Showing papers in "Journal of Non-newtonian Fluid Mechanics in 2012"

A critical overview of elasto-viscoplastic thixotropic modeling

Abstract: The literature on thixotropy modeling is reviewed, with particular emphasis on models for yield stress materials that possess elasticity. The various possible approaches that have been adopted to model the different facets of the mechanical behavior of this kind of materials are compared and discussed in detail. An appraisal is given of the advantages and disadvantages of algebraic versus differential stress equations. The thixotropy phenomenon is described as a dynamical system whose equilibrium locus is the flow curve, and the importance of using the flow curve as an input of the model is emphasized. Different forms for the evolution equation for the structure parameter are analyzed, and appropriate choices are indicated to ensure a truthful description of the thixotropy phenomenon.

Analytical solutions for Newtonian and inelastic non-Newtonian flows with wall slip

Abstract: This work presents analytical solutions for both Newtonian and inelastic non-Newtonian fluids with slip boundary conditions in Couette and Poiseuille flows using the Navier linear and non-linear slip laws and the empirical asymptotic and Hatzikiriakos slip laws. The non-Newtonian constitutive equation used is the generalized Newtonian fluid model with the viscosity described by the power law, Bingham, Herschel–Bulkley, Sisko and Robertson–Stiff models. While for the linear slip model it was always possible to obtain closed form analytical solutions, for the remaining non-linear models it is always necessary to obtain the numerical solution of a transcendent equation. Solutions are included with different slip laws or different slip coefficients at different walls.

Laminar Rayleigh-Bénard convection of yield stress fluids in a square enclosure

Abstract: In this study, two-dimensional steady-state simulations of laminar natural convection in square enclosures with differentially heated horizontal walls with the bottom wall at higher temperature have been conducted for yield-stress fluids obeying the Bingham model. Heat and momentum transport are investigated for nominal values of Rayleigh number (Ra) in the range 103–105 and a Prandtl number (Pr) range of 0.1–100. The mean Nusselt number Nu ¯ is found to increase with increasing values of Rayleigh number for both Newtonian and Bingham fluids. However, weaker convective transport in Bingham fluids leads to smaller values of Nu ¯ than that obtained in the case of Newtonian fluids with the same nominal value of Rayleigh number Ra. The mean Nusselt number Nu ¯ decreases with increasing Bingham number in the case of yield stress fluids, and, for large values of Bingham number Bn, the value rapidly approaches to unity ( Nu ¯ = 1.0 ) as thermal conduction dominates the heat transfer. However, this variation in the present configuration is found to be markedly different from the corresponding variation of Nu ¯ with Bn for the same nominal values of Ra and Pr in the differentially-heated vertical sidewall configuration. The effects of Prandtl number have also been investigated in detail and physical explanations are provided for the observed behaviour. Guided by a detailed scaling analysis, new correlations are proposed for the mean Nusselt number Nu ¯ for both Newtonian and Bingham fluids which are demonstrated to satisfactorily capture the correct qualitative and quantitative behaviours of Nu ¯ for the range of Ra, Pr and Bn considered in this analysis.

Polymer degradation of dilute solutions in turbulent drag reducing flows in a cylindrical double gap rheometer device

Abstract: The drag reduction by high molecular weight polymer additives in a turbulent flow is an important phenomenon that has received the attention of a number of researchers. However, the efficiency of those additives is not constant. Turbulence is also responsible for breaking the polymer molecules, decreasing their ability to reduce drag. This degradation phenomenon has recently received its deserved attention in the literature and investigations that take into account the effect of concentration, molecular weight, Reynolds number, and temperature can be found, although these parameters have not yet been explored in very wide ranges. In the present work we investigate this degradation phenomenon for aqueous solutions of two different polymers: Polyacrylamide (PAM) and Polyethylene oxide (PEO), in a cylindrical double gap rheometer device. The dependence of degradation on molecular weight, concentration, temperature, and Reynolds number is analysed for a wide range of these parameters. Our main results are displayed in terms of drag reduction ( DR ). All tests are performed to compute DR for a long period of time including the values obtained from the very beginning of the process. It is shown that DR increases with time until achieving a maximum value before starting to decrease as a consequence of degradation. We also display the results using a relative drag reduction quantity, DR ′, defined as the ratio of the current drag reduction to the maximum one obtained for a non-degraded solution. We propose an alternative decay function that relates DR ′ as a function of the Reynolds number, concentration, molecular weight, and temperature.

