Shear Banding of Repulsive Particulate Suspensions in Rotating Couette Flow

2008 ◽  
Author(s):  
Kyung H. Ahn ◽  
Sunjin Song ◽  
Seung J. Lee ◽  
Albert Co ◽  
Gary L. Leal ◽  
...  
Keyword(s):  
Couette Flow ◽  
Shear Banding ◽  
Particulate Suspensions

Weakly nonlinear theory of shear-banding instability in a granular plane Couette flow: analytical solution, comparison with numerics and bifurcation

2010 ◽  
Vol 666 ◽  
pp. 204-253 ◽  
Author(s):  
PRIYANKA SHUKLA ◽  
MEHEBOOB ALAM
Keyword(s):  
Couette Flow ◽  
Shear Banding ◽  
Base Flow ◽  
Plane Couette Flow ◽  
Weakly Nonlinear ◽  
Subcritical Bifurcation ◽  
Supercritical Bifurcation ◽  
Weakly Nonlinear Theory ◽  
Pitchfork Bifurcations ◽  
The Mean

A weakly nonlinear theory, in terms of the well-known Landau equation, has been developed to describe the nonlinear saturation of the shear-banding instability in a rapid granular plane Couette flow using the amplitude expansion method. The nonlinear modes are found to follow certain symmetries of the base flow and the fundamental mode, which helped to identify analytical solutions for the base-flow distortion and the second harmonic, leading to an exact calculation of the first Landau coefficient. The present analytical solutions are used to validate a spectral-based numerical method for the nonlinear stability calculation. The regimes of supercritical and subcritical bifurcations for the shear-banding instability have been identified, leading to the prediction that the lower branch of the neutral stability contour in the (H, φ0)-plane, where H is the scaled Couette gap (the ratio between the Couette gap and the particle diameter) and φ0 is the mean density or the volume fraction of particles, is subcritically unstable. The predicted finite-amplitude solutions represent shear localization and density segregation along the gradient direction. Our analysis suggests that there is a sequence of transitions among three types of pitchfork bifurcations with increasing mean density: from (i) the bifurcation from infinity in the Boltzmann limit to (ii) subcritical bifurcation at moderate densities to (iii) supercritical bifurcation at larger densities to (iv) subcritical bifurcation in the dense limit and finally again to (v) supercritical bifurcation near the close packing density. It has been shown that the appearance of subcritical bifurcation in the dense limit depends on the choice of the contact radial distribution function and the constitutive relations. The scalings of the first Landau coefficient, the equilibrium amplitude and the phase diagram, in terms of mode number and inelasticity, have been demonstrated. The granular plane Couette flow serves as a paradigm that supports all three possible types of pitchfork bifurcations, with the mean density (φ0) being the single control parameter that dictates the nature of the bifurcation. The predicted bifurcation scenario for the shear-band formation is in qualitative agreement with particle dynamics simulations and the experiment in the rapid shear regime of the granular plane Couette flow.

Transition to shear banding in pipe and Couette flow of wormlike micellar solutions

1999 ◽  
Vol 43 (4) ◽  
pp. 897-909 ◽  
Author(s):  
M. M. Britton ◽  
R. W. Mair ◽  
R. K. Lambert ◽  
P. T. Callaghan
Keyword(s):  
Couette Flow ◽  
Shear Banding ◽  
Micellar Solutions

scholarly journals Investigation of Shear Flow in a Planar Cylindrical Hybrid Geometry for Rheo-NMR Applications

2021 ◽  
Author(s):  
◽  
Sarah Stevenson
Keyword(s):  
Couette Flow ◽  
Method Development ◽  
Shear Banding ◽  
Conveyor Belt ◽  
Small Degree ◽  
Flow Profile ◽  
Concentric Cylinder ◽  
Complex Material ◽  
Mechanical Deformations ◽  
Planar Couette Flow

