Couette Cell Research Articles

Kinetics of aggregation of amyloid β under different shearing conditions: Experimental and modelling analyses

Amyloid β (Aβ40) is a class of amyloidogenic proteins known to aggregate into a fibrillar network. The rate of aggregation and fibril yield is sensitive to external energy input, such as shear. In this work, simple shear and shaking experiments are performed on Aβ40 solution using a Couette cell and an orbital shaker, respectively. Experiments show that, under uniform shear, both the mass of fibrils and aggregation rate increase with the shear rate. In the case of orbital shaking, the lag time decreases with the rotational speed of the shaker, but the final fibril mass is the same for all agitation speeds. To explain this contrasting behavior of aggregation kinetics, a population balance model is developed to account for the effect of shear on the aggregation of Aβ. The kinetic model includes primary nucleation, secondary nucleation, elongation, fragmentation, and depolymerization steps. The effect of steady uniform shear is encoded in the depolymerization rate constant (kd), and it is shown that kd decreases with shear rate initially and saturates at high shear rates. A competition between elongation and depolymerization rates yields different equilibrium masses of fibril at different shear rates. The model results agree quantitatively well with experimental data on the rate of aggregation and mass of fibrils as a function of shear rate. The modeling framework can be used to explain the shear rate-dependent aggregation of other amyloidogenic proteins.

Shear-induced nanostructural changes in micelles formed by sugar-based surfactants with varied anomeric configuration

HypothesisThe self-assembly of long tail sugar-based surfactants into worm-like micelles has recently been demonstrated, and the rheological properties of such systems have been shown to be tuneable through subtle modifications of the molecular characteristics of the surfactant monomer. In particular, the anomeric configuration of the hexadecylmaltoside headgroup was shown to induce profound changes in the nanostructure and rheology of the system. The origin of such changes is hypothesised to arise from differences in the structure and relaxation of the micellar networks in the semi-dilute regime. ExperimentsHere we explore the molecular background to the flow properties of the two anomers of hexadecylmaltoside (α- and β-C16G2) by directly connecting their rheological behaviour to the micelle morphology. For this purpose, 1–3 plane rheo-small-angle neutron scattering measurements, using a Couette cell geometry, probed the structural changes in the micellar phase under shear. The effect of surfactant anomeric configuration, surfactant concentration, temperature and mixing ratio of the two anomers were investigated. The static micelle structure in the semi-dilute regime was determined using the polymer reference interaction site model. FindingsThe segmental alignment of the micellar phase was studied under several flow conditions, showing that the shear-thinning behaviour relates to the re-arrangement of β-C16G2 worm-like micelles, whilst shorter α-C16G2 micelles are considerably less affected by the flow. The results are rationalised in terms of micelle alignment and disruption of the entangled network, providing a detailed mechanism by which sugar-based surfactants control the rheology of the fluid. To further enable future studies, we provide the complete code for modelling micelle structure in the semi-dilute regime using the polymer reference interaction site model.

Determination of viscosity average molar masses of polyethylene in a wide range using rheological measurements with a harmless solvent

Rheological measurements of polyethylene solutions in a novel nontoxic solvent were used to determine the Mark-Houwink parameters for PE of widely different molecular weights to assess the viscosity average molar mass for PE of several millions of g.mol−1. Solutions of high density polyethylene that had been previously characterized by size exclusion chromatography were prepared in a harmless naphthenic oil. The intrinsic viscosities were obtained by varying the concentrations of the different calibration samples solutions using a rotational rheometer equipped with a Couette cell. The intrinsic viscosities were determined by both Huggins and Kraemer descriptions of the viscosity variations with concentration. Subsequently, a calibration curve of intrinsic viscosities versus the molar mass was plotted, and the parameters of the Mark-Houwink-Sakurada equation were obtained for polyethylene in naphthenic oil. Using this equation and the newly estimated parameters, the viscosity average molar mass of a high molar mass polyethylene and a commercial ultra high molar mass polyethylene were been determined by measuring their respective intrinsic viscosities. Finally, the method has been validated by comparing these results to values obtained by standard viscosimetry in 1,2,4-trichlorobenzene and to the values given by the supplier, obtained by other methods.