Investigation of the effects of various parameters on pressure drop reduction in crude oil pipelines by drag reducing agents

Abstract: In this study, the effects of various parameters on pressure drop reduction caused by adding small amounts of drag reducing polymers has been investigated in crude oil pipelines. In order to make a comprehensive analysis of various operating parameters such as temperature, oil flow rate, pipe diameter, pipe roughness, type of drag reducing agent (DRA), and concentration of DRA, some experiments have been carried out with several concentrations of three different DRAs in four different operating temperatures. The obtained results indicate that the amount of drag reduction increases with temperature, oil flow rate, pipe roughness as well as DRAs concentration. The DRA1 causes the highest drag reduction. Also, the experiments showed that DR% increases with decreasing pipe diameter. Hence, the ability of DRA increases with the relative roughness of pipes.

Shear-induced sedimentation in yield stress fluids

Abstract: Stability of coarse particles against gravity is an important issue in dense suspensions (fresh concrete, foodstuff, etc.). On the one hand, it is known that they are stable at rest when the interstitial paste has a high enough yield stress; on the other hand, it is not yet possible to predict if a given material will remain homogeneous during a flow. Using MRI techniques, we study the time evolution of the particle volume fraction during the flows in a Couette geometry of model density-mismatched suspensions of noncolloidal particles in yield stress fluids. We observe that shear induces sedimentation of the particles in all systems, which are stable at rest. The sedimentation velocity is observed to increase with increasing shear rate and particle diameter, and to decrease with increasing yield stress of the interstitial fluid. At low shear rate (’plastic regime’), we show that this phenomenon can be modelled by considering that the interstitial fluid behaves like a viscous fluid–of viscosity equal to the apparent viscosity of the sheared fluid–in the direction orthogonal to shear. The behavior at higher shear rates, when viscous effects start to be important, is also discussed. We finally study the dependence of the sedimentation velocity on the particle volume fraction, and show that its modelling requires estimating the local shear rate in the interstitial fluid.

Full two-dimensional rapid chute flows of simple viscoplastic granular materials with a pressure-dependent dynamic slip-velocity and their numerical simulations

Abstract: We present a fully two-dimensional, novel Coulomb-viscoplastic sliding model, which includes some basic features and observed phenomena in dense granular flows like the exhibition of a yield strength and a non-zero slip velocity. The interaction of the flow with the solid boundary is modelled by a pressure and rate-dependent Coulomb-viscoplastic sliding law. The bottom boundary velocity is required for a fully two-dimensional model, whereas in classical, depth-averaged models its explicit knowledge is not needed. It is observed in experiments and in the field that in rapid flow of frictional granular material down the slopes even the lowest particle layer in contact with the bottom boundary moves with a non-zero and non-trivial velocity. Therefore, the no-slip boundary condition, which is generally accepted for simulations of ideal fluid, e.g., water, is not applicable to granular flows. The numerical treatment of the Coulomb-viscoplastic sliding model requires the set up of a novel pressure equation, which defines the pressure independent of the bottom boundary velocities. These are dynamically and automatically defined by our Coulomb-viscoplastic sliding law for a given pressure. A simple viscoplastic granular flow down an inclined channel subject to slip or no-slip at the bottom boundary is studied numerically with the marker-and-cell method. The simulation results demonstrate the substantial influence of the chosen boundary condition. The Coulomb-viscoplastic sliding law reveals completely different flow dynamics and flow depth variations of the field quantities, mainly the velocity and full dynamic pressure, and also other derived quantities, such as the bottom shear-stress, and the mean shear-rate, compared to the commonly used no-slip boundary condition. We show that for Coulomb-viscoplastic sliding law observable shearing mainly takes place close to the sliding surface in agreement with observations but in contrast to the no-slip boundary condition.