<p>Materials which exhibit peculiar behaviour due to applied mechanical deformations are abundant in everyday life. Rheo-NMR is an established technique which has been used to study these responses for the past three decades by combining methodologies from rheometry and nuclear magnetic resonance (NMR). The technique enhances standard rheological studies of bulk properties, such as viscosity and elasticity, by applying the tools of NMR (e.g. spectroscopy, diffusion, relaxometry, imaging, and velocimetry) to matter under deformation. This allows for the exploration of molecular origins and / or local responses within the material which lead to the macroscopic behaviour. These materials are deformed (most commonly sheared) inside geometric housings with a NMR experiment running in parallel. For complex material studies it is desirable for these geometries to provide a simple homogeneous deformation. In reality, all standard rheometry geometries have inhomogeneity characteristics. In fact there is evidence to suggest that some material responses may be influenced by a small degree of deviation from pure homogeneity. This makes it harder to isolate any inherent material behaviour due to a magnitude or rate of deformation from the specific characteristics of how the deformation was applied. This contribution reports on the continued design and method development of a novel geometry for rheo-NMR - a planar cylindrical hybrid (PCH) shear geometry. The geometry includes planar sections with the aim to provide planar Couette flow, a simple truly homogeneous shear profile. It comprises of two parallel sections of planar flow connected by two semi-circular sections of circular flow to give a closed flow path in the shape of a racetrack. Shear is applied by rotating a band around the inner section like a conveyor belt. The purpose of the PCH geometry is to study the complex responses of materials under shear in this atypical shear environment. A paragon of a model system for exploring the novel geometry is a shear banding wormlike micelle (WLM) solution. It has a well documented nonlinear response to steady shear and previous work demonstrated that the curvature of a standard concentric cylinder geometric housing influenced the observed WLM’s rheological response. Strikingly, what was discovered by this thesis research was that there was no visible appearance of this material separating into bands in the planar (or cylindrical) regions in the PCH geometry when probed with an NMR velocity encoded imaging experiment. The more Newtonian-like response of the complex material differs from the intriguing curved flow profile seen for an actual Newtonian sample (which additionally evolves over the planar region) meaning the WLM’s response is still complex in nature. From these findings it is clear that geometry did not impart the homogeneous planar Couette flow for a Newtonian sample. However it has introduced a new deformation environment to study complex materials, acting completely differently to the geometries typically used in rheo-NMR and rheometry. Implications of this and motivation for work study are discussed.</p>

Nonlinear stability and patterns in granular plane Couette flow: Hopf and pitchfork bifurcations, and evidence for resonance

2011 ◽  
Vol 672 ◽  
pp. 147-195 ◽  
Author(s):  
PRIYANKA SHUKLA ◽  
MEHEBOOB ALAM
Keyword(s):  
Couette Flow ◽  
Nonlinear Stability ◽  
Fundamental Mode ◽  
Second Harmonic ◽  
Shear Banding ◽  
Two Dimensional ◽  
Plane Couette Flow ◽  
Mean Flow ◽  
Flow Distortion ◽  
Pitchfork Bifurcations

The first evidence of a variety of nonlinear equilibrium states of travelling and stationary waves is provided in a two-dimensional granular plane Couette flow via nonlinear stability analysis. The relevant order-parameter equation, the Landau equation, has been derived for the most unstable two-dimensional perturbation of finite size. Along with the linear eigenvalue problem, the mean-flow distortion, the second harmonic, the distortion to the fundamental mode and the first Landau coefficient are calculated using a spectral-based numerical method. Two types of bifurcations, Hopf and pitchfork, that result from travelling and stationary instabilities, respectively, are analysed using the first Landau coefficient. The present bifurcation theory shows that the flow is subcritically unstable to stationary finite-amplitude perturbations of long wavelengths (kx ~ 0, where kx is the streamwise wavenumber) in the dilute limit that evolve from subcritical shear-banding modes (kx = 0), but at large enough Couette gaps there are stationary instabilities with kx = O(1) that lead to supercritical pitchfork bifurcations. At moderate-to-large densities, in addition to supercritical shear-banding modes, there are long-wave travelling instabilities that lead to Hopf bifurcations. It is shown that both supercritical and subcritical nonlinear states exist at moderate-to-large densities that originate from the dominant stationary and travelling instabilities for which kx = O(1). Nonlinear patterns of density, velocity and granular temperature for all types of instabilities are contrasted with their linear eigenfunctions. While the supercritical solutions appear to be modulated forms of the fundamental mode, the structural features of unstable subcritical solutions are found to be significantly different from their linear counterparts. It is shown that the granular plane Couette flow is prone to nonlinear resonances in both stable and unstable regimes, the signature of which is implicated as a discontinuity in the first Landau coefficient. Our analysis identified two types of modal resonances that appear at the quadratic order in perturbation amplitude: (i) a ‘mean-flow resonance’ which occurs due to the interaction between a streamwise-independent shear-banding mode (kx = 0) and a linear/fundamental mode kx ≠ 0, and (ii) an exact ‘1 : 2 resonance’ that results from the interaction between two waves with their wavenumber ratio being 1 : 2.

