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In this paper we propose a novel approach to solve the inverse problem of three-dimensional die design for extrudate swell, using a real-time active control scheme. To this end, we envisioned a feedback connection between the corner-line finite element method, used to predict the positions of the free surfaces of the extrudate, and the controller. The corner-line method allows for local mesh refinement and transient flow to be taken into account (Spanjaards et al., 2019). We show the validity of this method by showing optimization results for 2D axisymmetric extrusion flows of a viscoelastic fluid for different Weissenberg numbers. In 3D we first give a proof of concept by showing the results of a Newtonian fluid exiting dies with increasing complexity in shape. Finally, we show that this method is able to obtain the desired extrudate shape of extrudates of a viscoelastic fluid for different Weissenberg numbers and different amounts of shear-thinning.

Many microorganisms swim in fluids with complex rheological properties. Although much is now understood about motion of these swimmers in Newtonian fluids, the understanding is still developing in non-Newtonian fluids—this understanding is crucial for various biomimetic and biomedical applications. Here we study a common model for microswimmers, the squirmer model, in two common viscoelastic fluid models, the Giesekus fluid model and fluids of differential type (grade three), at zero Reynolds number. Through this article we address a recent commentary that discussed suitable values of parameters in these models and pointed at higher-order viscoelastic effects on squirming motion.

Microfluidic devices can be used to represent industrial and natural mixed extensional-shear flows and to measure, simultaneously, in-situ rheological properties of viscoelastic fluids. However, such measurements are challenging due to the nature of mixed flow kinematics. In this study, we present a new mathematical framework to quantify the extensional behavior of viscoelastic fluids in mixed flows through a hyperbolic contraction-expansion microfluidic device. This approach provides a better estimation of apparent extensional viscosity when the non-Newtonian fluid kinematic does not promote additional flow phenomena such as vortices, shear banding or high-velocity jet. We then apply this approach to analyze the mixed rheology of two different viscoelastic surfactant solutions. The results indicate that there is a critical flow rate where extensional properties of the studied viscoelastic fluids start losing importance possibly due to additional flow phenomena. We also found a viscoelastic transition regime from extensional tension-thickening to tension-thinning as flow rate increases.

A new transient 3D finite element method for predicting extrudate swell of domains containing sharp edges is proposed. Here, the sharp edge is maintained over a large distance in the extrudate by describing the corner lines as material lines. The positions of these lines can be used to describe the transverse swelling of the 2D free surfaces and expand the domain over which a 2D height function on the free surfaces is applied. Solving the 2D height functions gives the positions of the free surfaces. First a 2D axisymmetric case was tested for comparison, using three different constitutive models. The Giesekus, linear Phan-Thien Tanner (PTT) and exponential PTT constitutive models all showed convergence upon mesh- and time-step refinement. It was found that convergence remains challenging due to the singularity at the die exit. The new method is validated by comparing the final volume change of the extrudate of a 3D cylinder to the final volume change of a reference mesh of the 2D axisymmetric case. Finally, simulations were performed for different, complex, die shapes for a viscous fluid and for viscoelastic fluids. The results compared favorably with literature. Viscoelastic results, using the Giesekus model and the exponential PTT model, were compared for different Weissenberg numbers and different values for the non-linear parameters of the constitutive models. It was found that the swell is highly dependent on the rheological parameters and the constitutive model used.

This manuscript quantifies the hydrodynamic drag of a spherical droplet translating in unsteady Stokes flow when the droplet has a thin, complex membrane. All forces (e.g., Stokes drag, Basset forces, unsteady memory forces, etc.) have the same functional form as the drag of a clean spherical droplet, as long as one replaces the interior viscosity with an effective (frequency-dependent) one that depends on the viscoelastic moduli of the membrane. The shear elastic moduli of the membrane do not modify the unsteady drag of the droplet – only the dilatational modes matter. We demonstrate how this result can be obtained using simple symmetry/scaling arguments. The results are written for any linearly viscoelastic membrane, but we in particular examine the cases of a purely viscous membrane, purely elastic membrane, one-mode Maxwell membrane, and one-mode Kelvin-Voigt membrane. For the latter two models, we quantify how the membrane relaxation time alters the time-dependent motion of the droplet.

The stability behavior of a visco-elastic (Upper Convected Maxwell) liquid film flowing down an inclined plane is examined using the standard normal mode linear stability analysis in creeping flow limit. The inclined plane is coated with a deformable solid layer, and the gas-liquid interface is covered with a monolayer of an insoluble surfactant. There exist three modes of instabilities for this composite fluid-solid system: (i) the free surface gas-liquid (GL) mode, (ii) the surfactant or Marangoni mode, and (iii) the liquid-solid (LS) mode. Previous studies have shown that the Marangoni mode remains stable for film flowing down a rigid inclined plane. We show that when the rigid wall is replaced by a deformable wall, the Marangoni mode becomes unstable when a non-dimensional deformability parameter, defined as G = μ V / E s R , increases above a threshold value (μ, V, Es, and R are fluid viscosity, free-surface velocity, shear modulus of soft solid layer, and fluid thickness, respectively). It is well known that the GL mode remains stable for Newtonian liquid film at zero Reynolds number, but becomes unstable for a visco-elastic film flowing past a rigid inclined plane even in creeping flow limit purely because of fluid elasticity. Previous studies have shown that the presence of soft solid layer can suppress this free surface GL mode instability. The presence of surfactant also has a stabilizing effect on this GL mode instability in rigid limit. Here, we evaluate whether a soft solid coating can be used to obtain a stable flow configuration for a surfactant-covered visco-elastic film as well particularly (i) in view of the above mentioned Marangoni mode destabilization observed solely due to wall deformability, and (ii) when the surfactant stabilizing contribution remains insufficient to suppress the free-surface instability. We demonstrate that there exists a window in terms of parameter G where the free surface GL mode instability is suppressed without exciting any other mode. We also identify the parameter regimes where it is not possible to achieve stable film flow, however, in these cases, we show that the Marangoni mode can be selectively destabilized by appropriately selecting the thickness and shear modulus of solid layer.