Probing nonlinear velocity profiles of shear-thinning, nematic platelet dispersions in Couette flow using x-ray photon correlation spectroscopy

We report experiments employing x-ray photon correlation spectroscopy (XPCS) to characterize the velocity profiles of complex fluids in Couette flow. The approach involves modeling the XPCS correlation functions obtained with the incident x-ray beam passing tangentially through the Couette cell gap at various distances from the inner wall. We first demonstrate the technique with measurements on a dilute colloidal dispersion in the Newtonian liquid glycerol, where the expected linear velocity profiles are recovered. We then employ the technique to map the shear-rate-dependent velocity profiles of a shear-thinning dispersion of nematically ordered Gibbsite platelets. The nonlinear velocity profiles of the Gibbsite dispersion include a narrow slip region adjacent to the outer wall and a band with a small velocity gradient in the interior of the gap that evolves into a region increasingly resembling plug flow with increasing shear rate. Variations in the velocity profile along the vorticity direction indicate an instability in the interface between this region of small velocity gradient and a region of high velocity gradient near the inner wall. The analysis of the small-angle scattering patterns provides information about the spatial and temporal variations in the nematic order of the Gibbsite dispersion and their coupling to the velocity profile. Additional potential applications of this XPCS-based technique and comparisons with established methods for characterizing velocity profiles are discussed.

Validation of temperature-controlled rheo-MRI measurements in a submillimeter-gap Couette geometry.

A temperature-controlled submillimeter-gap (500 μm) rheo-magnetic resonance imaging (MRI) Couette cell has been developed to measure confined flow of soft structured materials under controlled temperature. The proposed setup enables performing rheo-MRI measurements using (i) a spatially uniform temperature control over the range 15°C to 40°C and (ii) a high spatial resolution up to 10μm, as a consequence of the improved mechanical stability of the in-house developed rotating elements. Here, we demonstrate the performance of the cell for the rheo-MRI velocimetry study of a thixotropic fat crystal dispersion, a complex fluid commonly used in food manufacturing. The submillimeter-gap geometry and variable temperature capability of the cell enable observing the effects of shear- and temperature-induced fat recrystallization on both wall slip and shear banding under strongly confined flow. Our improved rheo-MRI setup opens new perspectives for the fundamental study of strongly confined flow, cooperative effects, and the underlying interparticle interactions and for ultimately aiding optimization of products involved in spreading/extrusion, such as cosmetics and foods.

Rotational Particle Separation in Solutions: Micropolar Fluid Theory Approach.

We develop a new mathematical model for rotational sedimentation of particles for steady flows of a viscoplastic granular fluid in a concentric-cylinder Couette geometry when rotation of the Couette cell inner cylinder is prescribed. We treat the suspension as a micro-polar fluid. The model is validated by comparison with known data of measurement. Within the proposed theory, we prove that sedimentation occurs due to particles’ rotation and rotational diffusion.

Viscous resuspension of non-Brownian particles: determination of the concentration profiles and particle normal stresses

Abstract

Ionic strength and polyelectrolyte molecular weight effects on floc formation and growth in Taylor-Couette flows.

Polyelectrolyte-driven flocculation of suspended particulate in solution is an important process in a variety of industrial processes such as drinking water treatment and composite material synthesis. Flocculation depends on a wide variety of physicochemical and hydrodynamic properties, which affect floc size, growth rate, and floc morphology. Floc formation and growth behavior is explored here using two different molecular weights of a cationic polyacrylamide flocculant and anisotropic Na-bentonite clay particles under a variety of solution ionic strengths. A Taylor-Couette cell with radial injection capabilities was used to study the effects of solution ionic strength and polyelectrolyte molecular weight on floc size, growth rate, and floc morphology during the flocculation process with a constant global velocity gradient. The floc size generally decreased with increasing ionic strength whereas the floc growth rate initially increased then decreased. This likely occurred due to charge screening effects, where increased bentonite aggregate size and a less expanded polyelectrolyte conformation at higher ionic strengths results in a decreased ability for the polyelectrolyte to bridge multiple bentonite aggregates. The densification of bentonite aggregates at higher ionic strengths resulted in floc morphologies that were more resistant to shear-induced breakage. With the exceptions of optimal dose concentration and dispersion coefficients, there were no clear differences in the floc growth rate behaviors for the two molecular weights studied. This work contributes to an improved understanding of the physicochemical complexities of polyelectrolyte-driven flocculation that can inform dosing requirements for more efficient industrial operations.

Evolution of shear zones in granular packings under pressure.

