Showing papers in "Journal of Non-newtonian Fluid Mechanics in 2014"

Yield stress fluid flows: A review of experimental data

Abstract: Yield stress fluids are encountered in a wide range of applications: toothpastes, cements, mortars, foams, muds, mayonnaise, etc. The fundamental character of these fluids is that they are able to flow (i.e., deform indefinitely) only if they are submitted to a stress above some critical value. Otherwise they deform in a finite way like solids. The flow characteristics of such materials are difficult to predict as they involve permanent or transient solid and liquid regions that are generally hard to locate a priori. Here we review the present state of the art as it appears from experimental data for flows of simple (non-thixotropic) yield stress fluids under various conditions, viz., uniform flows in straight channels or rheometrical geometries, complex stationary flows in channels of varying cross-section such as extrusion, expansion, flow through a porous medium, transient flows such as flows around obstacles, spreading, spin-coating, squeeze flow, and elongation. The effects of surface tension, confinement, and secondary flows are also reviewed. We focus especially on experimental work identifying internal flow characteristics that can be compared with numerical predictions. It is shown in particular that: (i) deformations in the solid regime can play a critical role in transient flows; (ii) the yield character is not apparent in the flow field when the boundary conditions impose large deformations; (iii) the yield character is lost in secondary flows.

Effect of rheological models on the hemodynamics within human aorta: CFD study on CT image-based geometry

Abstract: The pulsatile blood flow through human aortic arch and three major branches are computationally studied to investigate the effect of blood rheology on the hemodynamic parameters. The human aorta model is reconstructed from the computed tomography (CT) images of specific patient. The results of nine non-Newtonian (Casson, K-L, Modified Casson, Carreau, Carreau-Yasuda, Cross, Power-law, Modified Power-law, and Generalized Power-law) models are analyzed and compared with those of Newtonian model and reveal very interesting hemodynamic features for each model. Among the applied non-Newtonian models, the Cross model displays significantly different distribution of wall shear stress (WSS) and velocity field through the aorta at diastole. Comparing the local shear stress magnitude in three branches at different critical cardiac instants shows that the shear thinning nature of blood can slightly influence WSS at diastole, in all branches. The effect of blood rheology appears clearly in the brachiocephalic and carotid branches, at peak systole. In the high-shear rate zones, the lowest WSS is estimated by the Carreau model. The Newtonian model has close prediction to the Cross model at peak systole. The power law model predictions remain the nearest to those of the Carreau model along the cardiac cycle.

Unsteady laminar flows of a Carbopol® gel in the presence of wall slip

Abstract: We present a comparative experimental study of unsteady laminar flows of a yield stress shear thinning fluid (Carbopol ® 980) in two distinct configurations: a parallel plate rheometric flow and a pressure driven pipe flow. Consistently with the observations in the case of the rheometric flow, the in situ characterisation of the unsteady pipe flow reveals three distinct flow regimes: solid (plug-like) , solid–fluid and fluid . In both configurations and as the flow forcing is gradually increased, the yielding emerges via an irreversible transition. The irreversibility of the deformation states is coupled to the wall slip phenomenon. Particularly, the presence of wall slip nearly suppresses the scaling of the deformation power deficit associated to the rheological hysteresis with the rate at which the material is forced. An universal scaling of the slip velocity with the wall velocity gradients and a slip length which is independent on the degree of the flow steadiness is observed in the pipe flow.

Cessation of viscoplastic Poiseuille flow with wall slip

Abstract: We solve numerically the cessation of axisymmetric Poiseuille flow of a Herschel–Bulkley fluid under the assumption that slip occurs along the wall. The Papanastasiou regularization of the constitutive equation is employed. As for the slip equation, a power-law expression is used to relate the wall shear stress to the slip velocity, assuming that slip occurs only above a critical wall shear stress, known as the slip yield stress. It is shown that, when the latter is zero, the fluid slips at all times, the velocity becomes and remains uniform before complete cessation, and the stopping time is finite only when the slip exponent s 1, the decay is much slower. Analytical expressions of the decay of the flat velocity for any value of s and of the stopping time for s < 1 are also derived. Using a discontinuous slip equation with slip yield stress poses numerical difficulties even in one dimensional time-dependent flows, since the transition times from slip to no-slip and vice versa are not known a priori. This difficulty is overcome by regularizing the slip equation. The numerical results showed that when the slip yield stress is non-zero, slip ceases at a finite critical time, the velocity becomes flat only in complete cessation, and the stopping times are finite, in agreement with theoretical estimates.