scholarly journals Investigation of Shear Flow in a Planar Cylindrical Hybrid Geometry for Rheo-NMR Applications

2021 ◽  
Author(s):  
◽  
Sarah Stevenson
Keyword(s):  
Couette Flow ◽  
Method Development ◽  
Shear Banding ◽  
Conveyor Belt ◽  
Small Degree ◽  
Flow Profile ◽  
Concentric Cylinder ◽  
Complex Material ◽  
Mechanical Deformations ◽  
Planar Couette Flow

<p>Materials which exhibit peculiar behaviour due to applied mechanical deformations are abundant in everyday life. Rheo-NMR is an established technique which has been used to study these responses for the past three decades by combining methodologies from rheometry and nuclear magnetic resonance (NMR). The technique enhances standard rheological studies of bulk properties, such as viscosity and elasticity, by applying the tools of NMR (e.g. spectroscopy, diffusion, relaxometry, imaging, and velocimetry) to matter under deformation. This allows for the exploration of molecular origins and / or local responses within the material which lead to the macroscopic behaviour. These materials are deformed (most commonly sheared) inside geometric housings with a NMR experiment running in parallel. For complex material studies it is desirable for these geometries to provide a simple homogeneous deformation. In reality, all standard rheometry geometries have inhomogeneity characteristics. In fact there is evidence to suggest that some material responses may be influenced by a small degree of deviation from pure homogeneity. This makes it harder to isolate any inherent material behaviour due to a magnitude or rate of deformation from the specific characteristics of how the deformation was applied. This contribution reports on the continued design and method development of a novel geometry for rheo-NMR - a planar cylindrical hybrid (PCH) shear geometry. The geometry includes planar sections with the aim to provide planar Couette flow, a simple truly homogeneous shear profile. It comprises of two parallel sections of planar flow connected by two semi-circular sections of circular flow to give a closed flow path in the shape of a racetrack. Shear is applied by rotating a band around the inner section like a conveyor belt. The purpose of the PCH geometry is to study the complex responses of materials under shear in this atypical shear environment. A paragon of a model system for exploring the novel geometry is a shear banding wormlike micelle (WLM) solution. It has a well documented nonlinear response to steady shear and previous work demonstrated that the curvature of a standard concentric cylinder geometric housing influenced the observed WLM’s rheological response. Strikingly, what was discovered by this thesis research was that there was no visible appearance of this material separating into bands in the planar (or cylindrical) regions in the PCH geometry when probed with an NMR velocity encoded imaging experiment. The more Newtonian-like response of the complex material differs from the intriguing curved flow profile seen for an actual Newtonian sample (which additionally evolves over the planar region) meaning the WLM’s response is still complex in nature. From these findings it is clear that geometry did not impart the homogeneous planar Couette flow for a Newtonian sample. However it has introduced a new deformation environment to study complex materials, acting completely differently to the geometries typically used in rheo-NMR and rheometry. Implications of this and motivation for work study are discussed.</p>

A conduction-cooled stage for high-resolution Cryo-SEM

1992 ◽  
Vol 50 (2) ◽  
pp. 1282-1283
Author(s):  
John G. Sheehan
Keyword(s):  
High Resolution ◽  
Liquid Nitrogen ◽  
Mechanical Stability ◽  
Cooling System ◽  
Cold Trap ◽  
Nitrogen Gas ◽  
Particulate Suspensions ◽  
Advantages And Disadvantages ◽  
Convection Cooling ◽  
Styrene Butadiene

The goal is to examine with high resolution cryo-SEM aqueous particulate suspensions used in coatings for printable paper. A metal-coating chamber for cryo-preparation of such suspensions was described previously. Here, a new conduction-cooling system for the stage and cold-trap in an SEM specimen chamber is described. Its advantages and disadvantages are compared to a convection-cooling system made by Hexland (model CT1000A) and its mechanical stability is demonstrated by examining a sample of styrene-butadiene latex.In recent high resolution cryo-SEM, some stages are cooled by conduction, others by convection. In the latter, heat is convected from the specimen stage by cold nitrogen gas from a liquid-nitrogen cooled evaporative heat exchanger. The advantage is the fast cooling: the Hexland CT1000A cools the stage from ambient temperature to 88 K in about 20 min. However it consumes huge amounts of liquid-nitrogen and nitrogen gas: about 1 ℓ/h of liquid-nitrogen and 400 gm/h of nitrogen gas. Its liquid-nitrogen vessel must be re-filled at least every 40 min.

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