Nonmonotonic Flow Research Articles

Rheology of nanocrystalline cellulose (CNC) gels: Thixotropy, yielding, wall slip, and shear banding

This study focuses on the rheological behavior of a cellulose nanocrystal gel. This system [5 wt. % cellulose nanocrystal (CNC) + 20 mM NaCl] is proved to be thixotropic, and the detected shear force tightly depends on the growth and break-up of the aggregates of CNC rods. From strain-controlled experiments, a nonmonotonic steady-state flow curve with a minimum stress value of ≈33 Pa is found, and the negative slope of stress versus shear rate suggests the existence of shear bands. From stress-controlled experiments (creep), the “static yield stress” is determined to be 67.5 ± 2.5 Pa. This difference proves that the local minimum stress of the flow curve does not coincide with the “static yield stress” determined by creep tests. However, this minimum stress can maintain flow provided that the material is already in a yielded state. At nominal shear rates below about 100 s−1, shearing is suggested to be localized in a shear band rather than over the whole material. The “dynamic yield stress” is found as “the minimum stress to maintain flow,” or the onset of shear banding. Moreover, wall slip also occurs at low nominal shear rates which is related to the interaction between the dynamic microstructure of the CNC gel and the wall: it is hypothesized that the low shear rates allow the CNC aggregates to extensively grow and, thus, the oversized CNC aggregates detach from the asperities of the wall. Our finding of the robust connection between yielding, thixotropy, wall slip, and shear banding shall shed new light on the nature of the nonmonotonic flow curves of yield stress and thixotropic materials.

Nonmonotonic rheology and stress heterogeneity in confined granular suspensions

We systematically investigated the impact of boundary confinement on the shear-thickening rheology of dense granular suspensions. Under highly confined conditions, dense suspensions were found to exhibit size-dependent or even rarely reported nonmonotonic (S-shaped) flow curves in steady states. By performing in situ boundary stress microscopy measurements, we observed enhanced flow heterogeneities in confined suspensions, where concentrated high-stress domains propagated stably either along or against the shear direction. By comparing the boundary stress microscopy results with macroscopic flow responses, we revealed the connection between nonmonotonic rheology and stress heterogeneity in confined suspensions. These findings suggest the possibility of controlling suspension rheology by imposing different boundary confinements.

Non-monotonic flow variations in a stylized (TASEP-based) traffic model featuring cars searching for parking

Non-monotonic flow variations in a stylized (TASEP-based) traffic model featuring cars searching for parking

On pressure-driven Poiseuille flow with non-monotonic rheology.

Shear thickening fluids are liquids that stiffen as the applied stress increases. If many of these types of fluids follow a monotonic rheological curve, some experimental and numerical studies suggest that certain fluids, like cornstarch, may exhibit a non-monotonic, S-shaped rheology. Such non-monotonic behavior has however proved very difficult to observe experimentally in classical rheometer. To explain such difficulties, the possible presence of vorticity banding in the rheometer has been considered. To prevent such instabilities, we use a capillary rheometer, which is a cylindrical tube, measuring the flow rate versus the applied pressure drop. With this setup, we indeed observe a non-monotonic behavior: the flow rate increases monotonically at low pressure drops up to a maximum, after which it abruptly decreases to an almost constant flow rate regardless of further increases in pressure drop. This maximum-jump-plateau behavior occurs over a wide range of concentrations and is reproducible without hysteresis, which is in agreement with an S-shaped rheology. However, the obtained flow versus pressure difference function does not agree with the classical Wyart-Cates rheological model, which predicts an S-shaped non-monotonic function, but with neither a jump nor a plateau. To understand this jump-plateau behavior, we remark that any rheological model would establish a relationship between the flow rate and the local pressure gradient, but not the total pressure drop. We thus discuss and analyze the implications of having an S-shaped non-monotonic flow rate-pressure gradient in Poiseuille flow. In particular, we discuss the possibility of a non-uniform pressure gradient in the direction of the flow, i.e., a kind of streamwise banding. The key issue is then the selection of the gradient pressure distribution along the tube. One solution could arise from an analogy of this problem with the spinodal decomposition. It, however, leads to an increase in flow rate with up to a plateau between two values of as determined by the Maxwell construction. To account for the bump-jump behavior, we have implemented a simple dynamical stochastic version of the Wyart-Cates model, where the thickening occurs with a characteristic time. As a result, with increasing the total pressure drop, the flow rate increases monotonically up to a maximum value. Beyond this point, the flow rate drops abruptly to a lower value, forming a slowly decreasing plateau. This behavior is likely to account for the maximum-jump-plateau observed in the experiments. We also show that in such a system, the final state is quite sensitive to the initial state of the fluid, especially its homogeneity. Our results then demonstrate that the mere presence of a non-monotonic rheological curve is sufficient to predict the occurrence of stress banding in the streamwise direction and a plateau flow rate, even if the suspension remains homogeneous.