Power-law fluid flow and heat transfer in a channel with a built-in porous square cylinder: Lattice Boltzmann simulation

Abstract: The lattice Boltzmann method (LBM) has been established as an efficient technique for solving a fluid dynamics problem in a complex porous medium. In this paper, the power-law fluid flow and heat transfer are studied numerically in a channel partially filled with an anisotropic porous block for three power-law indices, n = 0.8, 1 and 1.2. Combined pore level simulations of flow and heat transfer are performed for a 2D channel that is partially filled with square obstacles in both ordered and random arrangements. A step by step verification procedure is taken to ensure the accuracy and the physical correctness of the numerical simulation. The effects of the different arrangements of obstacles, Reynolds number, power index n, blockage ratio and porosity on the velocity and temperature profiles are studied. The local and averaged Nusselt numbers are also calculated on the channel walls. It is found that pseudo plastic fluids generate the highest heat transfer rate for all configurations of obstacles. For constant porosity and block size, the increase is noticeable when the arrangement of square obstacles is random. Also by decreasing the porosity, the value of averaged Nusselt number is increased. Two correlations for regular and random obstacle arrangements between the Nusselt number, Reynolds number, power index n, blockage ratio and porosity are presented. The values of averaged Nusselt number with the respective confidence interval are also reported in the case of random arrangement of obstacles.

Measurement of yield stress of cement pastes using the direct shear test

Abstract: The direct shear test is widely used in soil mechanics to determine the cohesion (C) and angle of internal friction (ϕ). This paper aims to assess the suitability of this test to evaluate yield stress (τ0) of cement pastes having different flowability levels. Special emphasis was taken to eliminate friction between shear boxes, thus allowing the measurement of C ranging from several kPa to just a few Pa. Tests have shown that the maximum shearing stress prior to failure is not a material constant, but rather varies with the normal stress as per the Mohr–Coulomb law. Good correlations between C and τ0 determined using the vane method were established. Nevertheless, the vane method was found to over-estimate τ0 when the blades are positioned inside the specimen, particularly for cohesive materials.

Electroosmotic flow of a power-law fluid in a non-uniform microchannel

Abstract: An analytical model is presented for electrokinetic flow of a power-law fluid through a slit channel with gradually varying channel height and wall potential. With the near-wall depletion effect taken into account, the present model is based on the lubrication approximation and the use of the Helmholtz–Smoluchowski slip boundary condition. It is found that interaction between the wall undulation and the wall potential modulation, under the combined action of hydrodynamic and electric forcings, may give rise to a rich set of nonlinear behaviors for flow of a non-Newtonian fluid in the channel. In particular, the linear superposition of flow components due separately to the two forcings is found to work only for a strictly uniform channel; non-uniformity in channel height or wall potential distribution will spoil such linearity.

Influence of rheological properties on air-blast atomization of coal water slurry

Abstract: An experimental investigation is conducted to determine the effect of rheological properties (viscoelasticity) on the air-blast atomization of coal water slurry. In air-blast atomization, aerodynamic force causes the liquid to deform and breakup. To observe breakup morphology of coal water slurry atomization, a high speed digital camera is used at various operating conditions. In this test, primary atomization is the condition that a cylindrical liquid jet surrounded by a coaxial annular airflow, and secondary atomization is the process that a liquid drop encounters a continuous air jet. The results show that the viscoelasticity of coal water slurry has great influence on the breakup morphology, breakup length, frequency characteristics. The corresponding correlations for these characteristics also are developed.

