Couette Geometry Research Articles

Shear-induced fragmentation of laponite suspensions

Simultaneous rheological and velocity profile measurements are performed in a smooth Couette geometry on laponite suspensions seeded with glass microspheres and undergoing the shear-induced solid-to-fluid (or yielding) transition. Under these slippery boundary conditions, a rich temporal behaviour is uncovered, in which shear localization is observed at short times, which rapidly gives way to a highly heterogeneous flow, characterized by intermittent switching from plug-like flow to linear velocity profiles. Such a temporal behaviour is linked to the fragmentation of the initially solid sample into blocks separated by fluidized regions. These solid pieces get progressively eroded over timescales ranging from a few minutes to several hours depending on the applied shear rate . The steady-state is characterized by a homogeneous flow with almost negligible wall slip. The characteristic timescale for erosion is shown to diverge below some critical shear rate * and to scale as ( − *)−n with n ≃ 2 above *. A tentative model for erosion is discussed together with open questions raised by the present results.

Structure, rheology and shear alignment of Pluronic block copolymer mixtures

The structure and flow behaviour of binary mixtures of Pluronic block copolymers P85 and P123 is investigated by small-angle scattering, rheometry and mobility tests. Micelle dimensions are probed by dynamic light scattering. The micelle hydrodynamic radius for the 50/50 mixture is larger than that for either P85 or P123 alone, due to the formation of mixed micelles with a higher association number. The phase diagram for 50/50 mixtures contains regions of cubic and hexagonal phases similar to those for the parent homopolymers, however the region of stability of the cubic phase is enhanced at low temperature and concentrations above 40 wt%. This is ascribed to favourable packing of the mixed micelles containing core blocks with two different chain lengths, but similar corona chain lengths. The shear flow alignment of face-centred cubic and hexagonal phases is probed by in situ small-angle X-ray or neutron scattering with simultaneous rheology. The hexagonal phase can be aligned using steady shear in a Couette geometry, however the high modulus cubic phase cannot be aligned well in this way. This requires the application of oscillatory shear or compression.

Wide-gap Couette flows of dense emulsions: Local concentration measurements, and comparison between macroscopic and local constitutive law measurements through magnetic resonance imaging

Flows of dense emulsions show many complex features among which long range nonlocal effects pose a problem for macroscopic characterization. In order to get around this problem, we study the flows of several dense emulsions, with droplet size ranging from 0.3to40microm , in a wide-gap Couette geometry. We couple macroscopic rheometric experiments and local velocity measurements through magnetic resonance imaging (MRI) techniques. As concentration heterogeneities are expected in the wide-gap Couette flows of multiphase materials, we also designed a method to measure the local droplet concentration in emulsions with a MRI device. In contrast to dense suspensions of rigid particles where very fast migration occurs under shear in wide-gap Couette flows, we show that no migration takes place in dense emulsions even for strains as large as 100 000 in our systems. As a result of the absence of migration and of finite size effect, we are able to determine very precisely the local rheological behavior of several dense emulsions. As the materials are homogeneous, this behavior can also be inferred from purely macroscopic measurements. We thus suggest that properly analyzed purely macroscopic measurements in a wide-gap Couette geometry can be used as a tool to study the local constitutive laws of dense emulsions. All behaviors are basically consistent with Herschel-Bulkley laws of index 0.5. The existence of a constitutive law accounting for all flows contrasts with previous results obtained within a microchannel by Goyon [Nature (London) 454, 84 (2008)]: the use of a wide-gap Couette geometry is likely to prevent here from nonlocal finite size effects; it also contrasts with the observations of Bécu [Phys. Rev. Lett. 96, 138302 (2006)]. We also evidence the existence of discrepancies between a perfect Herschel-Bulkley behavior and the observed local behavior at the approach of the yield stress due to slow shear flows below the apparent yield stress in the case of a strongly adhesive emulsion.

Macroscopic vs. local rheology of yield stress fluids

From MRI velocimetry we measure the local flow characteristics of a Carbopol gel in a Couette geometry under different inner cylinder rotation velocities. Associated with torque data under the same flow conditions we deduce the local, steady-state, simple shear, constitutive equation of the material within a relatively wide range of shear rates [10 −2; 100 s −1]. Then we show that in this range of shear rates this “local” behaviour is in excellent agreement with the “macroscopic” behaviour deduced from conventional rheometry with cone and plate and Couette geometries. We can conclude that this material effectively behaves as a simple yield stress fluid with a constitutive equation well represented by a Herschel–Bulkley model. This behaviour, likely due to the soft-jammed structure of the fluid, contrasts with that of aggregated systems which exhibit thixotropy and shear-banding at low shear rates.

