Criterion for purely elastic Taylor-Couette instability in the flows of shear-banding fluids

In the past twenty years, shear-banding flows have been probed by various techniques, such as rheometry, velocimetry and flow birefringence. In micellar solutions, many of the data collected exhibit unexplained spatio-temporal fluctuations. Recently, it has been suggested that those fluctuations originate from a purely elastic instability of the flow. In cylindrical Couette geometry, the instability is reminiscent of the Taylor-like instability observed in viscoelastic polymer solutions. In this letter, we describe how the criterion for purely elastic Taylor-Couette instability should be adapted to shear-banding flows. We derive three categories of shear-banding flows with curved streamlines, depending on their stability.Comment: 6 pages, 3 figure

Potential "ways of thinking" about the shear-banding phenomenon

Shear-banding is a curious but ubiquitous phenomenon occurring in soft matter. The phenomenological similarities between the shear-banding transition and phase transitions has pushed some researchers to adopt a 'thermodynamical' approach, in opposition to the more classical 'mechanical' approach to fluid flows. In this heuristic review, we describe why the apparent dichotomy between those approaches has slowly faded away over the years. To support our discussion, we give an overview of different interpretations of a single equation, the diffusive Johnson-Segalman (dJS) equation, in the context of shear-banding. We restrict ourselves to dJS, but we show that the equation can be written in various equivalent forms usually associated with opposite approaches. We first review briefly the origin of the dJS model and its initial rheological interpretation in the context of shear-banding. Then we describe the analogy between dJS and reaction-diffusion equations. In the case of anisotropic diffusion, we show how the dJS governing equations for steady shear flow are analogous to the equations of the dynamics of a particle in a quartic potential. Going beyond the existing literature, we then draw on the Lagrangian formalism to describe how the boundary conditions can have a key impact on the banding state. Finally, we reinterpret the dJS equation again and we show that a rigorous effective free energy can be constructed, in the spirit of early thermodynamic interpretations or in terms of more recent approaches exploiting the language of irreversible thermodynamics.Comment: 14 pages, 6 figures, tutorial revie

Elastic turbulence in shear banding wormlike micelles

We study the dynamics of the Taylor-Couette flow of shear banding wormlike micelles. We focus on the high shear rate branch of the flow curve and show that for sufficiently high Weissenberg numbers, this branch becomes unstable. This instability is strongly sub-critical and is associated with a shear stress jump. We find that this increase of the flow resistance is related to the nucleation of turbulence. The flow pattern shows similarities with the elastic turbulence, so far only observed for polymer solutions. The unstable character of this branch led us to propose a scenario that could account for the recent observations of Taylor-like vortices during the shear banding flow of wormlike micelles

Optimized cross-slot flow geometry for microfluidic extension rheometry

A precision-machined cross-slot flow geometry with a shape that has been optimized by numerical simulation of the fluid kinematics is fabricated and used to measure the extensional viscosity of a dilute polymer solution. Full-field birefringence microscopy is used to monitor the evolution and growth of macromolecular anisotropy along the stagnation point streamline, and we observe the formation of a strong and uniform birefringent strand when the dimensionless flow strength exceeds a critical Weissenberg number Wicrit 0:5. Birefringence and bulk pressure drop measurements provide self consistent estimates of the planar extensional viscosity of the fluid over a wide range of deformation rates (26 s1 "_ 435 s1) and are also in close agreement with numerical simulations performed by using a finitely extensible nonlinear elastic dumbbell model

Fingerprinting Soft Materials: A Framework for Characterizing Nonlinear Viscoelasticity

We introduce a comprehensive scheme to physically quantify both viscous and elastic rheological nonlinearities simultaneously, using an imposed large amplitude oscillatory shear (LAOS) strain. The new framework naturally lends a physical interpretation to commonly reported Fourier coefficients of the nonlinear stress response. Additionally, we address the ambiguities inherent in the standard definitions of viscoelastic moduli when extended into the nonlinear regime, and define new measures which reveal behavior that is obscured by conventional techniques.Comment: 10 pages, 3 figures, full-page double-space preprint forma

Bubble kinematics in a sheared foam

We characterize the kinematics of bubbles in a sheared two-dimensional foam using statistical measures. We consider the distributions of both bubble velocities and displacements. The results are discussed in the context of the expected behavior for a thermal system and simulations of the bubble model. There is general agreement between the experiments and the simulation, but notable differences in the velocity distributions point to interesting elements of the sheared foam not captured by prevalent models

Exploratory project 2019 - deep learning for particle-laden viscoelastic flow modelling

[extract] Objetives: explore the possibility of using Deep Learning (DL) techniques to evaluate the drag coefficient of small non-Brownian particles translating and settling in nonlinear viscoelastic fluids. The long-term objective is the development of a 3D numerical code for particle-laden viscoelastic flows (PLVF), which will contribute to understanding many advanced manufacturing and industrial operations, specifically the hydraulic fracturing process

Effects of elasticity, inertia and viscosity ratio on the drag coefficient of a sphere translating through a viscoelastic fluid

The ability to simulate the behavior of dilute suspensions, considering Eulerian-Lagrangian approaches, requires proper drag models, which should be valid for a wide range of process and material parameters. These drag models allow to calculate the momentum exchange between the continuous and dispersed phases. The currently available drag models are only valid for inelastic constitutive fluid models. This work aims at contributing to the development of drag models appropriate for dilute suspensions, where the continuous phase presents viscoelastic characteristics. To this aim, we parametrize the effects of fluid elasticity, namely, the relaxation and retardation times, as well as inertia on the drag coefficient of a sphere translating through a viscoelastic fluid, described by the Oldroyd-B model. To calculate the drag coefficient we resort to three-dimensional direct numerical simulations of unconfined viscoelas tic flows past a stationary sphere, at different Reynolds number, Re, over a wide range of Deborah numbers (< 9), and the polymer viscosity ratios. For low Re (< 1), we identified a non-monotonic trend for the drag coefficient correction (the ratio between the calculated drag coefficient and the one obtained for Stokes-flow). It initially decreases with the increase of De, for low De values (< 1), which is followed by a significant growth, due to the large elastic stresses that are developed on both the surface and wake of the sphere. These behaviors, observed in the inertia less flow regime, are amplified as the polymer viscosity ratio approaches unity. At higher Re (> 1), the drag coefficient correction is found to be always bigger than unity, but smaller than the enhancement calculated in creeping flow limit.The authors would like to acknowledge the funding by FEDER funds through the COMPETE 2020 Programme and National Funds through FCT - Portuguese Foundation for Science and Technology under the projects UID/CTM/50025/2013 and POCI-01-0247-FEDER-017656