Flow of viscoelastic fluids in porous media is ubiquitous in biological and industrial processes, and the choice of viscoelastic fluids is of foremost importance for their effect on macroscopic flow and transport properties. In this paper we study the macroscopic properties of flow and transport of viscoelastic fluids through a model porous media by means of Direct Numerical Simulation (DNS). We show that flow of a viscoelastic fluid modeled via a FENE-P constitutive model features three distinct regimes of flow resistance: a plateau at low Deborah numbers, and a shear-thinning phase followed by an abrupt flow thickening above a critical Deborah number, consistent with experimental observations. Congruous to this shear-thickening, we observe the onset of hydrodynamic instabilities resulting in fluctuations in pressure drop and flow resistance. These fluctuations intensify with increasing the fluid elasticity. Finally, we investigate Lagrangian attributes of viscoelastic flow and transport through porous media. We find that although the fluid elasticity broadens the Lagrangian velocity distributions, it does not alter the long-term particle dispersion in disordered porous media.

The analysis of motion and deformation of a drop falling into another immiscible media finds a wide range of applications, including, wastewater treatment using flocculation technique, petroleum engineering, medicine processing, metals extraction and heat exchangers. This paper presents an analytical solution based on a triple perturbation method, for cases in which viscoelastic drops are falling in another immiscible Newtonian media at low Reynolds numbers. Here, the Reynolds, Deborah and capillary numbers are considered to be the perturbation parameters. Moreover, an experimental investigation is carried out, which is also used to validate and extend the analytical data. Motion and deformation of immiscible drops of 0.01% polyacrylamide (PAA) in 80:20 glycerol/water falling through polydimethylsiloxane oil are studied, and this shows a good agreement with the presented analytical solution. It is shown that the viscoelastic drops remain spherical when the drop size is small - this corresponds to the domination of the capillary force. It is shown that as the volume of the droplet increases, normal components of the stress tensor exhibit a non-uniform distribution at the interface of the two fluids. Consequently, this can cause a dimple at the rear end of drops, depending on the magnitude of the surface tension force.

A stabilized finite element scheme is developed for computations of buoyancy driven 3D-axisymmetric viscoelastic two-phase flows with insoluble surfactants. The numerical scheme solves the Navier-Stokes equations for the fluid flow, Giesekus constitutive equation for the effects of viscoelasticity and simultaneously an evolution equation for the surfactant concentration on the interface. The interface is tracked by the coupled arbitrary Lagrangian-Eulerian (ALE) and Lagrangian approach. The interface-resolved moving meshes allow accurate incorporation of the interfacial tension force, Marangoni forces and the jumps in the material properties. Further, the tangential gradient operator technique is used to handle the curvature approximation in a semi-implicit manner. An one-level Local Projection Stabilization (LPS), which is based on an enriched approximation space and a discontinuous projection space, where both spaces are defined on a same mesh is used to stabilize the model equations. The stabilized numerical scheme allows us to use isoparametric second order conforming finite elements enriched with cubic bubble functions for velocity and viscoelastic stress, second order finite elements for surfactant concentration and discontinuous first order finite element for pressure. A number of computations are performed for a Newtonian drop rising in a viscoelastic fluid column and a viscoelastic drop rising in a Newtonian fluid column with insoluble surfactants on the interface. The influence of the Marangoni number, initial surfactant concentration and Peclet number on the dynamics of the rising drop are analyzed. The numerical study shows that a viscoelastic drop rising in a Newtonian fluid column develops an indentation around the rear stagnation point with a dimpled shape without insoluble surfactants. The presence of insoluble surfactants forces the drop to rise slowly but the drop at the tail end is pulled up more. However, a Newtonian drop rising in a viscoelastic fluid column experiences an extended trailing edge with a cusp-like shape without insoluble surfactants. The presence of surfactants pulls the tail end of the drop up slightly and makes the tail flatter with/without small undulations depending on the magnitude of the surfactant concentrations.

The relevance of 3D numerical simulations for the isothermal flow of neat polypropylene through a slit die and the subsequent swelling upon die exit is highlighted based on the finite element method using the ANSYS Polyflow software package. The input parameters of (i) the generalized Newtonian constitutive model with the Cross law viscosity function and (ii) the multimode viscoelastic Phan-Thien-Tanner (PTT) constitutive model are estimated from rheological data obtained with rotational and capillary rheometers. Model validation is performed based on die pressure and real time experimental HD imaging for 3D die swell characterization. The evolution of the swell ratios in both width and height directions is investigated downstream the die exit. It is demonstrated that the PTT based swell ratio in the width direction increases in a much lower rate than the swell ratio in the height direction until equilibrium is achieved in both directions. Therefore, the distance from the die exit in which the final extrudate shape is obtained strongly depends on the die width, which is ignored in conventional 2D numerical simulations. The findings are underpinned through a detailed analysis of the simulated 3D stress and velocity field distributions.

Understanding how the deformation history affects the retraction dynamics of viscoelastic liquid films can provide a tool to design materials. In this paper, we investigate the stretching and retraction of circular viscoelastic liquid films through finite element numerical simulations. We consider a discoid domain made of a viscoelastic liquid. Its central hole is first ‘closed’ and then released, being left free to open under the effect of inertial, surface, viscous, and elastic forces. We perform a parametric study of film retraction, aiming at understanding the effects of the physical and operating parameters on it. In particular, we consider different viscoelastic constitutive equations, namely, Oldroyd-B, Giesekus (Gsk), and Phan Thien-Tanner (PTT) models, and different values of the film initial thickness. For each liquid and geometry, we investigate the effects of the film stretching rate and of liquid inertia, elasticity, and flow-dependent viscosity on the dynamics of the hole opening.

Linear stability of time-dependent fluids obeying the Quemada model is numerically investigated in plane Couette flow past a saturated poroelastic layer. Having assumed that the permeable layer is viscoelastic and obeys the Kelvin model, the base flow/deformation were obtained for the main channel and also in the poroelastic layer using mixture theory. The base state so obtained was then subjected to infinitesimally small, normal-mode perturbations in order to determine its vulnerability to poroelastic instability. An eigenvalue problem was obtained which was numerically solved using the iterative shooting scheme (ISS). The main objective of the work was to investigate the role played by the movement of the upper plate on the stability of the core fluid (i.e., the fluid flowing through the main channel). Of equal importance was to determine the influence of the rheological behavior of the core fluid on the growth rate of unstable mode(s). Numerical results were obtained mostly under creeping-flow conditions demonstrating that anti-thixotropy of the core fluid lowers the critical velocity of the moving plate whereas the viscosity-gap ratio (i.e., the viscosity of the core fluid divided by the viscosity of the interstitial fluid in the poroelastic layer) has a stabilizing effect on the core flow. By allowing permeability to be a function of porosity, the degree of nonlinearity of this relationship was found to have a stabilizing or destabilizing effect on the core flow depending on the layer's porosity.