Free surface flow of a suspension of rigid particles in a non-Newtonian fluid: A lattice Boltzmann approach

Abstract: A numerical framework capable of predicting the free surface flow of a suspension of rigid particles in a non-Newtonian fluid is described. The framework is a combination of the lattice Boltzmann method for fluid flow, the mass tracking algorithm for free surface representation, the immersed boundary method for two-way coupled interactions between fluid and rigid particles and an algorithm for the dynamics and mutual interactions of rigid particles. The framework is able to simulate the flow of suspensions at the level of the largest suspended particles and, at the same time, the model is very efficient, allowing simulations of tens of thousands of rigid particles within a reasonable computational time. Furthermore, the framework does not require any fitting constants or parameters devoid of a clear physical meaning and it is stable, robust and can be easily generalized to a variety of problems from many fields.

Effect of viscoelasticity on liquid transfer during gravure printing

Abstract: Roll-to-roll patterning of small-scale features on a rapidly moving web is an industrially important process with a wide array of commercial applications both old and new. Examples include magazine printing and more recently the pattering of flexible electronics. Among the many existing web coating techniques for large-scale fabrication, slit die and gravure coating are the most commonly used. In gravure coating, an engraved roller with a regular array of shallow cavities/cells is used to pick up fluid from a bath. It is then passed through a flexible doctoring blade in order to meter off excess fluid before printing the fluid onto a flexible substrate. Here we present an experimental investigation into the effect that viscoelasticity has on the dynamics of liquid transfer from an idealized gravure cell to a flat rigid substrate. Although the dynamics of the actual gravure coating process is quite complex, we chose to study a simplified process by imposing an extensional flow using a modified filament stretching rheometer in which one of the endplates is replaced by a cell containing a single truncated conical gravure cell. The deformation and stretching of the resulting liquid bridges, the motion of the contact line within the gravure cell and the total amount of fluid removed from the gravure cell are studied as a function of the imposed stretch rate, the fluid rheology, and the geometry of the gravure cell. Two different viscoelastic solutions of high molecular weight polyethylene oxide in water were studied and compared to a series of Newtonian fluids. The results show that the primary impact of viscoelasticity is the addition of an elastic stress which increases the tension along the liquid bridge and significantly increases the bridge lifetime. For stretches where the gravure cell was placed on the bottom and the top plate moved vertically, viscoelasticity was found to significantly reduce the amount of fluid transferred to the top plate. However, by placing the gravure cell on top and reversing the relative direction of the inertial and gravitational stresses, viscoelasticity was found to significantly increase the amount of fluid transferred. Increasing the stretch rate was found to amplify these observations. Finally, increasing the contact angle between the fluid and the gravure cell and decreasing the aspect ratio of the gravure cell were both found to increase the amount of fluid transferred.

Analytical solutions for channel flows of Phan-Thien–Tanner and Giesekus fluids under slip

Abstract: Analytical and semi-analytical solutions are presented for the cases of channel and pipe flows with wall slip for viscoelastic fluids described by the simplified PTT (using both the exponential and the linearized kernel) and the Giesekus models. The slip laws used are the linear and nonlinear Navier, the Hatzikiriakos and the asymptotic models. For the nonlinear Navier slip only natural numbers can be used for the exponent of the tangent stress in order to obtain analytical solutions. For other values of the exponent and other nonlinear laws a numerical scheme is required, and thus, the solution is semi-analytical. For these cases the intervals containing the solution and the corresponding proof for the existence and uniqueness are also presented. For the Giesekus model the influence of the wall slip on the restrictions of the slip models is also investigated.

