The surface tells it all: relationship between volume and surface fraction of liquid dispersions.

The properties of liquid dispersions, such as foams or emulsions, depend strongly on the volume fraction ϕ of the continuous phase. Concentrating on the example of foams, we show experimentally and theoretically that ϕ may be related to the fraction ϕs of the surface at a wall which is wetted by the continuous phase - given an expression for the interfacial energy or osmotic pressure of the bulk system. Since the surface fraction ϕs can be readily determined from optical measurement and since there are good general approximations available for interfacial energy and osmotic pressure we thus arrive at an advantageous method of estimating ϕ. The same relationship between ϕ and ϕs is also expected to provide a good approximation of the fraction of the bubble or drop surface which is wetted by the continuous phase. This is a parameter of great importance for the rheology and ageing of liquid dispersions.

Slow crystallisation of a monodisperse foam stabilised against coarsening.

The evolution of a three-dimensional monodisperse foam was investigated using X-ray tomography over the course of seven days. The coarsening of the sample was inhibited through the use of perfluorohexane gas. The internal configuration of bubbles is seen to change markedly, evolving from a disordered arrangement towards a more ordered state. We chart this ordering process through the use of the coordination number, the bond orientational order parameter (BOOP) and the translational order parameter.

Z-cone model for the energy of an ordered foam.

We develop the Z-Cone Model, in terms of which the energy of a foam may be estimated. It is directly applicable to an ordered structure in which every bubble has Z identical neighbours. The energy (i.e. surface area) may be analytically related to liquid fraction. It has the correct asymptotic form in the limits of dry and wet foam, with prefactors dependent on Z. In particular, the variation of energy with deformation in the wet limit is consistent with the anomalous behaviour found by Morse and Witten [Europhysics Letters, 1993, 22, 549] and Lacasse et al. [Physical Review E, 54, 5436], with a prefactor Z/2.

Buckling of a linear chain of hard spheres in a harmonic confining potential: Numerical and analytical results for low and high compression.

We extend a previous analysis of the buckling properties of a linear chain of hard spheres between hard walls under transverse harmonic confinement. Two regimes are distinguished-low compression, for which the entire chain buckles, and higher compression, for which there is localized buckling. With further increase of compression, second-neighbor contacts occur; beyond this compression the structure is no longer planar, and is not treated here. A continuous model is developed which is amenable to analytical solution in the low compression regime. This is helpful in understanding the scaling properties of both finite and infinite chains.

Can liquid foams and emulsions be modeled as packings of soft elastic particles?

When two immersed bubbles are pushed against each other, a facet is formed at their contact, leading to an increase of interfacial energy and hence a repulsive interaction force. Foams (and concentrated emulsions) in mechanical equilibrium may thus be modeled as an assembly of soft elastic interacting particles. Such a model has been used in many studies of their structure and mechanical properties, in particular near the jamming transition (or wet limit) where the contact forces are so small that bubbles remain roughly spherical. We review analytical ab initio models and simulations, based on the equilibration of pressure and surface tension forces or, equivalently, minimization of interfacial energy. Two-body interaction behavior dominates asymptotically at packing fractions approaching the jamming transition, but the interaction is intrinsically anharmonic and cannot be captured by a power law. This phenomenon was first identified by D. Morse and T. Witten: we offer a detailed analysis and transparent derivation of their classic result. For packing fractions well above the jamming transition point, the coupling among contacts mediated by bubble volume conservation has a significant impact on the macroscopic elastic response of foam. This effect is captured by a many-body interaction law, derived from first principles. Applications are explored in two and three dimensions, as are future directions for this kind of theory.

Rheological properties of the soft-disk model of two-dimensional foams.

The soft-disk model previously developed and applied by Durian [D. J. Durian, Phys. Rev. Lett. 75, 4780 (1995)] is brought to bear on problems of foam rheology of longstanding and current interest, using two-dimensional systems. The questions at issue include the origin of the Herschel-Bulkley relation, normal stress effects (dilatancy), and localization in the presence of wall drag. We show that even a model that incorporates only linear viscous effects at the local level gives rise to nonlinear (power-law) dependence of the limit stress on strain rate. With wall drag, shear localization is found. Its nonexponential form and the variation of localization length with boundary velocity are well described by a continuum model in the spirit of Janiaud etal [Phys. Rev. Lett. 97, 038302 (2006)]. Other results satisfactorily link localization to model parameters, and hence tie together continuum and local descriptions.

Graphene-coated polymer foams as tuneable impact sensors.

The use of graphene-based nanocomposites as electromechanical sensors has been broadly explored in recent times with a number of papers describing porous, foam-like composites. However, there are no reported foam-based materials that are capable of large dynamic compressive load measurements and very few studies on composite impact sensing. In this work, we describe a simple method of infusing commercially-available foams with pristine graphene to form conductive composites, which we refer to as G-foam. Displaying a strain-dependent electrical response, G-foam was found to be a reasonably effective pressure sensing material. More interestingly, G-foam is a sensitive impact-sensing material. Through the addition of various amounts of polymer filler, the mechanical properties of the composites can be tuned leading to the controllable variation of the impact sensing range. We have developed a simple model which quantitatively explains all our impact sensing data.

Optimizing transport in a homogeneous network.

Many situations in physics, biology, and engineering consist of the transport of some physical quantity through a network of narrow channels. The ability of a network to transport such a quantity in every direction can be described by the average conductivity associated with it. When the flow through each channel is conserved and derives from a potential function, we show that there exists an upper bound of the average conductivity and explicitly give the expression for this upper bound as a function of the channel permeability and channel length distributions. Moreover, we express the necessary and sufficient conditions on the network structure to maximize the average conductivity. These conditions are found to be independent of the connectivity of the vertices.

The continuum theory of shear localization in two-dimensional foam.

We review some recent advances in the rheology of two-dimensional liquid foams, which should have implications for three-dimensional foams, as well as other mechanical systems that have a yield stress. We focus primarily on shear localization under steady shear, an effect first highlighted in an experiment by Debrégeas et al. A continuum theory which incorporates wall drag has reproduced the effect. Its further refinements are successful in matching results of more extensive observations and making interesting predictions regarding experiments for low strain rates and non-steady shear. Despite these successes, puzzles remain, particularly in relation to quasistatic simulations. The continuum model is semi-empirical: the meaning of its parameters may be sought in comparison with more detailed simulations and other experiments. The question of the origin of the Herschel-Bulkley relation is particularly interesting.