New results are reported on the simulation of the rise of a deforming gas bubble surrounded by a liquid exhibiting a blend of shear-thinning and viscoelastic properties. A new hybrid model has been developed which combines the Carreau model for emulating the shear-thinning property of the liquid with the Chilcott–Rallison (FENE-CR) model for treating the viscoelastic property of the liquid. The new hybrid model allows one to independently prescribe the shear-thinning and viscoelastic properties (parameters) to be used in a simulation. Computations are implemented using the coupled level-set and volume-of-fluid (CLSVOF) method for tracking the deforming gas-liquid interface. The interfacial jump conditions are enforced with the sharp interface approach. In this study, four parameters, the Eotvos number, Carreau model parameter for slope of decreasing viscosity, Deborah number, and viscoelastic polymer dumbbell length parameter, are varied in order to gain understanding for gas bubble morphology in liquids exhibiting both shear-thinning and viscoelastic properties. It is found that the extent of bubble deformation and the liquid stress field are strongly dependent on these 4 parameters with minimal correlation between the shear-thinning and viscoelastic parameters. The ability to vary shear-thinning and viscoelastic parameters independently of one another in the new hybrid Carreau and FENE-CR model enables one to conveniently predict gas bubble behavior in complex liquid polymers by parameterizing the new model from basic measurements of the polymers.

A rigorously-defined method that maps and quantifies the time-resolved dynamical yielding process of elastoviscoplastic materials is proposed and investigated. Building on the foundations of linear viscoelastic theory for oscillatory deformations, the method utilizes the motion of an instantaneous phase angle between the stress and strain of the rheological response within deformation space to quantify the yielding transition. Principal component analysis demonstrates that this phase angle velocity is based on the natural description for a material response in deformation space. The response of the Carreau model with constitutive parameters selected to correspond to a regularized viscoplastic fluid that undergoes an apparent yielding transition at a critical shear rate, and of a Carbopol microgel are investigated as canonical examples of theoretical and experimental model yield stress fluids. Calculation of the phase angle velocity clearly identifies the yield transition as being gradual. This approach provides a physically-motivated understanding of the dynamical processes occurring during yielding of elastoviscoplastic materials.

Thin liquid sheets are ubiquitous in many industrial processes, such as atomization and curtain coating. In the latter, the thickness of the deposited layer is limited by the breakup of the liquid curtain below a critical flow rate. The stability of a liquid sheet depends on the disturbance characteristics, sheet thickness and fluid properties. Experimental analyses have shown that thinner stable liquid curtains can be obtained with viscoelastic liquids; however, the underlining physical mechanisms associated with the increased stability are not fully understood. This work presents a numerical analysis of the effect of viscoelasticity on the stability of a thin liquid sheet. We first derive linear stability criteria for both planar and axisymmetric perturbations of Newtonian and Oldroyd-B liquids. The time evolution of planar and axisymmetric perturbations in an Oldroyd-B liquid sheet is evaluated using asymptotic expansion of the flow variables and a fully-implicit time integration scheme. The breakup time is calculated as a function of Deborah number and polymer to solvent viscosity ratio. The results show that the liquid rheological behavior does not change the linear stability criterion, however it has a strong effect on the growth rate of the disturbance and consequently on the breakup time.

A viscoelastic model for cellulose nanofiber (CNF) suspensions using a population balance equation for fiber floc aggregation-breakage was proposed. A Krieger–Dougherty model was used to describe the dependence of viscosity on the volume fraction of flocs, and a White–Metzner type model was used to represent the effect of viscoelasticity. The rheological properties of the present model were investigated, and this model was confirmed to describe shear thinning in viscosity and viscoelastic responses of stress growth, depending on the relaxation time. Furthermore, flows of CNF suspensions through a circular tube were analyzed using the present model. The velocity profile changes with time according to the temporal change in the distribution of the effective volume fraction of fiber flocs. The numerical prediction of the velocity profile captures the typical properties of shear-thinning fluids. The development rate of the floc size distribution depends on the velocity gradient and affects the temporal changes of both velocity and stress fields. The development of the stress field is delayed longer for a longer relaxation time. These phenomena affect the temporal change in the floc size distribution and hence also affect the growth of the velocity field through the effective volume fraction of flocs. These results indicated that the present model can describe the viscoelastic behavior of CNF suspensions in flows.

In this paper the small-amplitude oscillation and linear instability of an electrically charged liquid droplet suspended in a vacuum is studied. The liquid is assumed to be viscoelastic and leaky dielectric. The problem is linearized and a characteristic equation is derived. The complex frequency is solved numerically as a function of the relevant dimensionless parameters. The effects of surface charge and the electrical properties of the liquid on the oscillation and instability characteristics of the droplet are investigated for several cases of viscoelasticity and the quadrupole mode n = 2 . In the case of large or small elasticities, increasing the charge level leads to a decrease in the critical Ohnesorge number at which a supercritical bifurcation occurs and narrows down the interval of the Ohnesorge number for oscillation. For large viscosities, oscillation can be induced by elasticity when the relative stress relaxation time is between 0.004 and 10 approximately, and the electric field may diminish this upper limit to a certain extent. The existence of the electric field also gives rise to new aperiodic branches first appearing at large viscosities or elasticities with smaller damping rates. The effect of finite conductivity on the oscillation behavior of the droplet is rather complicated. Most significantly, when the electrical relaxation time is of the order of the capillary time or a little smaller, new supercritical and subcritical bifurcations with new intervals that favor the appearance of oscillation occur at moderate/relatively large viscosities or elasticities. In addition, it is found that the Rayleigh limit expressed in the form χ = n + 2 where χ the electrical Bond number and n is the order of the mode is identical with that for a perfectly conducting, inviscid droplet. Above the Rayleigh limit, the viscoelastic droplet becomes unstable, and high-order modes may be dominant over the quadrupole one when the charge level is high enough.