Incomplete fluid-fluid displacement of yield stress fluids in near-horizontal pipes: Experiments and theory

Abstract: We present results of a primarily experimental study of buoyant miscible displacement flows of a yield stress fluid by a higher density Newtonian fluid along a long pipe, inclined at angles close to horizontal. We focus on the industrially interesting case where the yield stress is significantly larger than a typical viscous stress in the displacing fluid, but where buoyancy forces may be significant. We identify two distinct flow regimes: a central-type displacement regime and a slump-type regime for higher density ratios. In the central-type displacement flows, we find non-uniform static residual layers all around the pipe wall with long-wave variation along the pipe. In the slump-type displacement we generally detect two propagating displacement fronts. A fast front propagates in a thin layer near the bottom of the pipe. A much slower second front follows, displacing a thicker layer of the pipe but sometimes stopping altogether when buoyancy effects are reduced by spreading of the front. In the thin lower layer the flow rate is focused which results in large effective Reynolds numbers, moving into transitional regimes. These flows are frequently unsteady and the displacing fluid can channel through the yield stress fluid in an erratic fashion. We show that the two regimes are delineated by the value of the Archimedes numbers (equivalently, the Reynolds number divided by the densimetric Froude number), a parameter which is independent of the imposed flow rate. We present the phenomenology of the two flow regimes. In simplified configurations, we compare computational and analytical predictions of the flow behaviour (e.g. static layer thickness, axial velocity) with our experimental observations.

The significant influence of internal stresses on the dynamics of bubbles in a yield stress fluid

Abstract: The shape and trajectory of bubbles in Carbopol gels were accurately observed over long periods. As the concentration increases, the trajectories are observed to evolve from vertical and rectilinear to three-dimensional shapes. Local strain and velocity fields have been determined. Bubble injection is quasi-static in order to obtain a separation governed by the equilibrium among surface tension, buoyancy and stresses applied to the bubble. Internal stresses in the fluid, of structural origin and induced by the mechanical history in the fluid volume, remain in the fluid for at least several months. They play a major role in bubble formation and propagation.

Flow of power-law fluids in a cavity driven by the motion of two facing lids – A simulation by lattice Boltzmann method

Abstract: The study of a non-Newtonian fluid flow behavior in mixing cavities is of great importance in process industries. In the present work, a Bhatnagar–Gross–Krook (BGK) approximation based lattice Boltzmann method (LBM) is presented to simulate non-Newtonian power law fluid flows in a double sided lid driven cavity. First, the code is validated against numerical results taken from the published sources for power law fluid flow in cavity driven by the uniform motion of lid. Next, the code is applied for two different cases-parallel wall motion and anti-parallel wall motion of two sided lid driven cavity. The influence of power law index (n) and Reynolds number (RePL) on the variation of velocity and center of vortex location of fluid has been analyzed with the help of velocity profiles and streamline plots. Additionally, we also study the effect of speed ratio on development of vortex in a cavity. Further, the effect of n on variation of drag coefficient has been presented. Finally, we present the location of vortex center and computational time required for a system to reach the steady state.

Numerical simulation of drop impact and jet buckling problems using the eXtended Pom–Pom model

Abstract: This work presents numerical simulations of two fluid flow problems involving moving free surfaces: the impacting drop and fluid jet buckling. The viscoelastic model used in these simulations is the eXtended Pom–Pom (XPP) model. To validate the code, numerical predictions of the drop impact problem for Newtonian and Oldroyd-B fluids are presented and compared with other methods. In particular, a benchmark on numerical simulations for a XPP drop impacting on a rigid plate is performed for a wide range of the relevant parameters. Finally, to provide an additional application of free surface flows of XPP fluids, the viscous jet buckling problem is simulated and discussed.

