Characterization of Effective Diffusion within Viscoelastic Fluids with Elastic Instabilities

We considered effective diffusion, characterized by magnitudes of effective diffusion coefficients, in order to quantify mass transport due to the onset and development of elastic instabilities. Effective diffusion coefficient magnitudes were determined using different analytic approaches, as they were applied to tracked visualizations of fluorescein dye front variations, as circumferential advection was imposed upon a flow environment produced using a rotating Couette flow arrangement. Effective diffusion coefficient results were provided for a range of flow shear rates, which were produced using different Couette flow rotation speeds and two different flow environment fluid depths. To visualize the flow behavior within the rotating Couette flow environment, minute amounts of fluorescein dye were injected into the center of the flow container using a syringe pump. This dye was then redistributed within the flow by radial diffusion only when no disk rotation was used, and by radial diffusion and by circumferential advection when disk rotation was present. Associated effective diffusion coefficient values, for the latter arrangement, were compared to coefficients values with no disk rotation, which were due to molecular diffusion alone, in order to quantify enhancements due to elastic instabilities. Experiments were conducted using viscoelastic fluids, which were based on a 65% sucrose solution, with different polymer concentrations ranging from 0 ppm to 300 ppm. Associated Reynolds numbers based on the fluid depth and radially averaged maximum flow velocity ranged from 0.00 to 0.5. The resulting effective diffusion coefficient values for different flow shear rates and polymer concentrations quantified the onset of elastic instabilities, as well as significant and dramatic changes to local mass transport magnitudes, which are associated with the further development of elastic instabilities.

Viscous dissipation effect on steady natural convection Couette flow with convective boundary condition

The present article explores the effect of viscous dissipation on steady natural convection Couette flow subject to convective boundary condition. Due to the nonlinearity and coupling of the governing equations in the present situation, the homotopy perturbation method was employed to obtain the solutions of the energy and momentum equations. The impacts of the controlling parameters were investigated and discussed graphically. In the course of investigation, it was found that fluid temperature increases with an increase in viscous dissipation while the reverse trend was observed in fluid velocity. However, it was also discovered that heat generation leads to a decrease in the rate of heat transfer on the heated plate and it increases on the cold plate. Finally, it was concluded that the velocity boundary layer thickness increases with an increase in Biot number.

Secondary instabilities in Taylor–Couette flow of shear-thinning fluids

The stability of the Taylor vortex flow in Newtonian and shear-thinning fluids is investigated in the case of a wide gap Taylor–Couette system. The considered radius ratio is $\eta = R_1/R_2=0.4$ . The aspect ratio (length over the gap width) of experimental configuration is 32. Flow visualization and measurements of two-dimensional flow fields with particle image velocimetry are performed in a glycerol aqueous solution (Newtonian fluid) and in xanthan gum aqueous solutions (shear-thinning fluids). The experiments are accompanied by axisymmetric numerical simulations of Taylor–Couette flow in the same gap of a Newtonian and a purely viscous shear-thinning fluid described by the Carreau model. The experimentally observed critical Reynolds and wavenumbers at the onset of Taylor vortices are in very good agreement with that obtained from a linear theory assuming a purely viscous shear-thinning fluid and infinitely long cylinders. They are not affected by the viscoelasticity of the used fluids. For the Newtonian fluid, the Taylor vortex flow (TVF) regime is found to bifurcate into a wavy vortex flow with a high frequency and low amplitude of axial oscillations of the vortices at ${Re} = 5.28 \, {Re}_c$ . At ${Re} = 6.9 \, {Re}_c$ , the frequency of oscillations decreases and the amplitude increases abruptly. For the shear-thinning fluids the secondary instability conserves axisymmetry. The latter is characterized by an instability of the array of vortices leading to a continuous sequence of creation and merging of vortex pairs. Axisymmetric numerical simulations reproduce qualitatively very well the experimentally observed flow behaviour.

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>