Numerical simulations of viscoelastic fluids in the Stokes limit with a four-roll mill background force were performed at a range of Weissenberg number (non-dimensional relaxation time). For small Weissenberg number the flow is steady and symmetric but upon increasing the Weissenberg number (corresponding to increased elasticity or flow memory time), the flow becomes unstable leading to a variety of temporal evolutions to different periodic and aperiodic solutions. These dynamics were analyzed using a Proper Orthogonal Decomposition (POD) that extracted elastic modes in terms of their contribution to the energy of the system. The temporal behavior of the system, captured by the decomposition, indicates that the motion of the stagnation points drives the different flow transitions. In particular, a transition to an asymmetric state occurs when the extensional stagnation points lose their pinning to the background forcing. A further transition to higher frequency modal dynamics occurs when the stagnation points that were initially tied by the forcing to the centers of the rolls, begin to move. The relative frequencies of the motion of these stagnation points is a critical factor in determining the complexity of the flow, measured by the number of modes needed to capture most of the energy in the system. Even when the flows are more complex a small number of modes is sufficient to capture the time evolution of these flows, demonstrating the usefulness of the POD applied to viscoelastic fluids at zero Reynolds number.

The motion of a tiny air bubble in an aqueous solution of cetyl trimethyl ammonium bromide and sodium salicylate (CTAB/NaSal), which forms wormlike micelles, was observed using a high-speed polarization camera. Complex local flow is observed around the bubble surface because the bubble shape deforms repeatedly at 100 Hz. The camera can be used to measure the retardation distribution, which is related to the stress field around the bubble. Different retardation and orientation angle distributions were observed during the contraction and expansion phases. In the contraction phase, a strong retardation distribution appears at the tail of the cusped bubble. The occurrence of uniaxial elongation deformation is considered to be due to the negative wake because they are closely correlated. In contrast, a weak retardation distribution spreads at the upper side of the bubble during the expansion phase, where biaxial extensional deformation occurs due to expansion of the bubble surface. These significant changes in strong elastic stress distributions, which correspond to the orientation angle profiles, can result in increase of bubble rising velocities.

A numerical study on the impingement and spreading of an isothermal viscoelastic droplet on a solid surface is presented in this work. The time-dependent incompressible Navier–Stokes equations are used to describe the fluid flow in the liquid droplet, whereas the viscoelasticity in the moving droplet is described by the Giesekus constitutive equation. A finite element scheme with the arbitrary Lagrangian–Eulerian (ALE) approach is proposed to solve the coupled time-dependent incompressible Navier–Stokes equation and the Giesekus constitutive equation in a time-dependent domain. In addition, a three-field formulation based on the Local Projection Stabilization (LPS) is used in the numerical scheme. The stabilized scheme allows us to use equal order interpolation spaces for the velocity and the viscoelastic stress, whereas inf-sup stable finite elements are used for the velocity and the pressure. The coupled system is solved by a monolithic approach in a 3D-axisymmetric configuration. In addition to the mesh convergence study, parametric studies of the Weissenberg number, Newtonian solvent ratio, polymeric viscosity, Reynolds number and the equilibrium contact angle are performed to demonstrate the effects of viscoelasticity on the flow dynamics of the droplet on wetting surfaces. The numerical study shows that the wetting diameter of the droplet increases with an increase in the viscoelasticity of the fluid. Further, the viscoelastic effects during the spreading process increases with an increase in the Reynolds number. Moreover, the viscoelastic effects on the flow dynamics are not influenced by the equilibrium contact angle.

We numerically investigate inertial flows of viscoelastic fluids within a three-dimensional cross-slot geometry of square cross-section. Our study focuses on the inertial instability that occurs above a critical Reynolds number (Re) resulting in a transition to a steady flow asymmetry. We investigate numerically the effects of elasticity upon its characteristics by employing the upper-convected Maxwell (UCM), the Oldroyd-B and the modified Chilcott–Rallison finitely extensible nonlinear elastic (FENE–MCR) models. In so doing, we show that the UCM and the Oldroyd-B model results are restricted to very low nominal Weissenberg numbers at non-negligible Reynolds numbers, due to a significant increase in the strain rate at the stagnation point caused by inertia. The resulting steady-asymmetric flow at these critical conditions gives rise to the formation of a single axially-aligned spiral vortex, which is formed along the outlet channels of the geometry in good agreement with experimental observations. Below these critical conditions the flow remains steady-symmetric, varying from a nearly two-dimensional flow at very low Re to a more complex three-dimensional flow at higher Re. In a recent publication [Burshtein et al. [Phys. Rev. X, 7, 041039, (2017)]], we demonstrated experimentally, accompanied by limited complementary numerical simulations, the impact of elasticity upon the critical conditions for which the instability develops and the behaviour of the subsequent growth of vorticity of the single spiral vortex. Our results here show how different viscoelastic models influence the instability in a 3D cross-slot and demonstrate an interesting behaviour of the first normal-stress difference, providing an additional insight on the potential mechanisms which are responsible for the suppression of the spiral-vortex. We also elucidate the role played by solvent-to-total viscosity ratio and the extensibility parameter in the FENE–MCR model on the instability.

In this paper, the lateral migration of a neutrally buoyant spherical particle in a pressure-driven rectangular-shaped channel flow of Giesekus viscoelastic fluids is numerically investigated with a fictitious domain method. The particle trajectories are shown for the channel aspect ratio 2, the ratio of the particle diameter to the channel height 0.15, the Reynolds number 1 and 50, and the Weissenberg number up to 2.5. When the fluid inertial effect is negligible, the particle migrates toward the channel centerline or the closest corner depending on its initial position, and the corner-attraction region is enlarged as the Weissenberg number increases. When both fluid inertial and elastic effects are important, most particles migrate toward the face centers of the shorter walls. The particle migration trajectories are significantly affected by the secondary flow.

A phenomenological constitutive model that accounts for thixotropy, viscoelasticity and yielding behavior is presented. It uses the fluidity to specify the microscopic state. The model is composed of two differential equations, one tensorial equation that relates the stress to the rate of strain and one scalar evolution equation for the fluidity. The equation for stress is a modified version of the Oldroyd-B model in which the relaxation and retardation times are functions of the fluidity. In contrast to the existing phenomenological models for thixotropic materials, the evolution equation that describes the microscopic state only involves material functions that are directly measurable by means of standard rheological tests.