Identification of an ER Fluid in Unsteady Flow with Random Electric Field and Solidification

An identification procedure to simultaneously determine electrorheological (ER) and viscous characteristics of an ER fluid is presented. The analysis is performed under unsteady flow conditions with randomly varying electric field and intermittent solidification of the fluid. Tests conducted using a standard viscometer and cylindrical couette geometry indicate that there is some interaction between viscous and ER effects and that some residual structuring persists in the fluid after removal of the electric field.

Shear Rate Corrections for Herschel-Bulkley Fluids in Couette Geometry

AbstractA methodology is presented to invert the flow equation of a Herschel-Bulkley fluid in Couette concentric cylinder geometry, thus enabling simultaneous computation of the true shear rates, γ̇HB, and of the three Herschel-Bulkley rheological parameters. The errors made when these rheological parameters are computed using Newtonian shear rates, γ̇N, as it is normal practice by research and industry personnel, can then be estimated. Quantification of these errors has been performed using narrow gap viscometer data from literature, with most of them taken with oil-field rheometers. The results indicate that significant differences exist between the yield stress and the flow behavior index computed using γ̇HB versus the parameters obtained using γ̇N and this is an outcome of the higher γ̇HB values. Predicted true shear rates and rheological parameters are in very good agreement with results reported by other investigators, who have followed different approaches to invert the flow equation, both for yield-pseudoplastic and power-law fluids.

Stochastic dynamics of a sheared granular medium

We experimentally investigate the response of a sheared granular medium in a Couette geometry. The apparatus exhibits the expected stick-slip motion and we probe it in the very intermittent regime resulting from low driving. Statistical analysis of the dynamic fluctuations reveals notable regularities. We observe a possible stability property for the torque distribution, reminiscent of the stability of Gaussian independent variables. In this case, however, the variables are correlated and the distribution is skewed. Moreover, the whole dynamical intermittent regime can be described with a simple stochastic model, finding good quantitative agreement with the experimental data. Interestingly, a similar model has been previously introduced in the study of magnetic domain wall motion, a source of Barkhausen noise. Our study suggests interesting connections between different complex phenomena and reveals some unexpected features that remain to be explained.

Ultrasound velocimetry in a shear-thickening wormlike micellar solution: Evidence for the coexistence of radial and vorticity shear bands

We carried out pointwise local velocity measurements on 40 mM cetylpyridinium chloride-sodium salicylate (CPyCl-NaSal) wormlike micellar solution using high-frequency ultrasound velocimetry in a Couette shear cell. The studied wormlike solution exhibits Newtonian, shear-thinning and shear-thickening rheological behavior in a stress-controlled environment. Previous rheology, flow visualization and small-angle light/neutron scattering experiments in the shear-thickening regime of this system showed the presence of stress-driven alternating transparent and turbid rings or vorticity bands along the axis of the Couette geometry. Through local velocity measurements we observe a homogeneous flow inside the 1mm gap of the Couette cell in the shear-thinning (stress-plateau) region. Only when the solution is sheared beyond the critical shear stress (shear-thickening regime) in a stress-controlled experiment, we observe inhomogeneous flow characterized by radial or velocity gradient shear bands with a highly sheared band near the rotor and a weakly sheared band near the stator of the Couette geometry. Furthermore, fast measurements performed in the shear-thickening regime to capture the temporal evolution of local velocities indicate coexistence of both radial and vorticity shear bands. However the same measurements carried out in shear rate controlled mode of the rheometer do not show such rheological complexity.

On the effect of microstructural changes of blood on energy dissipation in Couette flow

Red blood cell aggregation affects the flow of blood at low shear rates; not only the behaviour of the fluid deviates from its Newtonian characteristics, but, depending on the shearing history of the flow, the non-Newtonian characteristics may be influenced. It is not clear how the time and flow-dependent characteristics of the microstructural network developed in blood affect its mechanical properties. The present study aims to improve understanding of the effect of dynamic flow conditions on microstructural characteristics and consequently on the mechanical properties of the fluid. Viscosity measurements on blood samples from healthy volunteers (H=0.45) were taken with a double-walled Couette rheometric cell, under unsteady and quasi-unsteady flow conditions. The aggregation extent index A(alpha), and the microstructural integrity index A(I) were assessed with an optical shearing system and image analysis. Results showed that energy losses in Couette geometries may depend on the structural integrity of the developed RBC network.