Rheo-optics of giant micelles: SALS patterns of cetyltrimethylammonium tosylate solutions in presence of sodium bromide

In this work, we present a systematic study based on Small-Angle Light Scattering (SALS) patterns of the simple shear flow response of semi-diluted solutions of cetyltrimethylammonium tosylate (CTAT; 5.5 wt.% - 0.12 M) in the presence of sodium bromide (NaBr) at different [NaBr]={0,0.12,0.19,0.25,0.3} M concentrations. We evidence a relationship between rheological and light scattering data that reveals a transition into a fast-breaking regime in the dynamics of wormlike micelles formed by the CTAT/NaBr system (Macías et al., 2011; Fierro et al., 2021). This transition into a micellar fast-breaking regime with salt addition ([NaBr]≥0) appears marked by the following features: (i) a decrease in the relaxation time of the material λ0, accompanied by (ii) a decrease of the viscosity level at low shear rates η0 (Macías et al., 2011; Fierro et al., 2021; Schubert et al., 2003; Alkschbirs et al., 2015; Bandyopadhyay et al., 2003). With these, (iii) the formation of butterfly-like patterns is recorded originating from concentration fluctuations, evolution that is accompanied by: (iv) shear banding in the form of non-monotonic flow curves and (v) slow oscillatory transient responses in start-up flow tests captured theoretically with the Bautista–Manero–Puig (BMP) model. In addition, the Cox–Merz rule is fulfilled at molar salt-to-surfactant ratios of R≥1.5. This results in shorter structure-recovery time-scales than the characteristic-time of the flow (Macías et al., 2011; Fierro et al., 2021; Manero et al., 2002). In the case of the elastic modulus G0, the variation was small, which suggests a transition from an entangled to a multiconnected network, as suggested by Kadoma & van Egmond (1997), Kadoma et al. (1997) and Fierro et al. (2021). From a theoretical perspective, we provide predictions for the shear–stress and the first normal-stress growth coefficients in transient start-up simple shear flow using the BMP model. Here, banding R=1.5 solutions display overshot responses at relatively high shear rates (γ̇=10−30s−1), in-line with experimental findings on the start-up flow of wormlike micellar solutions (Soltero et al., 1999; Lerouge et al., 2004; Hu & Lips 2005; Pipe et al., 2010; Mohammadigoushki et al., 2019). Our results are consistent with those reported in other investigations (Macías et al., 2011; Fierro et al., 2021; Schubert et al., 2003; Alkschbirs et al., 2015; Bandyopadhyay et al., 2003; Kadoma et al., 1997; Soltero et al., 1999; Lerouge et al., 2004; Hu & Lips 2005; López-Barrón et al., 2014) and reveal the influence of the Br−-ion used on the mechanical and optical response of the CTAT-NaBr system.

Inner structures of rapid free-surface granular avalanche over a small bump obstacle: Expansion fan, oblique shock wave, and contact anisotropy

This study investigates the inner flow characteristics of a rapid granular avalanche passing over a small bump obstacle fixed on an inclined chute using the discrete element method. Both the cross-sectional mean flow properties, such as free-surface height, mean flow velocity, and mean stresses, and the inner local flow properties, including granular temperature, coordination number, pressure, contact force orientation, and granular fabrics, were comprehensively investigated. Upstream of the obstacle, a wide compression region where mean stresses strengthen and exhibit anisotropy was observed. Employing the kinetic theory of granular gas, we revealed a smooth supersonic-to-subsonic transition near the obstacle, a phenomenon distinct from typical gas dynamics. These upstream flow phenomena are attributed to the generation of stream-wise-oriented contact force chains as the flow impacts the obstacle. Downstream of the obstacle, a complex non-monotonic expansion–compression–expansion process was observed. We demonstrated that this non-monotonic flow process reflects an inner gasdynamic-like phenomenon characterized by an expansion fan followed by an oblique shock wave. Moreover, the force chains and the inner shock structure were found to significantly influence the evolution of stream-wise velocity profiles. These findings underscore the significance of inner flow structures in shaping the dynamics of granular avalanche flow interacting with obstacles.