Modelling of stress and strain amplification effects in filled polymer melts

Abstract: When hard filler particles are added to a polymer melt, it is usually assumed that its zero-shear viscosity and therefore the stress increase according to Einstein’s or a similar formula. In some papers one finds an alternative approach in which the local strain field is increased according to these formulas. Although both approaches provide the same increase of the shear stress in the linear limit, it can be shown that the second approach violates the energy conservation law as the macroscopic and microscopic dissipated energies are not equal anymore. In this contribution we propose a new stress and strain amplification approach in which both the stress and strain tensors are modified to describe the behavior of filled polymer melts in the non-linear shearing regime. The new approach is tested using two relatively simple constitutive models: the Wagner model [1] and the original Doi–Edwards model [2] . This combined approach enables us to explain, for example, the peculiar behavior of the overshoot peak observed recently in filled LDPE melts [3] .

On creeping flow of a Bingham plastic fluid past a square cylinder

Abstract: In this work, the 2-D creeping flow of Bingham plastic fluids past a cylinder of square cross-section has been studied numerically. The governing differential equations (continuity and momentum) have been solved over a wide range of Bingham number as 1 ⩽ Bn ⩽ 105. Similar to the case of a circular cylinder, three zones of unyielded regions are seen to be present in the vicinity of the submerged cylinder, namely, caps attached to the top and bottom surfaces of the square cylinder, two sectors situated on the lateral sides undergoing rigid-body like motion and the usual far away unyielded regions. The influence of the Bingham number on their size and on the stress (normal and shear components) field in the vicinity of the cylinder is discussed in detail. In addition, the corresponding rate of strain, pressure and stress contours are also presented to facilitate the visualization of the structure of the flow field for scores of values of Bingham number. Also, the present numerical drag results have been correlated with the Bingham number via a simple expression thereby enabling their interpolation for the intermediate values of Bingham numbers.

Direct simulations of spherical particles sedimenting in viscoelastic fluids

Abstract: A direct simulation methodology for solid spheres moving through viscoelastic (FENE-CR) fluids has been developed. It is based on a lattice-Boltzmann scheme coupled with a finite volume solver for the transport equation of the conformation tensor, which directly relates to the elastic stress tensor. An immersed boundary method imposes no-slip conditions on the spheres moving over the fixed grid. The proposed method has been verified by comparison with computational data from the literature on the viscoelastic flow past a stationary cylinder. Elastic effects manifest themselves in terms of drag reduction and for-aft asymmetry around the cylinder. Single sphere sedimentation in viscoelastic fluids shows velocity overshoots and subsequent damping before a steady settling state is reached. In multi-sphere simulations, the interaction between spheres depends strongly on the (elastic) properties of the liquid. Simulations of sedimentation of multiple spheres illustrate the potential of the method for application in dense solid–liquid suspensions. The sedimentation simulations have Reynolds numbers of order 0.1 and Deborah numbers ranging from 0 to 1.0.

Startup flow of gelled crudes in pipelines

Abstract: The startup flow of thixotropic yield stress fluids in tubes is studied numerically. In the situation of interest, the structured fluid is displaced by another fluid, under the application of a constant entrance pressure. The fluid is assumed to obey a recently proposed model for thixotropic yield-stress fluids that relies on a structure parameter. The momentum conservation principle is employed in a simplified form that arises by assuming quasi-steady flow, i.e. the shear stress radial distribution is assumed to be linear as it is in steady flow. Inertial effects are also included in the analysis. A numerical procedure was developed to integrate the differential equations that arise, and the average velocity as well as the radial distribution of the structure parameter are obtained for different combinations of the rheological and flow parameters, allowing the determination of the necessary conditions for a successful startup. Among other features, the approach is capable of predicting the “avalanche effect [5] ,” i.e. situations of no flow for long time periods and then the sudden onset of motion.

