure of di-valent and tri-valent metals

Pseudopotential and second order perturbation theory applied to divalent and trivalent metal structure

Viscous instabilities in flowing foams: A Cellular Potts Model approach

The Cellular Potts Model (CPM) succesfully simulates drainage and shear in foams. Here we use the CPM to investigate instabilities due to the flow of a single large bubble in a dry, monodisperse two-dimensional flowing foam. As in experiments in a Hele-Shaw cell, above a threshold velocity the large bubble moves faster than the mean flow. Our simulations reproduce analytical and experimental predictions for the velocity threshold and the relative velocity of the large bubble, demonstrating the utility of the CPM in foam rheology studies.Comment: 10 pages, 3 figures. Replaced with revised version accepted for publication in JSTA

A periodic microfluidic bubbling oscillator: insight into the stability of two-phase microflows

This letter describes a periodically oscillating microfoam flow. For constant input parameters, both the produced bubble volume and the flow rate vary over a factor two. We explicit the link between foam topology alternance and flow rate changes, and construct a retroaction model where bubbles still present downstream determine the volume of new bubbles, in agreement with experiment. This gives insight into the various parameters important to maintain monodispersity and at the same time shows a method to achieve controlled polydispersity.Comment: 4 page

Topological model of soap froth evolution with deterministic T2-processes

We introduce a topological model for the evolution of 2d soap froth. The topological rearrangements (T2 processes) are deterministic (unlike the standard stochastic model): the final topology depends on the areas of the neighboring cells. The new model gives agreement with experiments in the transient regime, where the previous models failed qualitatively, and also improves agreement in the scaling state.Comment: latex, 12 pages, 2 figure

Rate Dependence and Role of Disorder in Linearly Sheared Two-Dimensional Foams

The shear flow of two dimensional foams is probed as a function of shear rate and disorder. Disordered foams exhibit strongly rate dependent velocity profiles, whereas ordered foams show rate independence. Both behaviors are captured quantitatively in a simple model based on the balance of the time-averaged drag forces in the foam, which are found to exhibit power-law scaling with the foam velocity and strain rate. Disorder modifies the scaling of the averaged inter-bubble drag forces, which in turn causes the observed rate dependence in disordered foams.Comment: 4 Figures, 4 page

Experimental evidence of flow destabilization in a 2D bidisperse foam

Liquid foam flows in a Hele-Shaw cell were investigated. The plug flow obtained for a monodisperse foam is strongly perturbed in the presence of bubbles whose size is larger than the average bubble size by an order of magnitude at least. The large bubbles migrate faster than the mean flow above a velocity threshold which depends on its size. We evidence experimentally this new instability and, in case of a single large bubble, we compare the large bubble velocity with the prediction deduced from scaling arguments. In case of a bidisperse foam, an attractive interaction between large bubbles induces segregation and the large bubbles organize themselves in columns oriented along the flow. These results allow to identify the main ingredients governing 2D polydisperse foam flows