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

2021 ◽  
Author(s):  
◽  
Sarah Stevenson

<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>

2021 ◽  
Author(s):  
◽  
Sarah Stevenson

<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>


1999 ◽  
Vol 11 (4) ◽  
pp. 893-904 ◽  
Author(s):  
Mohamed Tij ◽  
Vicente Garzó ◽  
Andrés Santos

1989 ◽  
Vol 41 (11) ◽  
pp. 1328-1335
Author(s):  
V. M. Solopenko

1992 ◽  
Vol 97 (10) ◽  
pp. 7687-7694 ◽  
Author(s):  
Paz Padilla ◽  
So/ren Toxvaerd

2010 ◽  
Vol 666 ◽  
pp. 204-253 ◽  
Author(s):  
PRIYANKA SHUKLA ◽  
MEHEBOOB ALAM

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.


Author(s):  
Vicente Garzó ◽  
Andrés Santos

1999 ◽  
Vol 43 (4) ◽  
pp. 897-909 ◽  
Author(s):  
M. M. Britton ◽  
R. W. Mair ◽  
R. K. Lambert ◽  
P. T. Callaghan

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