Stress transmission in realistic granular media often occurs under external load and in the presence of boundary slip. We investigate shear localization in a split-bottom Couette cell with smooth walls subject to a confining pressure experimentally and by means of numerical simulations. We demonstrate how the characteristics of the shear zone, such as its center position and width, evolve as the confining pressure and wall slip modify the local effective friction coefficient of the material. For increasing applied pressure, the shear zone evolves toward the center of the cylinder and grows wider and the angular velocity reduces compared to the driving rate of the bottom disk. Moreover, the presence of slip promotes the transition from open shear zones at the top surface to closed shear zones inside the bulk. We also systematically vary the ratio of the effective friction near the bottom plate and in the bulk in simulations and observe the resulting impact on the surface flow profile. Besides the boundary conditions and external load, material properties such as grain size are also known to influence the effective friction coefficient. However, our numerical results reveal that the center position and width of the shear zone are insignificantly affected by the choice of the grain size as far as it remains small compared to the radius of the rotating bottom disk.

Shearing of granular materials in a confined split-bottom Couette cell

Formation of shear bands is one of the most remarkable phenomena in the dynamics of granular matter. Several parameters have been so far identified to influence the behavior of the shear bands. We carried out experiments to investigate the evolution of the shear bands in the split-bottom Couette cell in the presence of confining pressure. We employed the Particle Image Velocimetry (PIV) to characterize the shear band both in the absence and presence of external pressure. Our results show that the location and width of the shear band are affected by both the confining pressure and the filling height. The shear zone evolves towards the middle of the cylinder and expands to a broader region with increasing applied pressure or filling height; also the angular velocity decreases relative to the rotation rate of the bottom disk. Our findings are consistent with prior empirical observations on the formation of wide shear bands at free surfaces.

Heaps of sand in flows within a split-bottom Couette cell.

In this paper, we study the flow of angular grains in a split-bottom Couette cell. Grains departing from a spherical shape result in collective flow fields that form a heap on the free surface. Here we extend on previous observations in split-bottom cells, exploring a wider range of flows within the inertial regime and finding a richness collection of behaviours. Surface height profiles and velocity profiles are accurately measured with digital image analysis. These measurements allow the characterization of the flow regimes within the cell and the heap morphology. We show that the known flow regimes in split-bottom geometries, like the universal and wall-collapsed regimes, can also be observed in moderately high inertial flows, extending the range for studying universal shear banding. The heap morphology is amplified by the flow inertia, with a partial collapse when the cell comes to a halt. Moreover, at high angular velocities, flows under low confinement will spread radially outwards, while flows under high confinement will develop localized particle ejections. Our results complement the observation of free-surface deformations of flows of nonspherical grains. These observations suggest a need for considering deformable free surface boundary conditions in the simulation of angular grains during shear, with repercussions in the characterization and prediction of natural mass flows.

Effects of elasticity and flow ramp up on kinetics of shear banding flow formation in wormlike micellar fluids

We report experiments on spatiotemporal evolution of the velocity profiles in shear-banding wormlike micelles upon inception of the flow in a Taylor–Couette (TC) cell. Both moderately entangled and highly entangled solutions are considered over a broad range of fluid elasticity E. Fluid elasticity, E = Wi/Re, characterizes the relative importance of the elastic to inertial effects. For both moderately and highly entangled solutions, upon inception of the shear, and during the stress decay period, fluid moves in the opposite direction to that of the imposed motion in a subset of the gap beyond critical thresholds of elasticity and flow ramp up rate, which depend on the fluid entanglement density. Surprisingly, beyond a second critical threshold of the fluid elasticity, the transient backflow disappears in moderately entangled solutions, highlighting the importance of the micellar entanglement on transient evolution of the flow in shear banding systems. More interestingly, we report the formation of multibanded quasisteady velocity profiles under certain conditions of fluid elasticity and flow ramp up rate. The multibanded profiles are characterized by a low shear band near the inner cylinder, a high shear band in the middle of the TC gap, and another low shear band near the outer cylinder. Finally, we show that the apparent wall slip at the inner cylinder of the TC cell is more pronounced for highly entangled solutions and decreases as the fluid elasticity increases. Experimental observations are compared with the existing simulations of the Vasquez–Cook–McKinley model, and several suggestions are made for future simulations.