Thermorheological properties of a Carbopol gel under shear

Abstract: An experimental investigation of the thermo-rheological properties of aqueous solutions of a commercial polyacrylic acid (Carbopol®) at various concentrations is presented. The rheological parameters of the solutions are assessed by performing increasing/decreasing controlled stress stepped ramps and interpreting the results within the framework of a recent model which can correctly describe the irreversibility of deformation states in a range of low deformation rates, Putz and Burghelea [39] . For each polymer concentration a temperature invariance of the elastic moduli, consistency and the power law index is found. Below a critical temperature T c , the measured yield stress can be described by an Arrhenius type dependence. Above T c an anomalous temperature dependence is observed which manifests itself through an increase of the yield stress with the temperature. A qualitative but yet incomplete understanding of this anomalous behavior can be obtained within the framework of the Eyring theory of flow as an activated process. A phenomenological interpretation for the emergence of the critical temperature T c is given. The concentration dependence of elastic moduli, consistency and the Arrhenius pre-factors consistently indicate the existence of an overlap concentration c ★ which we interpret as an onset of jamming of swollen polyacrylic acid molecules. A detailed comparison of the experimental findings with results from the literature is presented and several open questions are stated.

Numerical simulation of 3D-unsteady viscoelastic free surface flows by improved smoothed particle hydrodynamics method

Abstract: In this paper, a working smoothed particle hydrodynamics (SPH) method is introduced to solve three-dimensional (3D) transient viscoelastic flows with complex free surfaces In order to alleviate the unphysical behavior of fracture and particle clustering in fluid stretching which is the so-called tensile instability, an artificial stress term is incorporated into the momentum equation To facilitate the enforcement of 3D wall boundaries, a new boundary treatment technique, which can observably improve the computational efficiency, is proposed The proposed SPH method is validated by solving the Hagen–Poiseuille flow of an Oldroyd-B fluid and comparing the SPH results with the available analytical solutions Two challenging fluid flow problems, namely, a viscoelastic drop impacting on a rigid plate and jet buckling, are simulated to demonstrate the capability of the proposed SPH method in handing 3D viscoelastic free surface flows Results for a Newtonian fluid are also shown for comparison All numerical results obtained are in agreement with the available data

Transient electro-osmotic flow of generalized Maxwell fluids through a microchannel

Abstract: Non-Newtonian fluids such as blood, colloids, and cell suspensions are often manipulated in microfluidic devices and exhibit extraordinary flow behaviors, not existing in Newtonian fluids. This paper represents an analytical solution of transient velocity for electroosmotic flow of generalized Maxwell fluids through both a micro-parallel channel and a microtube, using the method of Laplace transform. The solution involves analytically solving the linearlized Poisson–Boltzmann equation, together with the Cauchy momentum equation and the general Maxwell constitutive equation. By numerical computations, the influence of normalized relaxation time on transient EOF velocity is investigated for different parametric values.

Electrokinetically-driven non-Newtonian fluid flow in rough microchannel with complex-wavy surface

Abstract: A numerical investigation is performed into the flow characteristics of electrokinetically-driven non-Newtonian fluids in rough microchannels with a complex-wavy surface. In performing the simulations, the flow behavior of the non-Newtonian fluids is characterized using a power-law model and the complex-wavy surface is modeled via the superimposition of two sinusoidal functions. The simulations examine the respective effects of the flow behavior index, the non-dimensional Debye–Huckel parameter, and the complex wavy-surface geometry parameters on the flow field characteristics, volumetric flow rate and electric field intensity. The results show that the flow behavior of non-Newtonian fluids is significantly dependent on the value of the flow behavior index in the power-law model. Specifically, the volumetric flow rate increases as the flow behavior index reduces. For a pseudoplastic fluid, the volumetric flow rate increases with an increasing value of the non-dimensional Debye–Huckel parameter due to the corresponding reduction in viscosity. By contrast, for a dilatant fluid, the volumetric flow rate reduces as the Debye–Huckel parameter increases. Finally, it is shown that the velocity profile near the complex wavy surface is more sensitive to changes in the waveform geometry than that in the center of the channel. Overall, the results presented in this study provide a useful insight into the manipulation of non-Newtonian fluids within real-world microchannels characterized by surface roughness.