Performance of the finite volume method in solving regularised Bingham flows: Inertia effects in the lid-driven cavity flow

Abstract: We extend our recent work on the creeping flow of a Bingham fluid in a lid-driven cavity, to the study of inertial effects, using a finite volume method and the Papanastasiou regularisation of the Bingham constitutive model (Papanastasiou, 1987) [7]. The finite volume method used belongs to a very popular class of methods for solving Newtonian flow problems, which use the SIMPLE algorithm to solve the discretised set of equations, and have matured over the years. By regularising the Bingham constitutive equation it is easy to extend such a solver to Bingham flows since all that this requires is to modify the viscosity function. This is a tempting approach, since it requires minimum programming effort and makes available all the existing features of the mature finite volume solver. On the other hand, regularisation introduces a parameter which controls the error in addition to the grid spacing, and makes it difficult to locate the yield surfaces. Furthermore, the equations become stiffer and more difficult to solve, while the discontinuity at the yield surfaces causes large truncation errors. The present work attempts to investigate the strengths and weaknesses of such a method by applying it to the lid-driven cavity problem for a range of Bingham and Reynolds numbers (up to 100 and 5000 respectively). By employing techniques such as multigrid, local grid refinement, and an extrapolation procedure to reduce the effect of the regularisation parameter on the calculation of the yield surfaces (Liu et al., 2002) [55], satisfactory results are obtained, although the weaknesses of the method become more noticeable as the Bingham number is increased.

Experimental investigation of the Rayleigh–Bénard convection in a yield stress fluid

Abstract: An experimental study of the Rayleigh–Benard convection in a yield stress fluid (Carbopol® 980) uniformly heated from below in a rectangular cavity with high aspect ratio is presented. By combined integral measurements of the temperature difference between two parallel plates and the local flow velocity within a wide range of heating powers P two distinct regimes are observed. For heating powers smaller then a critical value P c a purely conductive regime is observed. A gradual increase of the heating power beyond this onset reveals a convective regime manifested through a nonlinear dependence of the temperature difference between plates on the heating power. Simultaneously with this, local measurements of the flow fields reveal a nonlinear increase of the roll pattern amplitude. Regardless the concentration of Carbopol® and in spite of a significant shear thinning behaviour, the Rayleigh–Benard convection in the Carbopol® gel is found to emerge as an imperfect bifurcation that can be correctly modelled by the Landau theory of phase transitions. A critical slowing down phenomenon is observed corresponding to the onset of convection. The scaling laws of the convective onset P c and of the corresponding temperature difference Δ T c with the relevant material properties are discussed. The onset of the instability can be described in terms of a critical yield number rather than in terms of a critical Rayleigh number. The paper closes with a comparison of our findings with existing previous works.

Hydrodynamic shear thickening of particulate suspension under confinement

Abstract: We study the rheology of dense suspensions of non-Brownian repulsive particles. The suspensions consist of two-dimensional discoidal particles confined by walls orthogonal to the shear gradient direction and are simulated by the method of smoothed particle hydrodynamics. The strength of hydrodynamic shear thickening is primarily determined by the distribution of hydrodynamic clusters formed during shear flow while confinement plays a geometrical role and indirectly affects viscosity. Under strong confinement a percolating network of clusters develops into a jamming structure at high shear rate and as a result, the viscosity increases substantially. Extrapolating the viscosity to the limit of very weak confinement shows that confinement is essential to observe hydrodynamic shear thickening in these non-Brownian suspensions.