A nonlinear elastic analysis of static stress and lateral pressure coefficient for granular Couette systems

Whether or not the classical theory of elasticity is valid for static granular matter is a basic question of granular physics. We present in this work stress distributions inside hollow cylindrical (Couette geometry) specimens， calculated with the nonlinear elastic equations recently reported in literature. Most of these results can be experimentally measured， and are useful for clarifying the basic question by testing the applicability of the nonlinear elastic equations to granular matter. Moreover they can also be used for analyzing the lateral pressure coefficient of interest in soil engineering.

A rheo-optical study of shear rate and optical anisotropy in wormlike micelles solutions.

The flow behaviour of wormlike micelles solutions composed of the surfactant cetylpyridinium chloride (CPCl) and counter-ion sodium salicylate (NaSal) at a molar ratio [CPCl]/[NaSal] = 2 in brine [NaCl] = 0.5 M in a cylindrical Couette geometry was examined using homodyne PCS and ellipsometry. Homodyne PCS was used to profile local shear rate and ellipsometry to concurrently profile local optical anisotropy of the fluid. Shear thinning was observed and was correlated to an increase in turbidity and a breakdown in the stress-optic law. A stress plateau observed in mechanical measurements was correlated with the partitioning of the fluid into regions of low shear rate/low turbidity/high birefringence and high shear rate/high turbidity/low birefringence. The partitioning observed was inconsistent with a simple interpretation of the lever rule.

Boundary Slip and Surface Interaction: A Lattice Boltzmann Simulation

The factors affecting slip length in Couette geometry flows are analysed by means of a two-phase mesoscopic lattice Boltzmann model including non-ideal fluid-fluid and fluid-wall interactions. The main factors influencing the boundary slip are the strength of interactions between fluid-fluid and fluid-wall particles. Other factors, such as fluid viscosity, bulk pressure may also change the slip length. We find that boundary slip only occurs under a certain density (bulk pressure). If the density is large enough, the slip length will tend to zero. In our simulations, a low density layer near the wall does not need to be postulated a priori but emerges naturally from the underlying non-ideal mesoscopic dynamics. It is the low density layer that induces the boundary slip. The results may be helpful to understand recent experimental observations on the slippage of micro flows.

Rheology of a Polymer‐Based Hybrid Suspension Composed of Concentrated Poly[(D,L‐lactide)‐co‐glycolide] Solution and Inorganic Salt Particles

Suspensions composed of a solution of a biodegradable polyester in a volatile organic solvent, and solid inorganic particles of size in the order of hundreds of microns have been very important in the fabrication of porous scaffolds in the field of tissue engineering. This article reports the basic rheological investigations of this complex fluid type. A Couette geometry covered by silicon oil was found to be an appropriate geometry to retain stability of the rheological measurements. Suspension viscosity increased with the particle volume fraction, and the extent of the increase was much larger than that predicted by the Einstein suspension equation. Both start-up dynamics at the inception of steady shear and relaxation after an abrupt change of oscillatory shear frequency in the suspension showed significantly different behaviors from those in the associated polymer solution. Particle reorganization upon change of rheological state was anticipated.

In situ small-angle neutron scattering and rheological measurements of shear-induced gelation

The microscopic structure of shear-induced gels for a mixed solution of 2-hydroxyethyl cellulose and nanometer-size spherical droplets has been investigated by in situ small-angle neutron scattering (SANS) with a Couette geometry as a function of shear rate gamma. With increasing gamma, the viscosity increased rapidly at gamma approximately 4.0 s(-1), followed by a shear thinning. After cessation of shear, the system exhibited an extraordinarily large steady viscosity. This phenomenon was observed as a shear-induced sol-gel transition. Real-time SANS measurements showed an increase in the scattering intensity exclusively at low scattering angle region. However, neither orientation of polymer chains nor droplet deformation was detected and the SANS patterns remained isotropic irrespective of gamma. It took about a few days for the gel to recover its original sol state. A possible mechanism of gelation is proposed from the viewpoint of shear-induced percolation transition.

Shear turbulence on a sparse spectral grid

We simulate turbulence in a plane Couette geometry by a spectral method intermediate between full resolution and the complete elimination of small modes common in large eddy simulations. The wave number grid is sparse in spanwise and downstream direction, with a total number of modes proportional to Re(3/4) lnRe. At a Reynolds number of 2000 we could suppress more than 80% of the modes and still obtain a fairly accurate resolution of the boundary layer structures and friction factors. For a wide range of resolutions, the mean velocities are described by logarithmic profiles, with von Karman constant near a value of 0.4.