Quantitative aspects on the ill-posedness of the Prandtl and hyperbolic Prandtl equations

We address the Prandtl equations and a physically meaningful extension known as hyperbolic Prandtl equations. For the extension, we show that the linearised model around a non-monotonic shear flow is ill-posed in any Sobolev spaces. Indeed, shortly in time, we generate solutions that experience a dispersion relation of order k3\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\root 3 \\of {k}$$\\end{document} in the frequencies of the tangential direction, akin the pioneering result of Gérard-Varet, D., Dormy, E.: On the ill-posedness of the Prandtl equation. J. Am. Math. Soc., 23(2), 591–609 (2010) for Prandtl (where the dispersion was of order k\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\sqrt{k}$$\\end{document}). We emphasise, however, that this growth rate does not imply (a-priori) ill-posedness in Gevrey-class m, with m>3\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$m>3$$\\end{document}. We relate these aspects to the original Prandtl equations in Gevrey-class m, with m>2\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$m>2$$\\end{document}: We show that the result in Gérard-Varet, D., Dormy, E.: On the ill-posedness of the Prandtl equation. J. Am. Math. Soc., 23(2), 591–609 (2010) determines a dispersion relation of order k\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\sqrt{k}$$\\end{document} for a short time proportional to ln(k)/k\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\ln (\\sqrt{k})/\\sqrt{k}$$\\end{document}. Therefore, the ill-posedness in Gérard-Varet, D., Dormy, E.: On the ill-posedness of the Prandtl equation. J. Am. Math. Soc., 23(2), 591–609 (2010) in its generality is momentarily constrained to Sobolev spaces rather than extending to the Gevrey classes.

The Strong Integral Input-to-State Stability Property in Dynamical Flow Networks

Dynamical flow networks serve as macroscopic models for, e.g., transportation networks, queuing networks, and distribution networks. While the flow dynamics in such networks follow the conservation of mass on the links, the outflow from each link is often non-linear due to, e.g., flow capacity constraints and simultaneous service rate constraints. Such non-linear constraints imply a limit on the magnitude of exogenous inflow that is able to be accommodated by the network before it becomes overloaded and its state trajectory diverges. This paper shows how the Strong integral Input-to-State Stability (Strong iISS) property allows for quantifying the effects of the exogenous inflow on the flow dynamics. The Strong iISS property enables a unified stability analysis of classes of dynamical flow networks that were only partly analyzable before, such as networks with cycles, multi-commodity flow networks and networks with non-monotone flow dynamics. We present sufficient conditions on the maximum magnitude of exogenous inflow to guarantee input-to-state stability for a dynamical flow network, and we also present cases when this sufficient condition is necessary. The conditions are exemplified on a few existing dynamical flow network models, specifically, fluid queuing models with time-varying exogenous inflows and multi-commodity flow models.

Interplay between wall slip and shear banding in a thixotropic yield stress fluid.

We study the local dynamics of a thixotropic yield stress fluid that shows a pronounced non-monotonic flow curve. This mechanically unstable behavior is generally not observable from standard rheometry tests, resulting in a stress plateau that stems from the coexistence of a flowing band with an unyielded region below a critical shear rate c. Combining ultrasound velocimetry with standard rheometry, we discover an original shear-banding scenario in the decreasing branch of the flow curve of model paraffin gels, in which the velocity profile of the flowing band is set by the applied shear rate  instead of c. As a consequence, the material slips at the walls with a velocity that shows a non-trivial dependence on the applied shear rate. To capture our observations, we propose a differential version of the so-called lever rule, describing the extent of the flowing band and the evolution of wall slip with shear rate. This phenomenological model holds down to very low shear rates, at which the dimension of the flowing band becomes comparable to the size of the individual wax particles that constitute the gel microstructure, leading to cooperative effects. Our approach provides a framework where constraints imposed in the classical shear-banding scenario can be relaxed, with wall slip acting as an additional degree of freedom.