In this predominately predictive modelling finite volume/element study, a comparative analysis is performed for time-dependent and viscoelastoplastic flow in a circular contraction-expansion geometry of aspect-ratio 10:1:10. For this, a hybrid finite volume/element scheme is employed. A new and revised micellar model is investigated, under the denomination of BMP+_τp, which reflects a bounded extensional viscosity response and an N1Shear-upturn at large deformation rates (lost in earlier model-variants), a versatile model capable of supporting plasticity, shear-thinning, strain softening-hardening and shear-banding. Many of these features are common to wormlike micellar and polymer solutions. Then, findings are contrasted against a de Souza Mendes model. Two flow regimes are addressed: plastic flow (low flow-rate Q ≤ 1 units, solvent-fraction β 1; minimised plasticity; β = 1/9); as quantified via flow-structure, yield-fronts and pressure-drops. Under the plastic regime, elasticity-increase causes asymmetry about the contraction-plane, whilst yield-stress and enhanced strain-hardening promote solid-like features, apparent through augmented unyielded-regions and rising pressure-drops. Concerning the viscoelastic regime and vortex-structures, extensional-deformation experienced correlates with hardening expectation in uniaxial-extension, whilst streamline activity in vortex-cells correlates with normal-stress response in shear. Adjustment in strain-hardening/softening response with Q-rise, provides translation from weaker salient-corner vortex centres to stronger elastic corner-vortices; yet, when softening finally prevails, asymmetric upstream/downstream salient-corners vortex patterns are recovered. For strong-hardening and solvent-dominated β∼0.8 fluids (as with Boger fluids), an intermediate lip-vortex-formation phase is noted, alongside coexistence of salient-corner vortices. Such a vortex-coexistence phase is distinctly absent in solute-concentrated fluids.

This paper is concerned with the temporal stability analysis of an infinitely long thread of a viscoelastic fluid surrounded by another immiscible viscoelastic fluid. The study provides an extension of the dispersion relation derived by Tomotika that captures the effects of elasticity on the fastest growing mode. The general case of two Jeffreys fluids is presented first, from which limiting cases, such as the Maxwell model or the Newtonian model, are discussed. We show that the presence of elasticity in the constitutive equation of the external medium decreases the value of the growth rate correspondent to the fastest growing mode. This implies a more stable fluid thread, thus longer breakup lengths. When both fluids have similar elastic properties, the dispersion relation reduces to the Newtonian limit and the interface behaves as if the fluids were purely viscous.

We study the stability of pressure-driven channel flow of a thixotropic-viscoelasto-plastic fluid. Several recent experiments have shown that channel flows of shear-thinning polymer solutions can be linearly unstable even at very low Reynolds numbers. We use the Bautista–Manero–Puig model (BMP) to attempt to capture the physics of these instabilities. We obtain an analytic solution for the steady-state velocity profile, dependent on our fluid parameters, that is able to predict a large variety of base states. We derive dimensionless groups to compare the effects of viscoelasticity, thixotropy and plasticity on the flow stability. We find that sinuous perturbations are slightly more unstable than varicose modes, and we identify the values of our model parameters for which the instability has its strongest effects. We conclude that dominant thixotropy can stabilise the flow, but instability occurs when the characteristic timescale of viscoelasticity is much longer than both those of plasticity and thixotropy. The most dangerous situation is a plug flow with an apparent yield surface just within the channel, and we find that the growth rate of the instability scales with the rate of thixotropic structure recovery.

We study both theoretically and experimentally the forced and free oscillations of a viscoelastic pendant drop in the linear regime. The Jeffreys model is numerically solved using the zero-shear viscosity of the steady shear flow in a rotational rheometer, and the stress relaxation time measured with a filament stretching elongational rheometer. The damping factor characterizing the first oscillation mode is one order of magnitude larger than that measured in the experiments. Three possible conclusions can be drawn from this study: (i) the Jeffreys model severely underestimates the viscosity decrease due to elasticity; (ii) the zero-shear viscosity measured in the rotational rheometer is much larger than the effective viscosity responsible for energy dissipation in the pendant droplet oscillations; and (iii) the relaxation time measured with the filament stretching elongational rheometer is much smaller than that characterizing those oscillations. The failure of the Jeffreys model necessarily entails that of all nonlinear constitutive relationships which the Jeffreys model can be derived from, like the commonly used Oldroyd-B model.

In this paper, the well-known Saffman-Taylor instability of an immiscible quasilinear viscoelastic-Newtonian displacement in a Hele-Shaw cell is studied numerically for the first time. The volume of fluid method is applied to predict the formation of two phases. Here, a quasilinear viscoelastic fluid is considered as the displacing fluid and a Newtonian fluid as the displaced fluid. The Oldroyd-B constitutive equation, which is physically useful for Boger liquids, is considered for the viscoelastic phase. The effect of dimensionless parameters, consisting of the viscosity ratio, the viscosity ratio of viscoelastic fluid, the elasticity number, and the capillary number on Saffman-Taylor instability are studied in detail. The results illustrate that increasing the capillary number, elasticity number, and the viscosity ratio of viscoelastic fluid stabilizes the displacement, while enhancing the viscosity ratio has a destabilizing effect on the displacement. As a main result, it is found that the elasticity of the displacing fluid has a stabilizing effect on the flow field in the presence of capillary forces, which can be attributed to enhancing the extensional viscosity that resists against the stretching of the fingers.

Complex fluid–fluid interfaces determine for a large part the macroscopic material properties of foams and emulsions that appear in applications such as food, materials processing and consumer care products. As a step towards predicting these properties, a 2D axisymmetric and a 3D finite element model have been developed for simulating the dynamics of a single Newtonian drop in a Newtonian matrix fluid with a rheologically complex sharp interface in between. Interfaces with constant interfacial tension and with viscous, elastic and viscoelastic extra interfacial stresses are considered. The model has been validated by means of the method of manufactured solutions and by comparison with results from other studies using different discretisation methods. Higher-order convergence in space and time is obtained, demonstrating correct implementation of our numerical methods. Benchmark solutions for a drop with a Kelvin–Voigt interface under simple shear flow have been provided. Compared to a viscous interface, the drop deformation becomes smaller and the drop becomes less oriented in the direction of flow if interfacial elasticity is added.