A simple thixotropic–viscoelastic constitutive model produces unique signatures in large-amplitude oscillatory shear (LAOS)

Abstract: Here we demonstrate that a simple thixotropic constitutive model produces unique signatures in large-amplitude oscillatory shear (LAOS) distinct from other nonlinear mechanisms and separate from viscoelastic time dependence. Our approach is to define the simplest model that produces the essential features of both thixotropy and viscoelasticity, a structure-parameter evolution equation coupled to a three-element fluid (Jeffreys model). In strain-controlled LAOS, the response of the model depends on four dimensionless parameters: two deformation parameters (Deborah and Weissenberg) and two material parameters (the ratio of viscoelastic to thixotropic timescales and the ratio of infinite shear viscosity to aggregate viscosity). We present numerical results for the full nonlinearities across this four-dimensional parameter space. The dimensionality is reduced by considering the asymptotically-nonlinear regime (Weissenberg number expansion). We present the first analytical solution for a thixotropic model in this asymptotically-nonlinear LAOS regime, which produces distinct power function scaling not predicted by other known solutions to nonlinear viscoelastic models. With this separation of thixotropic from viscoelastic timescales, this canonical model predicts that short thixotropic timescales can be experimentally observed with nonlinear oscillatory deformation. This is relevant to recent suggestions in distinguishing thixotropic versus “simple” yield stress fluids with no experimentally observable thixotropy.

Dissipative particle dynamics simulation of droplet suspension in shear flow at low Capillary number

Abstract: The dissipative particle dynamics (DPD) method is used to simulate droplet suspension. The deformation of a single droplet is first studied to validate the method and a good agreement with previous theoretical, numerical and experimental results is obtained. Droplet-droplet interaction is calibrated by simulating the process of two droplets collision. A larger repulsion force is imposed between particles from different droplet to prevent two droplets from coalescing. Dilute to semi-dilute emulsions are simulated with more than a hundred droplets suspended in another immiscible fluid. Shear thinning and non-zero normal stress differences are captured in the simulations. These phenomena are related with the mean droplet deformation parameter and mean inclination angle. The droplet deformation contributes to the increasing of suspension viscosity. Decreasing the inclination angle aligns the droplets more with the flow direction, contributing more to shear thinning. Fluid inertia increases the suspension viscosity. A good agreement is achieved between our zero shear viscosity results and previous model/experimental work.

Numerical simulation of the viscoelastic flow in a three-dimensional lid-driven cavity using the log-conformation reformulation in OpenFOAM®

Abstract: In this work we implement the log-conformation reformulation for viscoelastic constitutive equations as proposed by Fattal and Kupferman (2004) in the open-source CFD-software OpenFOAM®, which is based on the collocated finite-volume method (FVM). The implementation includes an efficient eigenvalue and eigenvector routine and the algorithm finally is second-order accurate both in time and space, when using it in conjunction with an adequate convection scheme such as the CUBISTA scheme (Alves et al., 2003). The newly developed solver is first validated with the analytical solution for a startup Poiseuille flow of a viscoelastic fluid and subsequently applied to the three-dimensional and transient simulation of a lid-driven cavity flow, in which the viscoelastic fluid is modeled by the Oldroyd-B constitutive equation. The results are presented for both the first-order upwind scheme and the CUBISTA scheme on four hexahedral meshes of different size in order to check for mesh convergence of the results and a tetrahedral mesh to show the applicability to unstructured meshes. The results obtained for various values of the Weissenberg number are presented and discussed with respect to the location of the primary vortex center, streamline patterns and velocity and stress profiles besides others. We are able to obtain sufficiently mesh converged results for Weissenberg numbers, which would have been impossible to obtain without use of the log-conformation reformulation. An upper limit for the Weissenberg number in terms of stability could not be found.

The effect of a variable plastic viscosity on the restart problem of pipelines filled with gelled waxy crude oils

Abstract: The effect of a variable plastic viscosity is numerically investigated on the success of the restart operation for a pipeline filled with fully-gelled waxy crude oil. To investigate the separate effects of structure- and shear-dependent viscosity, waxy crude oil is assumed to obey the Houska rheological model. In order to precisely capture the shape and position of the yielding surface, a variational approach is used to formulate the restart problem for this particular fluid model. The numerical results show that a variable plastic viscosity has a significant effect on the restart operation. For certain set of parameters the restart operation is shown to fail if the plastic viscosity is constant but is successful if the plastic viscosity is (moderately) structure-dependent. However, the time needed by the liquefied gel to discharge from the pipe outlet section is increased if the plastic viscosity is structure-dependent. Surprisingly, the shear-thinning behavior of waxy crude oil is predicted to lower the (steady) flow rate even when the restart is successful.

