Reinhard Höhler

Rheology of liquid foam

Liquid foams can behave like solids or liquids, depending on the applied stress and on the experimental timescale. Understanding the origin of this complex rheology which gives rise to many applications and which resembles that of many other forms of soft condensed matter made of closely packed soft units requires challenging theoretical questions to be solved. We briefly recall the basic physics and physicochemistry of foams and review the experiments, numerical simulations and theoretical models concerning foam rheology published in recent years.

A high rate flow-focusing foam generator

We use a rigid axisymmetric microfluidic flow-focusing device to produce monodisperse bubbles, dispersed in a surfactant solution. The gas volume fraction of the dispersion collected out of this device can be as large as 90%, demonstrating that foam with solid-like viscoelastic properties can be produced in this way. The polydispersity of the bubbles is so low that we observe crystallization of our foam. We measure the diameter of the bubbles and compare these data to recent theoretical predictions. The good control over bubble size and foam gas volume fraction shows that our device is a flexible and promising tool to produce calibrated foam at a high flow rate.

Liquid dispersions under gravity: volume fraction profile and osmotic pressure

Many physical properties of concentrated dispersions of immiscible fluids are captured by the concept of an osmotic pressure, which measures how much energy is required to deform the bubbles or drops upon compaction. This pressure has a strong impact on the flow and drainage behavior of dispersions. Nevertheless, theoretical models describing its variation with the volume fraction ϕ of the continuous phase are so far available only in the limits of low or high ϕ and experimental data are scarce. We report an experimental study of osmotic pressure in foams and emulsions, showing how the effects of ϕ, disorder, grain size, polydispersity and interfacial tension can all be captured by a single law which satisfies previously established theoretical constraints. Building on this result, we propose the first equation which accurately describes the variation of the volume fraction with the height of a fluid dispersion under gravity.

Topological transition dynamics in a strained bubble cluster

We study experimentally the dynamics of strain-induced T1 neighbour switching in clusters of 3D bubbles. To determine the physico-chemical processes that set the time scale of such rearrangements, foaming solutions of a wide range of well characterized bulk and interfacial rheological properties are used. At low strain rates, the time scale is set by a balance between surface tension and surface viscous forces, and we present a simple physical model that explains these findings, on the basis of previous experimental and theoretical work with 2D foams.1 At higher strain rates, rearrangement dynamics are driven by the applied strain. In a wider context, our study of T1s in bubble clusters provides insight into the structural relaxations that accompany the flow of 3D foams.

Shear induced normal stress differences in aqueous foams

A finite simple shear deformation of an elastic solid induces unequal normal stresses. This nonlinear phenomenon, known as the Poynting effect, is governed by a universal relation between shear strain and first normal stresses difference, valid for nondissipative isotropic elastic materials. We provide the first experimental evidence that an analog of the Poynting effect exists in aqueous foams where, besides the elastic stress, there are significant viscous or plastic stresses. These results are interpreted in the framework of a constitutive model, derived from a physical description of foam rheology.

Constitutive equation to describe the nonlinear elastic response of aqueous foams and concentrated emulsions

We present a constitutive equation that describes the nonlinear elastic response of aqueous foams and concentrated emulsions that undergo affine deformations. We derive it from the expression for interfacial energy of strained aqueous foam or concentrated emulsions using the formalism of large deformation continuum mechanics. By linearizing the strain energy potential, we obtain a constitutive equation of Mooney–Rivlin form. The predicted nonlinear elastic response is compared to that in previous models and numerical simulations. Furthermore, we discuss the approximations used, particularly those regarding the nonaffine character of deformation in real foams and concentrated emulsions.

Slow viscoelastic relaxation and aging in aqueous foam

Like emulsions, pastes and many other forms of soft condensed matter, aqueous foams present slow mechanical relaxations when subjected to a stress too small to induce any plastic flow. To identify the physical origin of this viscoelastic behaviour, we have simulated how dry disordered coarsening 2D foams respond to a small applied stress. We show that the mechanism of long time relaxation is driven by coarsening-induced rearrangements of small bubble clusters. These findings are in full agreement with a scaling law previously derived from experimental creep data for 3D foams. Moreover, we find that the temporal statistics of coarsening-induced bubble rearrangements are described by a Poisson process.

The coupling between foam viscoelasticity and interfacial rheology

We study the impact of interfacial rheology on the linear viscoelastic relaxations of disordered 3D foams. Their complex shear modulus G* = G′ + iG′′ is measured as a function of frequency, bubble size, liquid viscosity and surface dilatational modulus. We show that for foams with very rigid interfaces the variations of G* with frequency f between 1 and 100 Hz deviate from the behavior previously predicted as a generic consequence of topological disorder and observed for foams with mobile or moderately rigid interfaces. Our experiments demonstrate that the relaxations slow down as the bubble size or the foaming liquid viscosity increases. We show under which conditions, depending on the interfacial rigidity, the loss factor G′′/G′ can be collapsed on master curves by applying a scale factor to the frequency. The dependence of this scale factor on the bubble size and viscosity constitutes a robust criterion helping to identify the dominant dissipation mechanism.

Foam stability in microgravity

Within the context of the ESA FOAM project, we have studied the stability of aqueous and non-aqueous foams both on Earth and in microgravity. Foams are dispersions of gas into liquid or solid. On Earth, the lifetime of a foam is limited by the free drainage. By drainage, we are referring to the irreversible flow of liquid through the foam (leading to the accumulation of liquid at the foam bottom, and to a global liquid content decreases within the foam). When the liquid films become thinner, they eventually break, and the foam collapses. In microgravity, this process is no more present and foams containing large amounts of liquid can be studied for longer time. While the difference between foaming and not-foaming solutions is clear, the case of slightly-foaming solutions is more complicated. On Earth, such mixtures are observed to produce unstable froth for a couple of seconds. However, these latter solutions may produce foam in microgravity. We have studied both configurations for different solutions composed of common surfactant, proteins, anti-foaming agents or silicon oil. Surprising results have been obtained, emphasizing the role played by gravity on the foam stabilization process.

High-resolution diffusing-wave spectroscopy using optimized heterodyne detection

We show experimentally and theoretically that the use of optimized heterodyne detection in a diffusing-wave spectroscopy experiment leads to the detection of much smaller intensity autocorrelations than with conventional (either homodyne or heterodyne) setups. This enhanced resolution may be useful for the study of longtime dynamics of multiple-scattering disordered systems.