We extend the penalty immersed boundary (pIB) method to investigate the interaction between circular rigid particles and a surrounding viscoelastic Oldroyd-B fluid. The basic idea of the pIB method is the splitting of an immersed boundary, which here is a rigid body, notionally into two Lagrangian components: one is a massive component carrying all mass of the rigid body, and the other is massless. These two components are connected by a system of stiff springs with zero rest length. The massive component has no direct interaction with the surrounding fluid and behaves as though in a vacuum, following the dynamics of a rigid body, in which the acting forces and torques are generated from the system of stiff springs that connects the two Lagrangian components. The massless component interacts with the surrounding Oldroyd-B fluid: it moves at the local fluid velocity and exerts force locally on the fluid. We verify the pIB method combined with Oldroyd-B fluid model by investigating the effects of the wall and elasticity of the fluid on the lateral position of a circular particle falling under the influence of gravity and by studying convergence of the numerical solutions. We also simulate the interaction between multiple circular particles and the surrounding Oldroyd-B fluid and compare the dynamics of the particles in various flow conditions.

We investigate the elastoviscoplastic flow through porous media by numerical simulations. We solve the Navier–Stokes equations combined with the elastoviscoplastic model proposed by Saramito for the stress tensor evolution [1]. In this model, the material behaves as a viscoelastic solid when unyielded, and as a viscoelastic Oldroyd-B fluid for stresses higher than the yield stress. The porous media is made of a symmetric array of cylinders, and we solve the flow in one periodic cell. We find that the solution is time-dependent even at low Reynolds numbers as we observe oscillations in time of the unyielded region especially at high Bingham numbers. The volume of the unyielded region slightly decreases with the Reynolds number and strongly increases with the Bingham number; up to 70% of the total volume is unyielded for the highest Bingham numbers considered here. The flow is mainly shear dominated in the yielded region, while shear and elongational flow are equally distributed in the unyielded region. We compute the relation between the pressure drop and the flow rate in the porous medium and present an empirical closure as function of the Bingham and Reynolds numbers. The apparent permeability, normalized with the case of Newtonian fluids, is shown to be greater than 1 at low Bingham numbers, corresponding to lower pressure drops due to the flow elasticity, and smaller than 1 for high Bingham numbers, indicating larger dissipation in the flow owing to the presence of the yielded regions. Finally we investigate the effect of the Weissenberg number on the distribution of the unyielded regions and on the pressure gradient.

The effect of viscoelastic forces on the hole growth speed in a liquid curtain and on the critical flow rate below which a liquid curtain breaks was studied by high-speed visualization. Different Boger-like aqueous solutions were used as the viscoelastic liquids. The expansion of a hole initiated within the liquid curtain leads to the curtain breakup. The results show a strong stabilizing effect of the viscoelastic forces; the minimum flow rate for stable curtain falls drastically by adding small amounts of high molecular weight polymer. The results reveal that the mechanisms for the increased stability are that the initiation of the hole is delayed and the speed at which it expands is also reduced, as the viscoelastic forces become stronger.

Blood pulsatility, aneurysms, stenoses and general low shear stress hemodynamics enhance non-Newtonian blood effects which generate local changes in the space-time evolution of the blood pressure, flow rate and cross-sectional area of elastic vessels. Even though these local changes are known to cause global unexpected hemodynamical behaviors, all one-dimensional (1D) blood flow models are built under Newtonian fluid hypothesis. In this work, we present a time-dependent non-Newtonian extension of a 1D blood flow model, able to describe local space-time variations of the viscous behavior of blood. The rheological model is based on a simplified Maxwell viscoelastic equation for the shear stress with structure dependent coefficients. We compare the numerical predictions of the 1D non-Newtonian model to experimental rheological data available in the literature. Specifically, we explore four well documented shear stress protocols and we show that the results predicted by the 1D non-Newtonian model in a single artery accurately compare, both qualitatively and quantitatively, to the steady and unsteady shear stresses measured experimentally. We then use the 1D non-Newtonian model to compute the flow in idealized healthy and pathological symmetric and asymmetric networks of increasing size. We show that aggregation occurs in such networks occurs, leading to non-Newtonian blood behaviors especially in the presence of pathologies. This non-Newtonian extension of a 1D blood flow model will be useful in the future to improve our understanding of the large-scale hemodynamics in micro- and macro-circulation networks.

We employ a state-of-the-art microfabrication technique (selective laser-induced etching, SLE) to produce microfluidic cylinder geometries that explore new geometrical regimes. Using SLE, two microchannels are fabricated in monolithic fused silica substrate with height H = 2 mm and width W = 0.4 mm (aspect ratio α = H / W = 5 ) containing cylinders of radius r = 0.02 mm (blockage ratio β = 2 r / W = 0.1 ), centered at the channel mid-width, W/2. An ‘sc’ channel contains a single cylinder, while a ‘dc’ channel contains two axially-aligned cylinders separated by a distance L = 1 mm ( L = 50 r ). Compared with cylinder geometries fabricated by soft lithography (which typically have α ≪ 1 and β ≳ 0.5), these rigid glass devices provide a quasi-two-dimensional flow along the direction of the cylinder axis and also more clearly reveal the effects of the strong extensional wake regions located at the leading and trailing stagnation points. Using flow velocimetry and quantitative birefringence measurement techniques, we study the behaviour of a well-characterized viscoelastic polymer solution in flow around the cylinders. The small cylinder radii result in low inertia and very high elasticity numbers El ≈ 2400. For the sc device, we report strong flow modification effects around the cylinder as the flow rate is incremented. This is associated with the deformation of polymer molecules primarily in the upstream wake region, leading to the onset of a purely elastic flow asymmetry upstream of the cylinder. Stretched polymer molecules are advected around the cylinder and relax downstream of the cylinder, resulting in an extremely long elastic wake extending for > 300r downstream. In the dc channel, at lower flow rates, similar flow modification effects are observed to develop around, and downstream of, both cylinders. However, at higher flow rates the wake of the first cylinder extends > 50r downstream, and begins to interact with the second cylinder. The second cylinder becomes encapsulated by the wake of the first and is effectively obviated from the flow field. The results will be of relevance to understanding practical applications of viscoelastic fluids, for example in particle suspension and porous media flows, and also for benchmarking against numerical simulations using viscoelastic constitutive models.