Inkjet printing of weakly elastic polymer solutions

Abstract: Fluid assessment methods, requiring small volumes and avoiding the need for jetting, are particularly useful in the design of functional fluids for inkjet printing applications. With the increasing use of complex (rather than Newtonian) fluids for manufacturing, single frequency fluid characterisation cannot reliably predict good jetting behaviour, owing to the range of shearing and extensional flow rates involved. However, the scope of inkjet fluid assessments (beyond achievement of a nominal viscosity within the print head design specification) is usually focused on the final application rather than the jetting processes. The experimental demonstration of the clear insufficiency of such approaches shows that fluid jetting can readily discriminate between fluids assessed as having similar LVE characterisation (within a factor of 2) for typical commercial rheometer measurements at shearing rates reaching 104 rad s−1. Jetting behaviour of weakly elastic dilute linear polystyrene solutions, for molecular weights of 110–488 kDa, recorded using high speed video was compared with recent results from numerical modelling and capillary thinning studies of the same solutions. The jetting images show behaviour ranging from near-Newtonian to “beads-on-a-string”. The inkjet printing behaviour does not correlate simply with the measured extensional relaxation times or Zimm times, but may be consistent with non-linear extensibility L and the production of fully extended polymer molecules in the thinning jet ligament. Fluid test methods allowing a more complete characterisation of NLVE parameters are needed to assess inkjet printing feasibility prior to directly jetting complex fluids. At the present time, directly jetting such fluids may prove to be the only alternative.

Influence of surface properties on the flow of a yield stress fluid around spheres

Abstract: This experimental analysis addresses the non-inertial flow of a yield stress fluid around spheres. The analysis was conducted for two spheres with different surface conditions. Friction laws at their interface have been determined. For the bulk behaviour of the fluid, elastoviscoplasticity and viscoelasticity have also been characterised. The resulting parameters have been used to analyse the experimental results. The drag coefficient was determined with respect to hydrophobic properties and surface roughness. From this determination, a criterion enabling the prediction of a sphere’s stability in a yield stress fluid as a function of the fluid/sphere interfacial properties has been proposed. The kinematic fields have also been measured by PIV. These fields enable the quantification of the velocity fields around the spheres according to the adherence conditions of the fluid. This quantification has enabled the characterisation of the extent and the shape of sheared and static rigid zones. Moreover, the calculations of the drag force due to the shear stresses and the drag force due to the normal stresses have revealed the preponderance of the latter in the total drag force.

Fully-implicit log-conformation formulation of constitutive laws

Abstract: Subject of this paper is the derivation of a new constitutive law in terms of the logarithm of the conformation tensor that can be used as a full substitute for the 2D governing equations of the Oldroyd-B, Giesekus and other models. One of the key features of these new equations is that – in contrast to the original log-conf equations given by Fattal and Kupferman (2004) – these constitutive equations combined with the Navier–Stokes equations constitute a self-contained, non-iterative system of partial differential equations. In addition to its potential as a fruitful source for understanding the mathematical subtleties of the models from a new perspective, this analytical description also allows us to fully utilize the Newton–Raphson algorithm in numerical simulations, which by design should lead to reduced computational effort. By means of the confined cylinder benchmark we will show that a finite element discretization of these new equations delivers results of comparable accuracy to known methods.