Constant force extensional rheometry of polymer solutions

Abstract: We revisit the rapid stretching of a liquid filament under the action of a constant imposed tensile force, a problem which was first considered by Matta and Tytus [J. Non-Newton. Fluid Mech. 35 (1990) 215–229]. A liquid bridge formed from a viscous Newtonian fluid or from a dilute polymer solution is first established between two cylindrical disks. The upper disk is held fixed and may be connected to a force transducer while the lower cylinder falls due to gravity. By varying the mass of the falling cylinder and measuring its resulting acceleration, the viscoelastic nature of the elongating fluid filament can be probed. In particular, we show that with this constant force pull (CFP) technique it is possible to readily impose very large material strains and strain rates so that the maximum extensibility of the polymer molecules may be quantified. This unique characteristic of the experiment is analyzed numerically using the FENE-P model and two alternative kinematic descriptions; employing either an axially-uniform filament approximation or a quasi two-dimensional Lagrangian description of the elongating thread. In addition, a second order pertubation theory for the trajectory of the falling mass is developed for simple viscous filaments. Based on these theoretical considerations we develop an expression that enables estimation of the finite extensibility parameter characterizing the polymer solution in terms of quantities that can be extracted directly from simple measurement of the time-dependent filament diameter.

Fractional time-dependent Bingham model for muddy clay

Abstract: In this short communication, based on fractional calculus, we present the fractional Bingham model which can describe the time dependent behavior in the fluid with yield strength. The pulling sphere tests under three different speed conditions are be used to investigate the time dependence of muddy clay. The experimental results illustrate the muddy clay is a noticeable time-dependent Bingham fluid. Experimental results show that the fractional Bingham model can well depict the mechanical behaviors of the muddy clay, and give a good agreement with the experimental data. In addition, this study also finds that the order of the fractional Bingham model is larger than 1 in some cases, which breaks the commonly used assumption that the order should be in the interval [0, 1].

SPH simulations of a viscoelastic flow around a periodic array of cylinders confined in a channel

Abstract: In this paper a numerical study on the performance of the Smoothed Particle Hydrodynamics method (SPH) in the case of a flow of a viscoelastic liquid around a linear array of cylinders confined in a channel is presented. Numerical convergence in the case of a low Reynolds number Newtonian flow was demonstrated by Ellero et al. in [Int. J. Numer. Methods Eng. 86 (2011) 1027]. Here viscoelastic effects are incorporated in the SPH scheme according to the Oldroyd-B model presented in [Phys. Rev. E 79 (2009) 056707]. Good agreement of the dimensionless drag force acting on the cylinder with literature data is observed for a wide range of Weissenberg numbers We. The case of closely spaced cylinders is also investigated and the impact of We on the solution discussed. It turns out that in this case the Newtonian solution exhibits a stable secondary flow represented by two counter-rotating vortices. When elasticity is considered, above a critical Weissenberg number We c these vortices become unstable, breaking the plane symmetry and producing a quasi-periodic flow of mass in and out of the gap region between cylinders. Correspondingly, the flow becomes increasingly unsteady and a dramatic increase in the cylinder’s drag is observed. The results are in qualitative agreement with experimental observations made on Boger liquids under similar flow conditions.

Phase-field simulations of dynamic wetting of viscoelastic fluids

Abstract: We use a phase-field model to simulate displacement flow between a Newtonian and a viscoelastic fluid in a two-dimensional channel. The viscoelastic fluid is described by the Oldroyd-B model and the stress singularity at the contact line is regularized by the Cahn–Hilliard diffusion. In a small region near the contact line, the flow field features a large shear rate that produces a high polymer stress even at relatively low wetting speed. This polymer stress pulls the interface toward the viscoelastic fluid. As a result, the viscous bending at the contact line is enhanced when the advancing fluid is viscoelastic and weakened when the receding fluid is viscoelastic. However, the overall effect is limited by the small size of this strong shear region. These results are consistent with experimental observations. By examining the flow and stress field in the neighborhood of the contact line, we find that viscoelastic stress growth within a finite residence time provides a plausible explanation of the curious experimental observation that the contact line is affected by the viscoelasticity of the oligomeric solvent rather than the high molecular-weight polymer solute.

