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Register a new userPlastic flow of foams and emulsions in a channel
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Added by
Mauro Sbragaglia Dr
Publication date
2014
fields
Physics
and research's language is
English
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In order to understand the flow profiles of complex fluids, a crucial issue concerns the emergence of spatial correlations among plastic rearrangements exhibiting cooperativity flow behaviour at the macroscopic level. In this paper, the rate of plastic events in a Poiseuille flow is experimentally measured on a confined foam in a Hele-Shaw geometry. The correlation with independently measured velocity profiles is quantified. To go beyond a limitation of the experiments, namely the presence of wall friction which complicates the relation between shear stress and shear rate, we compare the experiments with simulations of emulsion droplets based on the lattice-Boltzmann method, which are performed both with, and without, wall friction. Our results indicate a correlation between the localisation length of the velocity profiles and the localisation length of the number of plastic events. Finally, unprecedented results on the distribution of the orientation of plastic events show that there is a non-trivial correlation with the underlying local shear strain. These features, not previously reported for a confined foam, lend further support to the idea that cooperativity mechanisms, originally invoked for concentrated emulsions (Goyon et al. 2008), have parallels in the behaviour of other soft-glassy materials.
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The physics of foams and emulsions has traditionally been studied using bulk foam/emulsion tests and single film platforms such as the Scheludko cell. Recently there has been a renewed interest in a third class of techniques that we term as single bubble/drop tests, which employ isolated whole bubbles and drops to probe the characteristics of foams and emulsions. Single bubble and drop techniques provide a convenient framework for investigating a number of important characteristics of foams and emulsions, including the rheology, stabilization mechanisms, and rupture dynamics. In this review we provide a comprehensive discussion of the various single bubble/drop platforms and the associated experimental measurement protocols including the construction of coalescence time distributions, visualization of the thin film profiles and characterization of the interfacial rheological properties. Subsequently, we summarize the recent developments in foam and emulsion science with a focus on the results obtained through single bubble/drop techniques. We conclude the review by presenting important venues for future research.
A variety of complex fluids consist in soft, round objects (foams, emulsions, assemblies of copolymer micelles or of multilamellar vesicles -- also known as onions). Their dense packing induces a slight deviation from their prefered circular or spherical shape. As a frustrated assembly of interacting bodies, such a material evolves from one conformation to another through a succession of discrete, topological events driven by finite external forces. As a result, the material exhibits a finite yield threshold. The individual objects usually evolve spontaneously (colloidal diffusion, object coalescence, molecular diffusion), and the material properties under low or vanishing stress may alter with time, a phenomenon known as aging. We neglect such effects to address the simpler behaviour of (uncommon) immortal fluids: we construct a minimal, fully tensorial, rheological model, equivalent to the (scalar) Bingham model. Importantly, the model consistently describes the ability of such soft materials to deform substantially in the elastic regime (be it compressible or not) before they undergo (incompressible) plastic creep -- or viscous flow under even higher stresses.
We study flow driven through a finite-length planar rigid channel by a fixed upstream flux, where a segment of one wall is replaced by a pre-stressed elastic beam subject to uniform external pressure. The steady and unsteady systems are solved using a finite element method. Previous studies have shown that the system can exhibit three steady states for some parameters (termed the upper, intermediate and lower steady branches, respectively). Of these, the intermediate branch is always unstable while the upper and lower steady branches can (independently) become unstable to self-excited oscillations. We show that for some parameter combinations the system is unstable to both upper and lower branch oscillations simultaneously. However, we show that these two instabilities eventually merge together for large enough Reynolds numbers, exhibiting a nonlinear limit cycle which retains characteristics of both the upper and lower branches of oscillations. Furthermore, we show that increasing the beam pre-tension suppresses the region of multiple steady states but preserves the onset of oscillations. Conversely, increasing the beam thickness (a proxy for increasing bending stiffness) suppresses both multiple steady states and the onset of oscillations.
The transitional regime of plane channel flow is investigated {above} the transitional point below which turbulence is not sustained, using direct numerical simulation in large domains. Statistics of laminar-turbulent spatio-temporal intermittency are reported. The geometry of the pattern is first characterized, including statistics for the angles of the laminar-turbulent stripes observed in this regime, with a comparison to experiments. High-order statistics of the local and instantaneous bulk velocity, wall shear stress and turbulent kinetic energy are then provided. The distributions of the two former quantities have non-trivial shapes, characterized by a large kurtosis and/or skewness. Interestingly, we observe a strong linear correlation between their kurtosis and their skewness squared, which is usually reported at much higher Reynolds number in the fully turbulent regime.
In the absence of coalescence, coarsening of emulsions (and foams) is controlled by molecular diffusion of dispersed phase between droplets/bubbles. Studies of dilute emulsions have shown how the osmotic pressure of a trapped species within droplets can ``osmotically stabilise the emulsion. Webster and Cates (Langmuir, 1998, 14, 2068-2079) gave rigorous criteria for osmotic stabilisation of mono- and polydisperse emulsions, in the dilute regime. We consider here whether analogous criteria exist for the osmotic stabilisation of mono- and polydisperse concentrated emulsions and foams, and suggest that the pressure differences driving coarsening are small compared to the mean Laplace pressure. An exact calculation confirms this for a monodisperse 2D model, finding a bubbles pressure as P_i = P + Pi + P_i^G, with P, Pi the atmospheric and osmotic pressures, and P_i^G a ``geometric pressure that reduces to the Laplace pressure only for a spherical bubble. For Princens 2D emulsion model, P_i^G is only 5% larger in the dry limit than the dilute limit. We conclude that osmotic stabilisation of dense systems typically requires a pressure of trapped molecules in each droplet that is comparable to the Laplace pressures the same droplets would have if spherical, as opposed to the much larger Laplace pressures present in the system. We study coarsening of foams and concentrated emulsions when there is insufficient of the trapped species present. Rate-limiting mechanisms are considered, their applicability and associated droplet growth rates discussed. In a concentrated foam or emulsion, a finite yield threshold for droplet rearrangement may be enough to prevent coarsening of the remainder.
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