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

<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>

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

<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>

Vorticity generation and conservation for two-dimensional interfaces and boundaries

The generation, redistribution and, importantly, conservation of vorticity and circulation is studied for incompressible Newtonian fluids in planar and axisymmetric geometries. A generalised formulation of the vorticity at the interface between two fluids for both no-slip and stress-free conditions is presented. Illustrative examples are provided for planar Couette flow, Poiseuille flow, the spin-up of a circular cylinder, and a cylinder below a free surface. For the last example, it is shown that, although large imbalances between positive and negative vorticity appear in the wake, the balance is found in the vortex sheet representing the stress-free surface.