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Register a new userTransition from a simple yield stress fluid to a thixotropic material
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Authors
Alexandre Ragouilliaux
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From MRI rheometry we show that a pure emulsion can be turned from a simple yield stress fluid to a thixotropic material by adding a small fraction of colloidal particles. The two fluids have the same behavior in the liquid regime but the loaded emulsion exhibits a critical shear rate below which no steady flows can be observed. For a stress below the yield stress, the pure emulsion abruptly stops flowing, whereas the viscosity of the loaded emulsion continuously increases in time, which leads to an apparent flow stoppage. This phenomenon can be very well represented by a model assuming a progressive increase of the number of droplet links via colloidal particles.
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Materials such as foams, concentrated emulsions, dense suspensions or colloidal gels, are yield stress fluids. Their steady flow behavior, characterized by standard rheometric techniques, is usually modeled by a Herschel-Bulkley law. The emergence of techniques that allow the measurement of their local flow properties (velocity and volume fraction fields) has led to observe new complex behaviors. It was shown that many of these materials exhibit shear banding in a homogeneous shear stress field, which cannot be accounted for by the standard steady-state constitutive laws of simple yield stress fluids. In some cases, it was also observed that the velocity fields under various conditions cannot be modeled with a single constitutive law and that nonlocal models are needed to describe the flows. Doubt may then be cast on any macroscopic characterization of such systems, and one may wonder if any material behaves in some conditions as a Herschel-Bulkley material. In this paper, we address the question of the existence of a simple yield stress fluid behavior. We first review experimental results from the literature and we point out the main factors (physical properties, experimental procedure) at the origin of flow inhomogeneities and nonlocal effects. It leads us to propose a well-defined procedure to ensure that steady-state bulk properties of the materials are studied. We use this procedure to investigate yield stress fluid flows with MRI techniques. We focus on nonthixotropic dense suspensions of soft particles (foams, concentrated emulsions, Carbopol gels). We show that, as long as they are studied in a wide (as compared to the size of the material mesoscopic elements) gap geometry, these materials behave as simple yield stress fluids: they are homogeneous, they do not exhibit steady-state shear banding, and their steady flow behavior in simple shear can be modeled by a local continuous monotonic constitutive equation which accounts for flows in various conditions and matches the macroscopic response.
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.
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.
We study the solid-to-liquid transition in a two-dimensional fully periodic soft-glassy model with an imposed spatially heterogeneous stress. The model we consider consists of droplets of a dispersed phase jammed together in a continuous phase. When the peak value of the stress gets close to the yield stress of the material, we find that the whole system intermittently tunnels to a metastable fluidized state, which relaxes back to a metastable solid state by means of an elastic-wave dissipation. This macroscopic scenario is studied through the microscopic displacement field of the droplets, whose time statistics displays a remarkable bimodality. Metastability is rooted in the existence, in a given stress range, of two distinct stable rheological branches as well as long-range correlations (e.g., large dynamic heterogeneity) developed in the system. Finally, we show that a similar behavior holds for a pressure-driven flow, thus suggesting possible experimental tests.
Normal stresses in complex fluids lead to new flow phenomena because they can be comparable to or even larger than the shear stress itself. In addition, they are of paramount importance for formulating and testing constitutive equations for predicting non-viscometric flow behavior. Very little attention has so far been paid to the normal stresses of yield stress fluids, mainly because they are very difficult to measure. We report the first systematic study of the first and second normal stress differences, N1 (>0) and N2 (<0), in both continuous and oscillatory shear of three model yield stress fluids. We show that both normal stress differences are quadratic functions of the shear stress both above and below the shear yield stress, leading to the existence of a yield normal stress.
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