The Oldroyd-B fluid has become the starting point for almost all complex flow calculations and analysis involving the behavior of dilute polymer solutions. The reasons for this are clear: based on the kinetic theory of high molecular weight “phantom” chains near equilibrium, the resulting model, in its simplest form, produces a single mode description of the solution constitutive equation in terms of a single symmetric dyad order parameter. The physical connection to the individual chains is therefore unambiguous through the end-to-end configuration tensor. The flow of the fluid resulting from the mathematical solution of the constitutive equation coupled to Cauchy’s equation of motion and continuity has been examined for decades and its strengths and weaknesses in predicting the features of non-linear viscometric and non-viscometric polymer solution flows are well known. Moreover, “simple” extensions (e.g. the FENE-P model) can ameliorate the most serious of these shortcomings. For example, the multi-mode Oldroyd-B model can provide quantitative predictions of the linear viscoelasticity of a wide range of polymer solutions. Remarkably, even with all its shortcomings, the Oldroyd-B fluid has been invaluable in predicting at least qualitatively, features as complex as purely elastic instabilities, turbulent drag modification, and even the effective rheology of particles suspended in polymer solutions. While remaining mindful of the model’s shortcomings, any student of these diverse fields may find the Oldroyd-B fluid an important starting point.

We investigate in silico the pulsatile blood flow in straight, rigid tubes using an elasto-viscoplastic, constitutive model coupled with thixotropy (TEVP) (Varchanis et al., 2019; Giannokostas et al., 2020). In addition to blood viscoelasticity, our model accounts for RBC aggregation through a kinetic equation that describes the level of blood structure at any instance and the viscoplasticity at stasis conditions. We evaluate the model parameters using steady, simple shear, and transient multi-shear rheometric experiments for human physiological subjects with normal blood aggregation. Then, we accurately reproduce previous experimental results (Thurston, 1975; Bugliarello and Sevilla, 1970; Thurston, 1976; Womersley, 1955) and provide reliable predictions for the pressure, stress, and velocity fields. We also investigate blood flow under sinusoidal and experimentally determined waveforms of the pressure-gradient with different frequencies, amplitudes, and patterns, providing a thorough parametric study. We find that the streamwise normal stress is of considerable magnitude. This stress component stretches the RBCs and their aggregates in the flow direction. Commonly used inelastic hemorheological models (e.g., Casson and Newtonian) cannot predict this. Typical values of the time-averaged wall normal-stress are found in the range of 2 Pa − 30 Pa , which are an order of magnitude larger than the corresponding wall shear-stress for the same hemodynamic conditions. The inelastic models systematically underestimate the shear-stress and overestimate the mean velocity. Finally, the TEVP model accurately predicts the phase-lags between the pressure-gradient and the flow-rate, and between the pressure-gradient and the structure-parameter for the whole range of the frequencies expressed in terms of the Womersley number, indicating its physical completeness and robustness.

Based on the original ideas by Oldroyd in 1947, Saramito in 2007 introduced a generally acceptable model for yield stress fluids that also accounts for their elasticity. We use this model to examine the buoyancy-driven rise of a bubble through Carbopol and predict the inverted teardrop shape that bubbles often attain when they translate through an elastoviscoplastic material. Such shapes are common in viscoelastic materials, but it is impossible to predict them using viscoplastic models without elasticity. Our results also show that generally, the fore-aft symmetry is lost and the negative wake is formed in the trailing edge of the bubble, even when creeping flow conditions are approached. We show that elastic and plastic forces are dominant in the smaller bubbles, whereas significant shear and extensional thinning occurs in the larger ones, making inertia forces dominant. The agreement of our predicted bubble shapes and rise velocities with their experimental counterparts is very satisfactory either for the smaller or the larger bubbles from those we examined. The former have an inverted teardrop shape and the latter have either an oblate or spherical cap shape. A deviation is found in the bubble radius for which the transition from the inverted teardrop shape to the oblate shape occurs. This deviation is attributed primarily to insufficient rheological characterization of the materials, particularly in terms of their nonlinear elasticity and their extensional properties.

This paper investigates the axisymmetric and the first non-axisymmetric linear instability of a charged viscoelastic jet under an applied axial magnetic field. The Oldroyd-B model is employed to account for the viscoelastic effect. Viscoelastic fluid is considered to be a leaky dielectric, and the surrounding inviscid gas a perfect dielectric. Results suggest that increasing the axial magnetic field suppresses both the axisymmetric and non-axisymmetric instabilities, and moves the main unstable range of the non-axisymmetric instability to small wavenumber regions. The magnetic field is coupled with the electric field by increasing the critical electric intensity of the dual effects on the axisymmetric mode; it also favors the transition from axisymmetric mode (jetting-dripping motion) to non-axisymmetric mode (jetting-whipping motion). It is also discovered that the magnetic field weakens the effects of fluid elasticity and deformation retardation time, but has little influence on the role played by the ambient gas.

The dynamics of streaky structures in a viscoelastic pipe flow of FENE-P fluids is studied numerically. The values of Weissenberg number ( W i , polymer relaxation time over flow turn-over time) and viscosity ratios are varied to evaluate the effects of viscoelasticity in the pipe. For Reynolds numbers 3000 ∼ 3500 (based on pipe radius and maximum laminar velocity) near the transition boundary, we select finite-amplitude two-dimensional rolls as initial conditions and add infinitesimal three-dimensional perturbations to trigger the transition. The 2D streamwise rolls are highly unstable to small 3D disturbances, which helps to better understand the evolution of large scale structures. The stronger temporal intermittency in viscoelastic flows makes it more difficult to identify a successful transition; we found that quantities directly related to viscoelasticity can serve as better indicators of transition to turbulence. The role of polymer stress is studied through the kinetic energy budget and it is found that polymer torque opposes the vorticity and become more dominant for higher W i , consistent with previous studies. The results show that the secondary instability of the streaky structures can be enhanced by viscoelasticity at low W i , while at high W i viscoelasticity delays the transition to turbulence, sometimes leading to relaminarization.