Revisiting the stability of circular Couette flow of shear-thinning fluids

Abstract: Three-dimensional linear stability analysis of Couette flow between two coaxial cylinders for shear-thinning fluids with and without yield stress is performed. The outer cylinder is fixed and the inner one is rotated. Three rheological models are used: Bingham, Carreau and power-law models. Wide range of rheological, geometrical and dynamical parameters is explored. New data for the critical conditions are provided for Carreau fluid. In the axisymmetric case, it is shown that when the Reynolds number is defined using the inner-wall shear-viscosity, the shear-thinning delays the appearance of Taylor vortices, for all the fluids considered. It is shown that this delay is due to reduction in the energy exchange between the base and the perturbation and not to the modification of the viscous dissipation. In the non axisymmetric case, contrary to Caton [1], we have not found any instability.

Multiple-relaxation-time lattice Boltzmann simulation of non-Newtonian flows past a rotating circular cylinder

Abstract: The flow field around a rotating circular cylinder is studied numerically using Lattice Boltzmann method via multi-relaxation-time approach. Simulations are performed at a fixed Reynolds number of 100 while dimensionless rotational ratio (β) and power–law index (n) range as, 0 ⩽ β ⩽ 2.5 and 0.4 ⩽ n ⩽ 1.8, respectively. The effects of dimensionless rotational ratio and the power–law index on the flow field, mean drag and lift coefficients, Strouhal number and pressure coefficient are investigated in detail. To verify the simulation, the results are compared to previous experimental and numerical data.

Experimental investigation of non-Newtonian liquid flow in microchannels

Abstract: Investigation on non-Newtonian fluid flow in microchannels is of both fundamental interest and practical significance. Flow characteristics of deionized water and the PAM solution over a wide range of Reynolds numbers in fused silica microtubes with diameters from 75 to 250 μm, fused silica square microchannels with equivalent diameters of 75 and 100 μm, and stainless steel microtubes with diameters from 120 to 300 μm, were studied experimentally. The obtained mass flow rate and friction factor for deionized water in smooth fused silica microchannels were in good agreement with theoretical predictions for conventional-sized channels while the deviation for stainless steel microtubes was observed due to the roughness. Friction factors of the PAM solution were much higher than conventional theoretical predictions. Flow behaviors of deionized water and the PAM solution under hydrophobic condition are also studied experimentally. The mass flow rate increased in hydrophobic microchannels compared to untreated microchannels. The drag reduction in hydrophobic channels is greater for rough stainless steel microtubes than for smooth fused silica channels. The effect of surface wettability on the shear thinning PAM solution is also observed to be more evident than on the Newtonian deionized water.

Spreading of axisymmetric non-Newtonian power-law gravity currents in porous media

Abstract: A relatively heavy, non-Newtonian power-law fluid of flow behavior index n is released from a point source into a saturated porous medium above an horizontal bed; the intruding volume increases with time as tα. Spreading of the resulting axisymmetric gravity current is governed by a non-linear equation amenable to a similarity solution, yielding an asymptotic rate of spreading proportional to t(α+n)/(3+n). The current shape factor is derived in closed-form for an instantaneous release (α = 0), and numerically for time-dependent injection (α ≠ 0). For the general case α ≠ 0, the differential problem shows a singularity near the tip of the current and in the origin; the shape factor has an asymptote in the origin for n ⩾ 1 and α ≠ 0. Different kinds of analytical approximations to the general problem are developed near the origin and for the entire domain (a Frobenius series and one based on a recursive integration procedure). The behavior of the solutions is discussed for different values of n and α. The shape of the current is mostly sensitive to α and moderately to n; the case α = 3 acts as a transition between decelerating and accelerating currents.