PEG-in-PDMS drops stabilised by soft silicone skins as a model system for elastocapillary emulsions with explicit morphology control.

HYPOTHESIS: The morphology of ordinary macro-emulsions is controlled by their high interfacial energies, i.e., by capillarity, leading to well-known structural features which can be tuned only over a narrow range. We claim here that a more explicit control over a much wider range of morphologies can be obtained by producing "elastocapillary emulsions" in which interfacial elasticity acts simultaneously with interfacial tension. EXPERIMENTS: We develop a model-system composed of PEG-in-PDMS emulsions, in which a catalyst diffuses from the PEG drops into the silicone matrix containing two reactive silicone polymers, which are cross-linked in a non-reactive silicone matrix to form a silicone gel of controlled thickness and mechanical properties on the drop surface. We characterise the cross-linking process of the gel in bulk and at the interface, and we analyse the skin growth kinetics. We then use the obtained understanding to produce emulsions with controlled elastocapillary interfaces using in-flow-chemistry in a purpose-designed millifluidic circuit. FINDINGS: We show that this approach allows to create interfaces over the full range of elastocapillary properties, and that very different emulsion morphologies can be generated depending on whether capillarity or elasticity dominates. These findings advance our fundamental understanding of the morphology of emulsions with complex interfaces, and they are of importance for the design of polymerised High Internal Phase Emulsions (polyHIPEs) with original structure/property relations. They will also be useful for the design of silicone capsules with fine-tuned mechanical properties.

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.

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

The physical properties of an ensemble of tightly packed particles like bubbles, drops or solid grains are controlled by their interactions. For the case of bubbles and drops it has recently been shown theoretically and computationally that their interactions cannot generally be represented by pair-wise additive potentials, as is commonly done for simulations of soft grain packings. This has important consequences for the mechanical properties of foams and emulsions, especially for strongly deformed bubbles or droplets well above the jamming point. Here we provide the first experimental confirmation of this prediction by quantifying the interactions between bubbles in simple model foams consisting of trains of equal-volume bubbles confined in square capillaries. The obtained interaction laws agree quantitatively with Surface Evolver simulations and are well described by an analytically derived expression based on the recently developed non-pairwise interaction model of Höhler et al. [Soft Matter, 2017, 13(7), 1371], based on Morse-Witten theory. While all experiments are done at Bond numbers sufficiently low for the hydrostatic pressure variation across one bubble to be negligible, we provide the full analysis taking into account gravity in the appendix for the interested reader. Even though the article focuses on foams, all results directly apply to the case of emulsions.