Shear-induced flow and dynamics of the nematic phase of Sunset Yellow lyotropic chromonic liquid crystal

ABSTRACT Fundamental understanding of rheological properties of lyotropic chromonic liquid crystals is inadequate compared to their thermotropic counterparts in spite of the growing interest in these materials. Here, we investigate the rheological properties of a lyotropic chromonic nematic liquid crystal (LCLC), prepared by dissolving 32 wt% of Sunset Yellow (SSY) in water. The flow curves (stress-strain rate, σ − γ ˙ ) at different temperatures exhibit three flow regimes R1, R2 and R3, respectively. At room temperature, in R1 ( γ ˙ < γ ˙ cl ) and R3 ( γ ˙ > γ ˙ cu ) the sample exhibits Newtonian flow behaviour ( σ ∝ γ ˙ ), whereas, in R2 ( γ ˙ cl < γ ˙ < γ ˙ cu ), it shows a power-law dependence ( σ ∼ γ ˙ β ). With increasing shear rate the change of stress from R1 to R2 is continuous, whereas the change is discontinuous from R2 to R3. We observe stress fluctuations under steady shear in regime R2 similar to those reported in worm-like micellar systems and in thermotropic twist-bend nematic liquid crystals. The non-monotonic flow behaviour and the stress dynamics are corroborated using in situ rheo-microscopy.

Study of turbulent transport in magnetized plasmas with flow using symplectic maps

Turbulent transport in a magnetized plasma of the kind found in tokamaks is modeled by a 2D wave spectrum that allows reduction to a symplectic map. The properties of particle transport when chaos sets in are analyzed in various circumstances including finite Larmor radius (FLR) effects and a background plasma flow. For large wave amplitudes, regular particle orbits become chaotic, which represents a type of Lagrangian turbulence. When chaos becomes global, it leads to the loss of particle confinement. Poloidal flows tend to decrease the chaos in some regions, and they can give rise to the formation of transport barriers. FLR effects not only reduce chaos but also give rise to non-local behavior. Thus, when the particles have a thermal distribution of Larmor radii, a non-Gaussian particle distribution function in space is obtained. However, the transport preserves its diffusive scaling when there is no flow. Previous results about the dependence of the diffusion coefficient with amplitude are re-derived analytically and numerically taking into account FLR effects. In the presence of general poloidal flows, the transport has to be described by a two-step map. They modify the nature of transport in the direction of the flow from diffusive to ballistic to super-ballistic, depending on the type of flow. The transverse transport, in turn, shows suppression of the oscillations with wave amplitude that are present in the absence of flow. When the plasma flow varies linearly with radius, the transport can be studied with a similar single-step map, and the transverse diffusion coefficient is reduced while parallel transport can become super-ballistic. For non-monotonic flows, there are accelerating modes that can produce ballistic-like particles while the bulk of the particles behaves diffusively.

Universal non-monotonic drainage in large bare viscous bubbles

Bubbles will rest at the surface of a liquid bath until their spherical cap drains sufficiently to spontaneously rupture. For large film caps, the memory of initial conditions is believed to be erased due to a visco-gravitational flow, whose velocity increases from the top of the bubble to its base. Consequently, the film thickness has been calculated to be relatively uniform as it thins, regardless of whether the drainage is regulated by shear or elongation. Here, we demonstrate that for large bare bubbles, the film thickness is highly nonuniform throughout drainage, spanning orders of magnitude from top to base. We link the film thickness profile to a universal non-monotonic drainage flow that depends on the bubble thinning rate. These results highlight an unexpected coupling between drainage velocity and bubble thickness profiles and provide critical insight needed to understand the retraction and breakup dynamics of these bubbles upon rupture.

On the nature of flow curve and categorization of thixotropic yield stress materials

Thixotropy is a phenomenon related to time dependent change in viscosity in the presence or absence of flow. The yield stress, on the other hand, represents the minimum value of stress above which steady flow can be sustained. In addition, the yield stress of a material may also change as a function of time. Both these characteristic features in a material strongly influence the steady state flow curve of the same. This study aims to understand the interrelation between thixotropy, yield stress, and their relation with the flow curve. In this regard, we study five thixotropic materials that show yield stress. The relaxation time of all the five systems shows power-law dependence on aging time with behaviors ranging from weaker than linear, linear to stronger than linear. Furthermore, the elastic modulus and yield stress have been observed to be constant for some systems while time dependent for the others. We also analyze the experimental behavior through a viscoelastic thixotropic structural kinetic model that predicts the observed experimental behavior of constant as well as time-dependent yield stress quite well. These findings indicate that a nonmonotonic steady-state flow curve in a structural kinetic formalism necessarily leads to time-dependent yield stress, while constant yield stress is predicted by a monotonic steady-state flow curve with stress plateau in the limit of low shear rates. The present work, therefore, shows that thixotropic materials may exhibit either monotonic or nonmonotonic flow curves. Consequently, thixotropic materials may show no yield stress, constant yield stress, or time-dependent yield stress.