Rheology of aqueous foams under pressure

Aqueous foams are found in a wide range of industrial applications such as cosmetic, pharmaceutical, and food industries. These foam-based products are typically packaged in aerosol cans that are pressurized up to 3 bar. With pressure fluctuations over time, issues like coarsening and liquid drainage could affect the formulation. However, the rheological studies of foams under pressure are limited by the poor sensitivity and complex designs of traditional pressure cells that impose a lower torque limit of approximately 100 μN ⋅m. In this study, we detail the design and validation of a high-sensitivity pressurized Couette cell that utilizes a novel design to provide sample pressurization (up to 5 bar) with significantly improved torque sensitivity (1 μN ⋅m in oscillatory and 10 μN ⋅m in shear flows). Foam samples present experimental challenges due to a reduction in sample volume when pressurized. This has serious implications if a standard cylindrical cup and bob geometry is used with foam samples as it will be underfilled under pressurized conditions leading to erroneous results. To overcome this difficulty, we have designed a new rotor appropriately dimensioned that ensures a sufficient sample level over the entirety of the rotor under pressurized conditions. We demonstrate the application of this device by characterizing a commercial aqueous foam using traditional rheological methods such as flow ramps, oscillatory strain amplitude sweep, frequency sweep, time sweep, and stress growth under pressurized conditions.

The translational and rotational motions of a cylindrical particle in a granular shear flow inside a split bottom Couette cell

The motion of a sample particle in a Couette-cell granular flow is measured using the magnetic particle tracking technology. This technology allows simultaneous measurements of translation and rotation of an individual grain in an opaque environment. The anisotropic sample particle is a cylinder with an aspect ratio 1, and the other grains in the flow are spherical balls. The trajectory shows that the particle in the studied Couette cell with a split bottom moves in a layered structure. The orientation distribution shows that the cylindrical particle prefers to align in specific directions, even though the aspect ratio is low and the shear motion should not cause strong alignment. A symbolic-based method is used to examine the jumping between spatial layers and the flipping among preferred directions. The result shows that the duration of particle staying in a preferred state is much longer than the duration of transition. In addition, a jumping particle has a higher chance to flip. In the bulk flow, the translational energy varies significantly along the radial direction. The magnitude of translational kinetic energy is generally much larger than the rotational motion.

A multi-component lattice Boltzmann approach to study the causality of plastic events.

Using a multi-component lattice Boltzmann (LB) model, we perform fluid kinetic simulations of confined and concentrated emulsions. The system presents the phenomenology of soft-glassy materials, including a Herschel-Bulkley rheology, yield stress, ageing and long relaxation time scales. Shearing the emulsion in a Couette cell below the yield stress results in plastic topological re-arrangement events which follow established empirical seismic statistical scaling laws, making this system a good candidate to study the physics of earthquakes. One characteristic of this model is the tendency for events to occur in avalanche clusters, with larger events, triggering subsequent re-arrangements. While seismologists have developed statistical tools to study correlations between events, a process to confirm causality remains elusive. We present here, a modification to our LB model, involving small, fast vibrations applied to individual droplets, effectively a macroscopic forcing, which results in the arrest of the topological plastic re-arrangements. This technique provides an excellent tool for identifying causality in plastic event clusters by examining the evolution of the dynamics after 'stopping' an event, and then checking which subsequent events disappear. This article is part of the theme issue 'Fluid dynamics, soft matter and complex systems: recent results and new methods'.

Buoyancy transfer in a two-layer system in steady state. Experiments in a Taylor–Couette cell

Our experimental study focuses on the density and velocity field in two layers of fluid separated by a sharp density interface. Turbulence is generated by a non-invasive stirrer, a Taylor–Couette tank, and the interface is stabilized with a source of saline fluid and a source of fresh water at the bottom and top of the tank, respectively. The same volume fluxes are withdrawn by two sinks to maintain a constant volume of fluid in the tank. Our results confirm past experiments and show that a strong vertical exchange of fluid occurs close to the inner cylinder and across the interface, where the vertical turbulent length scales appear to be suppressed. For low values of kinetic energy supplied to the system, the interface may act as a rigid boundary for the turbulent eddies, with a reduction of the vertical length scales although it seems not to affect the horizontal length scales. The vertical buoyancy flux extracted at the top of the tank is fairly well reproduced by the measured correlation between density and vertical velocity fluctuations across the interface. Quadrant analysis of the correlation terms reveals that the greatest contribution to salt flux is given by eddies that carry the lighter fluid from top to bottom across the interface. The mixing process is accompanied by a single wake-like disturbance, with a radial front advancing in the azimuthal direction across the interface, acting as a blade, and with a period that decreases with rotation rate. The wake favours the smoothing of the density step and, in a simplified model, we assume that the turbulent diffusion is active during a fraction of the cycle in the wake-mixing region, with diffusivity proportional to the transverse length scale and the speed of the wake. The mixing region is the domain between the nose of the wave-like perturbation and the section where the interface becomes ‘darker’ again after being mixed by the vortexes. The results of this model are in a fair agreement with the experiments. The potential energy of the interfacial perturbations is only a small part of the missing turbulent kinetic energy, defined as the difference in the turbulent kinetic energy between a well-mixed fluid and a two-layer fluid. Further analysis is needed to explain the mechanism of generating these perturbations and the factors that control their periodicity.