Wormlike Micellar Solutions: III. VCM Model Predictions in Steady and Transient Shearing Flows

Abstract: The two species, scission/reforming Vasquez–Cook–McKinley (VCM) model was formulated to describe the coupling between the viscoelastic fluid rheology and the kinetics of wormlike micellar assembly and deformation-induced rupture. The model self-consistently captures the nonlocal effects of stress-induced diffusion and has been studied in various limits for a number of canonical flow fields including Large Amplitude Oscillatory Shear (LAOS), steady and transient extensional flow as well as steady pressure-driven channel flow. However, a complete study of the spatiotemporal model predictions in shearing flow, both with (and without) inertia, and with (or without) the stress-concentration diffusive coupling, has not yet been reported. In this paper we present a comprehensive investigation of the full VCM model in steady and transient shearing flow including inertial and diffusive (non-local) effects. The consequences of varying the model parameters, the effect of the start-up ramp rate, and the role of geometry on the steady state flow curve are each investigated. As a result of the onset of shear-banding and nonlocal effects in the velocity, stress and concentration profiles, we show that the measured rheological properties in a wormlike micellar solution described by the VCM model can depend on the initial ramp rate as well as specific details of the geometry such as the length scale of the rheometric fixture chosen and its curvature. The complete time evolution of the rheological response at high Deborah numbers is examined, from the initial formation of inertial waves through nonlinear overshoots in the viscoelastic stresses, shear band formation (and elastic recoil in the local velocity), to the long time diffusion-mediated approach to a final steady state.

DNS and LES with an extended Smagorinsky model for wall turbulence in non-Newtonian viscous fluids

Abstract: To develop better computer modeling methods for wall turbulence in non-Newtonian viscous fluids, we performed direct numerical simulations (DNS) and large eddy simulations (LES) of turbulent channel flow of various non-Newtonian fluids, with viscosity described by the power-law model and the Casson model. We focused on low-Reynolds-number wall turbulence of non-Newtonian viscous fluid close to Newtonian fluid to observe the deviation of the turbulence structures of fully developed turbulent flow near a wall from Newtonian fluid. From the results of the DNS, we found that, as for Newtonian fluid, the turbulence structures of these viscous fluids could be generally normalized but with locally varying viscosity. Performing the LES with the Smagorinsky model as a subgrid scale (SGS) model extended according to the results of the DNS, we evaluated the reliability of the extended SGS model. For the various non-Newtonian viscous fluids considered, the mean velocity profiles obtained by these LESs with the extended model rather than the LES with the standard model corresponded closely with those obtained by DNS. Consequently, we demonstrated that the Smagorinsky model of turbulent flows for non-Newtonian viscous fluid can be treated universally via spatial scaling of the locally varying viscosity.

A new viscoelastic benchmark flow: Stationary bifurcation in a cross-slot

Abstract: In this work we propose the cross-slot geometry as a candidate for a numerical benchmark flow problem for viscoelastic fluids. Extensive data of quantified accuracy is provided, obtained via Richardson extrapolation to the limit of infinite refinement using results for three different mesh resolutions, for the upperconvected Maxwell, Oldroyd-B and the linear form of the simplified Phan-Thien–Tanner constitutive models. Furthermore, we consider two types of flow geometry having either sharp or rounded corners, the latter with a radius of curvature equal to 5% of the channel’s width. We show that for all models the inertialess steady symmetric flow may undergo a bifurcation to a steady asymmetric configuration, followed by a second transition to time-dependent flow, which is in qualitative agreement with previous experimental observations for low Reynolds number flows. The critical Deborah number for both transi

Viscoplastic Poiseuille flow in a rectangular duct with wall slip

Abstract: We solve numerically the Poiseuille flow of a Herschel–Bulkley fluid in a duct of rectangular cross section under the assumption that slip occurs along the wall following a slip law involving a non-zero slip yield stress. The constitutive equation is regularized as proposed by Papanastasiou. In addition, we propose a new regularized slip equation which is valid uniformly at any wall shear stress level by means of another regularization parameter. Four different flow regimes are observed defined by three critical values of the pressure gradient. Initially no slip occurs, in the second regime slip occurs only in the middle of the wider wall, in the third regime slip occurs partially at both walls, and eventually variable slip occurs everywhere. The performance of the regularized slip equation in the two intermediate regimes in which wall slip is partial has been tested for both Newtonian and Bingham flows. The convergence of the results with the Papanastasiou regularization parameter has been also studied. The combined effects of viscoplasticity and slip are then investigated. Results are presented for wide ranges of the Bingham and slip numbers and for various values of the power-law exponent and the duct aspect ratio. These compare favorably with available theoretical results and with numerical results in the literature obtained with both regularization and augmented Lagrangian methods.