Criteria for integro-differential modeling of plane-parallel flow of viscous incompressible fluid

For a liquid with a nonmonotonic flow curve in the stationary case in the region of the descending branch, setting the velocity at the boundary does not uniquely determine the shear stress, strain rate distribution, and velocity profile that arise since the problem is known to have many unstable solutions. At the same time, the problem of the motion of such fluid under the action of a given pressure difference has no more than three solutions, two of which are stable, and the third is unstable and not reproducible. Which of the two stable solutions is realized depends on the loading history. The problem of determining the velocity profile for a fluid characterized by a nonmonotonic rheological flow curve between parallel planes is considered. The existence of a solution is realized by reducing the problem posed to a singular integral equation of normal type, which is known by the Carleman – Vekua regularization method developed by S.G. Mikhlin and M.M. Smirnov equivalently reduces to the Fredholm integral equation of the second kind, and the solvability of the latter follows from the uniqueness of the solution delivered problem describing of criteria for integro–differential modeling of a plane-parallel flow of a viscous incompressible fluid.

Numerical Simulation of Rheological Models for Complex Fluids Using Hierarchical Grids.

In this work, we implement models that are able to describe complex rheological behaviour (such as shear-banding and elastoviscoplasticity) in the HiGTree/HiGFlow system, which is a recently developed Computational Fluid Dynamics (CFD) software that can simulate Newtonian, Generalised-Newtonian and viscoelastic flows using finite differences in hierarchical grids. The system uses a moving least squares (MLS) meshless interpolation technique, allowing for more complex mesh configurations while still keeping the overall order of accuracy. The selected models are the Vasquez-Cook-McKinley (VCM) model for shear-banding micellar solutions and the Saramito model for viscoelastic fluids with yield stress. Development of solvers and numerical simulations of inertial flows of these models in 2D channels and planar-contraction 4:1 are carried out in the HiGTree/HiGFlow system. Our results are compared with those predicted by two other methodologies: the OpenFOAM-based software RheoTool that uses the Finite-Volume-Method and an in-house code that uses the Vorticity-Velocity-Formulation (VVF). We found an excellent agreement between the numerical results obtained by these three different methods. A mesh convergence analysis using uniform and refined meshes is also carried out, where we show that great convergence results in tree-based grids are obtained thanks to the finite difference method and the meshless interpolation scheme used by the HiGFlow software. More importantly, we show that our methodology implemented in the HiGTreee/HiGFlow system can successfully reproduce rheological behaviour of high interest by the rheology community, such as non-monotonic flow curves of micellar solutions and plug-flow velocity profiles of yield-stress viscoelastic fluids.

Evaluation of constitutive models for shear-banding wormlike micellar solutions in simple and complex flows

Wormlike micellar solutions possess complex rheology: when exposed to a flow field, the wormlike micelles may orientate, stretch, and break into smaller micelles. Entangled wormlike micellar solutions exhibit shear banding characteristics: macroscopic bands with different local viscosities are organized and stacked along the velocity gradient direction, leading to a non-monotonic flow curve in simple shear. We present a systematic analysis of four commonly used constitutive models that can predict a non-monotonic flow curve and potentially describe the rheology of entangled wormlike micellar solutions with shear-banding characteristics: the Johnson–Segalman, the Giesekus, the thixotropic viscoelastic, and the Vasquez–Cook–McKinley (VCM) models. All four constitutive models contain a stress diffusion term, to account for a smooth transition between the shear bands and ensure a uniqueness of the numerical solution. Initially, the models are fitted to shear and extensional experimental data of a shear-banding wormlike micellar solution. Subsequently, they are employed to solve three non-homogeneous flows: the Poiseuille flow in a planar channel, the flow in a cross-slot geometry, and the flow past a cylinder in a straight channel. Each of these flows exposes the wormlike micellar solution to different flow kinematics (shear, extensional, and mixed), revealing different aspects of its rheological response. The predictive capability of each model is evaluated by directly comparing the numerical results to previously published experimental data obtained from microfluidic devices with corresponding flow configurations. While all the models can describe qualitatively the characteristic features observed experimentally in the benchmark flows, such as plug-like velocity profiles and elastic instabilities, none of them yields a quantitative agreement. Based on the overall performance of the models and also accounting for their differing numerical complexity, we conclude that the Giesekus model is at present the most suitable constitutive equation for simulating shear banding wormlike micellar solutions in flows that exhibit both shear and extensional deformations. However, the quantitative mismatch between model predictions and experiments with wormlike micellar solutions demand that improved constitutive models be developed in future works. • Comparison of popular constitutive models for wormlike micellar solutions. • Evaluation of their performance in rheometric and inhomogeneous shear flows. • Investigation of their predictions in extensional flows and elastic instabilities. • The models can only make qualitative predictions.