DEM simulation of dense granular flows in a vane shear cell: Kinematics and rheological laws

The rheology of dense granular flows is investigated through discrete element method (DEM) simulation of a vane shear cell. From the simulation, profiles of shear stress, shear rate, and velocity are obtained, which demonstrates that the flow features in the vane shear cell are equivalent to those in the classic annular Couette cell. A novel correlation for the apparent viscosity is formulated and leads to a new expression for μKT in the kinetic theory analysis. The μKT formulation is able to qualitatively capture the μ-I relation in the shear cell. A correlation length is added in the energy dissipation term to account for the effects of the particle motion correlation. A simplified correlation length model is derived based on DEM results and is compared with the literature. The modified granular kinetic energy equation is able to correctly predict the granular temperature profiles in the shear cell.

Engineered transparent emulsion to optically study particulate flows in yield stress fluids

We have engineered a model suspension consisting of rigid particles and yield stress fluids. The suspending fluid is an emulsion with adjustable density, rheological behavior, and refractive index. We explain the design procedure in detail. The optically transparent emulsion opens the possibility of exploring particle tracking/image velocimetry (PIV/PTV) techniques in studying dynamic flows involving particles in complex fluids. As a proof of concept, we have performed PTV to provide accurate measurements of solid volume fractions for the dispersion of particles in a Taylor–Couette cell.

Continuum modelling of primary and secondary granular flows in a torsional shear cell

In granular flows, the particles not only move along the principal streamlines but can also circulate perpendicularly to streamlines slowly in a vortex-like manner. Such behaviours have both scientific and practical significances, e.g. in convective mixing of particles, but their mechanisms are still under study. Previous experimental observations have stimulated two explanations for them: centrifugal force and volumetric dilatancy. Here a theoretical model is constructed to test these conjectures, which is based on the frictional plasticity and accounts for both dynamic effect and strain-dependent dilatancy. The simulation results show that, under the influence of gravity, the centrifugal force can indeed give rise to vortices in a Couette cell. In the absence of centrifugal force, granular vortices can still be observed depending on the shape of the yield surface. If the yield surface is a von Mises circle in the deviatoric plane, i.e. of Drucker-Prager type, no vortex is observed in continuum modelling. But for noncircular yield surfaces, a clear secondary flow is generated at some boundary conditions and increases in magnitude with the non-circularity of yield surface. Large granular dilatancy occurs in some regimes of high gradients, but altogether its influence on secondary flow is not critical. The role of boundary conditions is also discussed.

Single-shot velocity mapping by rewinding of velocity encoding with Echo-Planar Imaging.

The ability of single-shot NMR imaging methods to follow the time evolution of a velocity distribution within an object is strongly limited by the phase errors accumulated as velocity maps are acquired. In the particular case of Carr-Purcell based sequences combined with Echo Planar Imaging acquisition, phase accumulates through subsequent images, hampering the possibility to acquire several velocity maps, which would be useful to determine transient behavior. In this work, we propose the use of a rewinding velocity encoding module applied after the acquisition of each image during the CPMG echo train. In this way, the first velocity module imparts a velocity dependent phase prior to the image acquisition and the second pair cancels this phase out before the next refocusing radiofrequency pulse is applied. The performance and limits of this method are studied by acquiring 100 images of a co-rotating Couette cell over a period of 1.6 s as a function of the rotation speed. The method is applied to determine the kinematic viscosity of a water/alcohol mixture, which is a relevant topic in many physical, chemical and biological processes.