Drag increase at the very start of drag reducing flows in a rotating cylindrical double gap device

Abstract: In this note we present some results concerning the time required for turbulent structures to achieve their steady state, called here the developing time. Notably, there is a drag increase at the very start of the test. Such a drag increase is strongly dependent on the concentration, molecular weight, temperature, Reynolds number, and molecule conformation before the test start-up. The analysis conducted here improves the understanding of the way drag reduction evolves over time, which was considered in Pereira et al. (2013).

An integrated lattice Boltzmann and finite volume method for the simulation of viscoelastic fluid flows

Abstract: A novel integrated scheme for modeling incompressible polymer viscoelastic fluid flows is proposed. Lattice Boltzmann method (LBM) is incorporated into finite volume method (FVM) to solve the incompressible Navier–Stokes equations and the constitutive equation respectively, and is implemented using open source CFD toolkits to predict nonlinear dynamics of polymer viscoelastic fluid flows. The hybrid numerical scheme inherits the efficiency and scalability of LBM and maintains the accuracy and generality of FVM. It has been critically validated using the Oldroyd-B model and linear PTT model under Poiseuille flow, Taylor-Green vortex flow and 4 : 1 abrupt planar contraction flow, respectively. The results from the integrated scheme have good agreement with the analytical solutions and the numerical results of other FVM schemes in previous publications.

Migration and chaining of noncolloidal spheres suspended in a sheared viscoelastic medium. Experiments and numerical simulations

Abstract: Migration and chaining of noncolloidal spheres in a worm-like micellar, viscoelastic solution under shear flow have been studied both experimentally and by numerical simulations. The microstructure dynamics have been experimentally investigated in the flow-gradient and in the flow-vorticity planes. 2D simulations in the flow-gradient plane have been performed for the same geometry, and with a proper selection for the constitutive equation of the suspending liquid. Experimental results show the formation of particle chains in the bulk, along with migration of a considerable fraction of spheres to the walls. At long times, chains in the bulk are stable, and cross-flow migration of individual spheres is suppressed. Numerical simulations with a standard viscoelastic constitutive equation (Giesekus fluid) reproduce the same phenomena observed experimentally, both in terms of fast particle migration to the wall and bulk chain stability. No alignment is, instead, found in simulations with a constant-viscosity, elastic fluid (Oldroyd-B model), in agreement with previous experimental results with Boger fluids.

Simulations of an elastic particle in Newtonian and viscoelastic fluids subjected to confined shear flow

Abstract: The deformation and cross-streamline migration of an initially spherical neo-Hookean elastic particle suspended in confined shear flow of Newtonian and Giesekus viscoelastic fluids is studied through 3D arbitrary Lagrangian Eulerian finite element method numerical simulations. In both a Newtonian and a Giesekus liquid, when suspended in a symmetric position with respect to the walls of the flow cell, the particle deforms until reaching a steady ellipsoid-like shape, with a fixed orientation with respect to the flow direction. The dependences of such deformation and orientation on the flow strength, the geometric confinement, and the rheological properties of the suspending liquid are investigated. If the particle is initially closer to a wall of the channel than to the other, it also migrates transversally to the flow direction. In a Newtonian liquid, migration is always towards the center plane of the channel. In a Giesekus viscoelastic liquid, the migration direction depends on the competition between the elastic and the viscous forces arising in the suspending fluid; in a certain range of constitutive parameters, an ‘equilibrium vertical position’ in between the mid plane and the (upper/lower) wall of the channel is found, which acts as an attractor for particle migration.