A Family of Non-Monotonic Toral Mixing Maps

We establish the mixing property for a family of Lebesgue measure preserving toral maps composed of two piecewise linear shears, the first of which is non-monotonic. The maps serve as a basic model for the ‘stretching and folding’ action in laminar fluid mixing, in particular flows where boundary conditions give rise to non-monotonic flow profiles. The family can be viewed as the parameter space between two well-known systems, Arnold’s Cat Map and a map due to Cerbelli and Giona, both of which possess finite Markov partitions and straightforward to prove mixing properties. However, no such finite Markov partitions appear to exist for the present family, so establishing mixing properties requires a different approach. In particular, we follow a scheme of Katok and Strelcyn, proving strong mixing properties with respect to the Lebesgue measure on two open parameter spaces. Finally, we comment on the challenges in extending these mixing windows and the potential for using the same approach to prove mixing properties in similar systems.

Exponential mixing by orthogonal non-monotonic shears

Non-monotonic velocity profiles are an inherent feature of mixing flows obeying non-slip boundary conditions. There are, however, few known models of laminar mixing which incorporate this feature and have proven mixing properties. Here we present such a model, alternating between two non-monotonic shear flows which act in orthogonal (i.e. perpendicular) directions. Each shear is defined by an independent variable, giving a two-dimensional parameter space within which we prove the mixing property over open subsets. Within these mixing windows, we use results from the billiards literature to establish exponential mixing rates. Outside of these windows, we find large parameter regions where elliptic islands persist, leading to poor mixing. Finally, we comment on the challenges of extending these mixing windows and the potential for a non-exponential mixing rate at particular parameter values.

Humidity induced interparticle friction and its mitigation in fine powder flow

Humidity can affect the bulk behavior of fine hygroscopic powders at multiple levels and fewer mitigation approaches are presently available to counter its adverse effects. This work reports these approaches while investigating humidity influenced frictional behavior in fine cohesive starch powder flow under confined conditions. Interparticle friction and wall friction were examined under varying relative humidity (RH) using shear and wall friction tests in the quasi-static regime. The measured stress details from the bulk powder testing in the powder rheometer revealed increased stick-slip friction in the form of unsteady stresses at lower RH which gradually decreased with increase in RH. The surface texturing of particles and modifying contact stiffness through the dry coating alleviated the nonmonotonic powder flow at all the RH conditions. The stress oscillations and the consequent increase in measured friction were attributed to the discretely distributed surface moisture causing alternate sticking and slipping of the contacts. The lubricating effect of moisture at higher RH and the surface modification facilitated steady sliding, also accompanied by reduced coefficient of friction and wall friction angle. Furthermore, the different fluid film lubrication regimes were identified and highlighted the importance of fluid-particle interactions leading to undesirable bulk behavior in fine powders.

Rheology of Cohesive Granular Media: Shear Banding, Hysteresis, and Nonlocal Effects

Powders or cohesive granular materials are widely handled in industries. However, our understanding of the rheology of these materials is limited. Here, we provide a comprehensive analysis of the rheology of a cohesive granular medium, sheared in a normal-stress-imposed plane shear cell over a wide range of shear rate, employing numerical simulations. At high imposed shear rates, the flow is homogeneous, and the rheology is well described by the existing scaling laws, involving the inertial number and the effective cohesion number [S. Mandalet al., Insights into the Rheology of Cohesive Granular Media, Proc. Natl. Acad. Sci. U.S.A. 117, 8366 (2020)]. However, at low imposed shear rates, the flow is inhomogeneous, exhibiting the coexistence of flowing and nonflowing regions in the material, popularly known as shear banding. We thoroughly analyze the crucial features of this shear-banded flow regime and discuss striking similarities between the shear banding for granular media and other complex fluids. We reveal that the occurrence of shear banding is related to the existence of a nonmonotonic intrinsic rheological curve and that increasing adhesion increases the nonmonotonicity and the tendency toward shear localization. A simple theoretical model based on a nonlocal rheological model coupled with a nonmonotonic flow curve is proposed and is shown to successfully reproduce all the key features of the shear banding observed in the numerical simulations. The results have important implications for the handling of powders in industries.