Juggling bubbles in square capillaries: an experimental proof of non-pairwise bubble interactions

One-Step Generation of Alginate-Based Hydrogel Foams Using CO2 for Simultaneous Foaming and Gelation

The reliable generation of hydrogel foams remains a challenge in a wide range of sectors, including food, cosmetic, agricultural, and medical applications. Using the example of calcium alginate foams, we introduce a novel foam generation method that uses CO2 for the simultaneous foaming and pH reduction of the alginate solution to trigger gelation. We show that gelled foams of different gas fractions can be generated in a simple one-step process. We macroscopically follow the acidification using a pH-responsive indicator and investigate the role of CO2 in foam ageing via foam stability measurements. Finally, we demonstrate the utility of interfacial rheology to provide evidence for the gelation process initiated by the dissolution of the CO2 from the dispersed phase. Both approaches, gas-initiated gelation and interfacial rheology for its characterization, can be readily transferred to other types of gases and formulations.

Pressure-deformation relations of elasto-capillary drops (droploons) on capillaries

An increasing number of multi-phase systems exploit complex interfaces in which capillary stresses are coupled with solid-like elastic stresses. Despite growing efforts, simple and reliable experimental characterisation of these interfaces remains a challenge, especially of their dilational properties. Pendant drop techniques are convenient, but suffer from complex shape changes and associated fitting procedures with multiple parameters. Here we show that simple analytical relationships can be derived to describe reliably the pressure-deformation relations of nearly spherical elasto-capillary droplets ("droploons") attached to a capillary. We consider a model interface in which stresses arising from a constant interfacial tension are superimposed with mechanical extra-stresses arising from the deformation of a solid-like, incompressible interfacial layer of finite thickness described by a neo-Hookean material law. We compare some standard models of liquid-like (Gibbs) and solid-like (Hookean and neo-Hookean elasticity) elastic interfaces which may be used to describe the pressure-deformation relations when the presence of the capillary can be considered negligible. Combining Surface Evolver simulations and direct numerical integration of the drop shape equations, we analyse in depth the influence of the anisotropic deformation imposed by the capillary on the pressure-deformation relation and show that in many experimentally relevant circumstances either the analytical relations of the perfect sphere may be used or a slightly modified relation which takes into account the geometrical change imposed by the capillary. Using the analogy with the stress concentration around a rigid inclusion in an elastic membrane, we provide simple non-dimensional criteria to predict under which conditions the simple analytical expressions can be used to fit pressure-deformation relations to analyse the elastic properties of the interfaces via "Capillary Pressure Elastometry". We show that these criteria depend essentially on the drop geometry and deformation, but not on the interfacial elasticity. Moreover, this benchmark case shows for the first time that Surface Evolver is a reliable tool for predictive simulations of elastocapillary interfaces. This opens doors to the treatment of more complex geometries/conditions, where theory is not available for comparison. Our Surface Evolver code is available for download in the ESI.

The energy of fcc and hcp foams

We present Surface Evolver evaluations of the difference in energy between face-centred cubic (fcc) and hexagonal close-packed (hcp) foams in the usual idealized model, for liquid fractions ranging from the dry to the wet limit. The difference vanishes in both limits, and favours hcp for all intermediate liquid fractions, as has been proven. The maximum relative energy difference is very small, of the order of 10-5. The asymptotic dependence on liquid fraction is non-analytic in both limits: we present explicit expressions in both cases, derived from first principles. They have been obtained from identifying node interactions (dry limit) and contact interactions (wet limit) as the respective sources for energy differences between fcc and hcp. The wet limit is well described by Morse-Witten theory which has proven to be very powerful for the analytic computation of the surface energy of slightly deformed bubbles.

Validation of Milner's visco-elastic theory of sintering for the generation of porous polymers with finely tuned morphology

Sacrificial sphere templating has become a method of choice to generate macro-porous materials with well-defined, interconnected pores. For this purpose, the interstices of a sphere packing are filled with a solidifying matrix, from which the spheres are subsequently removed to obtain interconnected voids. In order to control the size of the interconnections, viscous sintering of the initial sphere template has proven a reliable approach. To predict how the interconnections evolve with different sintering parameters, such as time or temperature, Frenkel's model has been used with reasonable success over the last 70 years. However, numerous investigations have shown that the often complex flow behaviour of the spheres needs to be taken into account. To this end, S. Milner [arXiv:1907.05862] developed recently a theoretical model which improves on some key assumptions made in Frenkel's model, leading to a slightly different scaling. He also extended this new model to take into account the visco-elastic response of the spheres. Using an in-depth investigation of templates of paraffin spheres, we provide here the first systematic comparison with Milner's theory. Firstly, we show that his new scaling describes the experimental data slightly better than Frenkel's scaling. We then show that the visco-elastic version of his model provides a significantly improved description of the data over a wide parameter range. We finally use the obtained sphere templates to produce macro-porous polyurethanes with finely controlled pore and interconnection sizes. The general applicability of Milner's theory makes it transferable to a wide range of formulations, provided the flow properties of the sphere material can be quantified. It therefore provides a powerful tool to guide the creation of sphere packings and porous materials with finely controlled morphologies.

Thermally Driven Order-Disorder Transition in Two-Dimensional Soft Cellular Systems

Many systems, including biological tissues and foams, are made of highly packed units having high deformability but low compressibility. At two dimensions, these systems offer natural tesselations of a plane with fixed density, in which transitions from ordered to disordered patterns are often observed, in both directions. Using a modified cellular Potts model algorithm that allows rapid thermalization of extensive systems, we numerically explore the order-disorder transition of monodisperse, two-dimensional cellular systems driven by thermal agitation. We show that the transition follows most of the predictions of Kosterlitz-Thouless-Halperin-Nelson-Young (KTHNY) theory developed for melting of 2D solids, extending the validity of this theory to systems with many-body interactions. In particular, we show the existence of an intermediate hexatic phase, which preserves the orientational order of the regular hexagonal tiling but loses its positional order. In addition to shedding light on the structural changes observed in experimental systems, our study shows that soft cellular systems offer macroscopic systems in which the KTHNY melting scenario can be explored, in the continuation of Bragg's experiments on bubble rafts.