Stability of the boundary layer on a rotating disk for power-law fluids

Abstract: The stability of the flow due to a rotating disk is considered for non-Newtonian fluids, specifically shear-thinning fluids that satisfy the power-law (Ostwald-de Waele) relationship. In this case the basic flow is not an exact solution of the Navier–Stokes equations, however, in the limit of large Reynolds number the flow inside the three-dimensional boundary layer can be determined via a similarity solution. An asymptotic analysis is presented in the limit of large Reynolds number. It is shown that the stationary spiral instabilities observed experimentally in the Newtonian case can be described for shear-thinning fluids by a linear stability analysis. Predictions for the wavenumber and wave angle of the disturbances suggest that shear-thinning fluids may have a stabilising effect on the flow.

Effects of elasticity on the nonlinear collective dynamics of self-propelled particles

Abstract: Some rodlike self-propelled particles form collective structures because of hydrodynamic interactions characterized by large-scale self-driven flows. Using a continuum fluid dynamics approach, the effects of elasticity on the pseudo-steady state dynamics of the collective patterns are studied. The Oldroyd-B and Jeffery constitutive models are used to represent the suspending fluid as examples of non shear-thinning viscoelastic fluids. A coupling between the fluid and particle dynamics leads to self-driven structures that are shorter and evolve irregularly in comparison with the long periodic correlated structures in Newtonian fluids. Inspired by turbulent drag reduction by polymers, a mechanism has been suggested for how elasticity restricts the formation of the self-driven collective structures. Viscoelasticity forces the system to transition from an “active” state to a “suppressed” state.

On a modified non-singular log-conformation formulation for Johnson–Segalman viscoelastic fluids

Abstract: A modified log-conformation formulation of viscoelastic fluid flows is presented in this paper. This new formulation is non-singular for vanishing Weissenberg numbers and allows a direct steady numerical resolution by a Newton method. Moreover, an exact computation of all the terms of the linearized problem is provided. The use of an exact divergence-free finite element method for velocity–pressure approximation and a discontinuous Galerkin upwinding treatment for stresses leads to a robust discretization. A demonstration is provided by the computation of steady solutions at high Weissenberg numbers for the difficult benchmark case of the lid driven cavity flow. Numerical results are in good agreement, qualitatively with experiment measurements on real viscoelastic flows, and quantitatively with computations performed by others authors. The numerical algorithm is both robust and very efficient, as it requires a low mesh-invariant number of linear systems resolution to obtain solutions at high Weissenberg number. An adaptive mesh procedure is also presented: it allows representing accurately both boundary layers and the main and secondary vortices.

A new constitutive model for worm-like micellar systems – Numerical simulation of confined contraction–expansion flows

Abstract: This hybrid finite element/volume study is concerned with the modelling of worm-like micellar systems, employing a new micellar thixotropic constitutive model with viscoelasticity within network-structure construction–destruction kinetics. The work focuses on steady-state solutions for axisymmetric, rounded-corner, 4:1:4 contraction–expansion flows. This has importance in industrial and healthcare applications such as in enhanced oil-reservoir recovery. Material functions for the micellar models (time-dependent, thixotropic) have been fitted to match two different extensional configurations of the exponential Phan-Thien/Tanner (PTT) model (rubber network-based, non-thixotropic). This covers mild and strong-hardening response, and re solvent fraction, highly-polymeric (β = 1/9) and solvent-dominated (β = 0.9) fluids. Solution results are described through normalised Excess Pressure Drop (EPD), vortex intensity and stream function, stress (N1 and N2), and f-functional data. EPD predictions with the new micellar models prove to be consistent (at low rates, some rising) with Newtonian results, contrary to the base-reference modified Bautista–Manero (MBM) results. Markedly different vortex intensity trends are found in comparing micellar and EPTT solutions, which correspond with N2 − N1 and f data. In order to address the highly-elastic regime for thixotropic materials, a convoluted approach between EPPT and micellar models has been proposed. Here, numerically stable solutions are reported for impressively large We up to 300 and new vortex structures are revealed.