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Register a new userMixtures of foam and paste: suspensions of bubbles in yield stress fluids
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We study the rheological behavior of mixtures of foams and pastes, which can be described as suspensions of bubbles in yield stress fluids. Model systems are designed by mixing monodisperse aqueous foams and concentrated emulsions. The elastic modulus of the suspensions decreases with the bubble volume fraction. This decrease is all the sharper as the elastic capillary number (defined as the ratio of the paste elastic modulus to the bubble capillary pressure) is high, which accounts for the softening of the bubbles as compared to the paste. By contrast, the yield stress of most studied materials is not modified by the presence of bubbles. Their plastic behavior is governed by the plastic capillary number, defined as the ratio of the paste yield stress to the bubble capillary pressure. At low plastic capillary number values, bubbles behave as nondeformable inclusions, and we predict that the suspension dimensionless yield stress should remain close to unity. At large plastic capillary number values, we observe bubble breakup during mixing: bubbles are deformed by shear. Finally, at the highest bubble volume fractions, the yield stress increases abruptly: this is interpreted as a foamy yield stress fluid regime, which takes place when the paste mesoscopic constitutive elements are strongly confined in the films between the bubbles.
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Soft glassy materials such as mayonnaise, wet clays, or dense microgels display under external shear a solid-to-liquid transition. Such a shear-induced transition is often associated with a non-monotonic stress response, in the form of a stress maximum referred to as stress overshoot. This ubiquitous phenomenon is characterized by the coordinates of the maximum in terms of stress $sigma_text{M}$ and strain $gamma_text{M}$ that both increase as weak power laws of the applied shear rate. Here we rationalize such power-law scalings using a continuum model that predicts two different regimes in the limit of low and high applied shear rates. The corresponding exponents are directly linked to the steady-state rheology and are both associated with the nucleation and growth dynamics of a fluidized region. Our work offers a consistent framework for predicting the transient response of soft glassy materials upon start-up of shear from the local flow behavior to the global rheological observables.
We show that besides simple or thixotropic yield stress fluids there exists a third class of yield stress fluids. This is illustrated through the rheological behavior of a carbon black suspension, which is shown to exhibit a viscosity bifurcation effect around a critical stress along with rheopectic trends, i.e., after a preshear at a given stress the fluid tends to accelerate when it is submitted to a lower stress. Viscosity bifurcation displays here original features: the yield stress and the critical shear rate depend on the previous flow history. The most spectacular property due to these specificities is that the material structure can be adjusted at will through an appropriate flow history. In particular it is possible to tune the material yield stress to arbitrary low values. A simple model assuming that the stress is the sum of one component due to structure deformation and one component due to hydrodynamic interactions predicts all rheological trends observed and appears to well represent quantitatively the data.
Stability of coarse particles against gravity is an important issue in dense suspensions (fresh concrete, foodstuff, etc.). On the one hand, it is known that they are stable at rest when the interstitial paste has a high enough yield stress; on the other hand, it is not yet possible to predict if a given material will remain homogeneous during a flow. Using MRI techniques, we study the time evolution of the particle volume fraction during the flows in a Couette geometry of model density-mismatched suspensions of noncolloidal particles in yield stress fluids. We observe that shear induces sedimentation of the particles in all systems, which are stable at rest. The sedimentation velocity is observed to increase with increasing shear rate and particle diameter, and to decrease with increasing yield stress of the interstitial fluid. At low shear rate (plastic regime), we show that this phenomenon can be modelled by considering that the interstitial fluid behaves like a viscous fluid -- of viscosity equal to the apparent viscosity of the sheared fluid -- in the direction orthogonal to shear. The behavior at higher shear rates, when viscous effects start to be important, is also discussed. We finally study the dependence of the sedimentation velocity on the particle volume fraction, and show that its modelling requires estimating the local shear rate in the interstitial fluid.
Various experiments evidence spatial heterogeneities in sheared yield stress fluids. To account for heterogeneities in the velocity gradient direction, we use a simple model corresponding to a non-monotonous local constitutive curve and study a simple shear geometry. Different types of boundary conditions are considered. Under controlled macroscopic shear stress $Sigma$, we find homogeneous flow in the bulk and a hysteretic macroscopic stress - shear rate curve. Under controlled macroscopic shear rate $dot{Gamma}$, shear banding is predicted within a range of values of $dot{Gamma}$. For small shear rates, stick slip can also be observed. These qualitative behaviours are robust when changing the boundary conditions.
To enable robust rheological measurements of the properties of yield stress fluids, we introduce a class of modified vane fixtures with fractal-like cross-sectional structures. A greater number of outer contact edges leads to increased kinematic homogeneity at the point of yielding and beyond. The vanes are 3D printed using a desktop stereolithography machine, making them inexpensive (disposable), chemically-compatible with a wide range of solvents, and readily adaptable as a base for further design innovations. To complete the tooling set, we introduce a textured 3D printed cup, which attaches to a standard rheometer base. We discuss general design criteria for 3D printed rheometer vanes, including consideration of sample volume displaced by the vanes, stress homogeneity, and secondary flows that constrain the parameter space of potential designs. We also develop a conversion from machine torque to material shear stress for vanes with an arbitrary number of arms. We compare a family of vane designs by measuring the viscosity of Newtonian calibration oils with error <5% relative to reference measurements made with a cone-and-plate geometry. We measure the flow curve of a simple Carbopol yield stress fluid, and show that a 24-arm 3D printed fractal vane agrees within 1% of reference measurements made with a roughened cone-and-plate geometry. Last, we demonstrate use of the 24-arm fractal vane to probe the thixo-elasto-visco-plastic (TEVP) response of a Carbopol-based hair gel, a jammed emulsion (mayonnaise), and a strongly alkaline carbon black-based battery slurry.
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