Couette flow with a bidisperse particle mixture

We investigate the steady-state solutions of granular Couette flows with a bidisperse particle mixture. The Couette geometry allows us to study segregation in a simple nonuniform flow. Two continuum models using kinetic theory are examined, and their results are compared with particle dynamic (PD) simulations. A notable difference between the two models is their treatment of energy partition (equipartition versus nonequipartition). We consider mixtures of particles with different sizes, masses, and densities. For Couette flows, we find that energy equipartition breaks down with an increase in the system inelasticity and the mass ratio. The effect of the size ratio on nonequipartition of granular energy is very small if the two particle species have the same mass. Two forms of segregation are studied in the present work: total solids segregation in the system and solids species segregation. Total solids segregation is related to the distribution of the granular energy across the walls. Solids species segregation is due to a competition of three diffusion forces: the thermal diffusion force, the ordinary diffusion force, and the pressure diffusion force. For equal density but different size particles, we observe quantitative differences between the two continuum models, where one model predicts a much greater degree of both total solids and solids species segregation than the other model. For equal size but different mass particles, we observe qualitative differences between the models where one model and PD simulations predict a segregation transition based on the particle mass, which is not seen in the other model for the conditions we have examined.

Is the constitutive relation for entangled polymers monotonic?

The dynamic and steady state behavior of highly entangled polybutadiene solutions has been studied in shearing flow using high-spatial-resolution particle tracking velocimetry. In Couette geometry, the velocity profile is approximately linear upon the imposition of a step shear rate, but becomes significantly curved at later times, and attains the steady shape only after more than 100 strain units. In steady state, local shear rate varies smoothly across the gap and there is no shear banding. The constitutive relation is constructed from local stress and local shear rate extracted from velocity profiles. This procedure is not affected by the common problems of slip and edge instabilities as encountered with cone and plate geometry. The constructed constitutive curve is clearly monotonic for all tested solutions with entanglement numbers up to 47, notwithstanding a local power law index in the stress plateau as small as 0.01. The slope of the stress plateau is sensitive to both the chain polydispersity and entanglement number. Transient shear banding was observed under imposition of step shear in cone and plate geometry. This banding, however, disappears at longer times, which again confirms a monotonic steady state constitutive relation.

Rheological characterisation of starch based food products under unsteady temperature conditions and high heating rate

In order to simulate a thermal process, rheological measurements under unsteady temperature conditions at high heating and cooling rate were performed. A simple thermal model was established in a Couette geometry (concentric cylinders). This model takes into account the temperature gradient in the gap which is a function of heating rate and the time response of the system. Temperature gradient was used to explain observed rheological behaviour. The model was validated using Newtonians fluids (glycerol and sucrose solution (60% w/w )) as well as Non Newtonians fluids (gelatinised starch), where their thermal dependency is well known. The approach developed in this work was used to follow the rheological changes generated by starch gelatinisation during heat treatment.

Aging and solid or liquid behavior in pastes

We carried out systematic creep tests after different times of rest and over sufficiently long times with pasty materials of various internal structures in a Couette geometry. From an analysis of the data taking into account the inertia of the system and the heterogeneous distribution of stress, we show that: (i) for a stress below the yield stress these materials remain solid but undergo residual, irreversible deformations over long time which exhibit some trends typical of aging in glassy systems; (ii) as a result of thixotropy (or aging) in the solid regime the elastic modulus increases logarithmically with the time of rest; (iii) in the liquid regime the effective behavior of the material can be well represented by a truncated power-law model; (iv) a fundamental parameter of the solid-liquid transition is a critical effective shear rate (associated with the yield stress) below which the material cannot flow steadily.

Rheological aspects of dense lignite–water suspensions; structure development on consecutive flow loops

Aspects of dense lignite–water slurries (LWS) rheology were investigated using controlled stress and controlled strain rheometers with parallel disks and Couette geometries. During the preparation of the slurries, the achieved solids volume fractions were up to 0.425 and the particle size distributions were polydispersed with sizes up to 300 μm. In the ascending parts of consecutive flow loops, a slope transition of the flow curve was observed and studied in relation to the solids volume fraction. The obtained results with the different geometries and rheometers were qualitatively the same. By following the model proposed by Cheng (Rheol Acta 42:372–382, 2003) for thixotropic fluids, and taking into account the yield stress appearance, a suitable correlation for LWS is proposed, which is consistent with the experimental flow curves.