This work studies the dynamics of linear non-modal waves in viscoelastic pipe flows of FENE-P fluids using transient growth and resolvent analyses. We particularly focus on the time evolution of the amplification of the disturbance energy (using the 4th-order Runge–Kutta method) and discuss the dynamical traits of the Orr and the critical-layer mechanisms in the conformation tensor field when the transient energy increases. The helical mode undergoes a larger energy growth than the axisymmetric mode. The effects of various flow parameters have been investigated on the growth rate and energy amplification of the non-modal waves and the optimal flow structures. It is found that when the elastic effect is stronger, the amplitude of the optimal conformation tensor in the pipe centre region becomes greater from a non-modal perspective.

In this paper, we carried out an investigation of the dynamics of an air bubble rising in viscoelastic liquids with increasing volumes via volume-of-fluid based direct numerical simulations (DNS) with local adaptive mesh refinement techniques. The exponential Phan-Thien Tanner (EPTT) model is adopted for describing the rheological behaviours of the shear-thinning viscoelastic fluid. The well-known jump discontinuity in the terminal rise velocity at a critical bubble volume is captured, which agrees qualitatively with the experimental observation in the literature. On this basis, the numerical simulations have been performed for different rheological properties in wider flow regimes, providing new insights into the local flow field and the stress distribution around the deformable rising bubbles. A characteristic dimensionless regime map has also been proposed to distinguish the peculiar behaviours of a bubble rising in viscoelastic fluids at different Galilei ( G a ) and Eotvos ( E o ) numbers. We found that at low G a and low E o numbers, the large elastic stresses concentrate in the small region near the bubble’s trailing end, leading to the formation of bubble cusp. The appearance of the negative wake is the main reason for the velocity jump to occur. However, for higher G a of 10, the viscous forces become less dominating. The fluctuations of the polymeric stresses are substantially intensified with increasing bubble volume, and large bubbles experience a pulsating rising velocity with oscillation shapes. On the other hand, at intermediate G a and high E o of 10, the modest surface tension induces a cap with a thin skirt trailing the bubble main body at early times. Due to the polymer stretching, the strong extensional flow behind the small bubble eventually forces the bubble tail to break up. The above analyses on the bubble dynamics at constant Morton ( M o ) numbers facilitate the extrapolation of the volume effects at different flow regimes and, therefore, will guide the applications in the future.

Bubbles rising steadily in Carbopol often have an inverted teardrop shape with pointed tail, in contrast to steady bubble rise computations using simple yield stress fluid models. The cause of the pointed tail is suspected to be viscoelasticity, but another possibility is that the tail arises during the bubble formation and the shape is retained via some form of fluid memory effect (elastic, thixotropic or yield stress). Here we present results of a study in which we eliminate all possibility of memory effects using a multi-layered experimental design, but still find the pointed tail in steady bubble propagation. Thus, the tail shape can only result from a combination of the rheology and steady fluid deformation around the rising bubble. Further experiments show that the same steady shapes are found for quite different initial bubble shapes.

Lubricants can exhibit significant viscoelastic effects due to the addition of high molecular weight polymers. The overall behavior of the mixture is vastly different from a simpler Newtonian fluid. Therefore, understating the influence of viscoelasticity on the load carrying capacity of the film is essential for lubricated contacts. A new modeling technique based on lubrication theory is proposed to take into account viscoelastic effects. As a result, we obtain a modified equation for the pressure, i.e. the viscoelastic Reynolds (VR) equation. We have first examined a parabolic slider to mimic a roller bearing configuration. An increase of the load carrying capacity is observed when polymers are added to the lubricant. Furthermore, our results are compared with existing models based on the lubrication approximation and direct numerical simulations (DNS). For small Weissenberg number ( W i ), i.e. the ratio between the polymer relaxation time and the residence time scale, VR predicts the same pressure of the linearized model, in which ϵ W i is the perturbation parameter ( ϵ is the ratio between the vertical length scale and the horizontal length scale). However, the difference grows rapidly as viscoelastic effects become stronger. Excellent quantitative and qualitative agreement is observed between DNS and our model over small to moderate Weissenberg number. While DNS is numerically unstable at high values of the Weissenberg number, VR does not have the same issue allowing to capture the evolution of the stress and pressure also when the viscoelastic effects are strong. It is shown that even in high shear flows, normal stresses have the largest impact on load carrying capacity and thus cannot be neglected. Furthermore, the additional pressure due to viscoelasticity comprises two components, the first one due to the normal stress and the second one due to the shear stress. Afterwards, the methodology used for the parabolic slider is extended to a plane slider where, instead, the load decreases by adding polymers to the fluid. In particular, under the effect of the polymers surface slopes enhance the rate at which pressure gradients increase, whereas curvature opposes this along the contact. Therefore, the increase of the load carrying capacity observed for viscoelastic lubricants is due to its shape close to the inlet, which is steeper than the plane slider.

We describe a customized Capillary Breakup Extensional Rheometer (CaBER) with improved dynamic performance and added features for temperature control over the range from room temperature up to 250 °C. The system is aimed at characterizing the extensional rheological behavior of weakly rate-thickening fluids that are widely utilized in the automotive industry. We examine the shear rheology and filament-thinning dynamics of two commercially available automotive fluids with the same viscosity index. Comparisons of the rheological properties of the two samples reveal that although they have identical shear viscosities, they exhibit significant and distinct rate-thickening behavior in the strong extensional flow that is generated close to filament breakup. For the more elastic sample, the exponential filament-thinning dynamics are well-described by the Oldroyd-B model; however, this viscoelastic model poorly describes the response of the more weakly rate-thickening fluid. To address this limitation, we propose a simple Inelastic Rate-Thickening (IRT) model that more robustly describes the measured material response. The two constitutive parameters of the model represent the zero-shear-rate viscosity of the fluid and the rate of extensional thickening in the fluid. Numerical calculations with the IRT model show that the radii of thinning fluid filaments deviate from a linear decay in time and approach a quadratic dependence very close to breakup. By carefully fitting the measured temporal evolution of the mid-plane radius we can therefore systematically differentiate the extensional rheological response of the two oils. More generally, we show that the weakly rate-thickening regime can be distinguished from the well-known elasto-capillary response predicted by the Oldroyd-B model, via a constraint on the relaxation time (or more specifically the elasto-capillary number) of the fluid. The weakly rate-thickening behavior documented in these oils is representative of the relatively unstudied extensional rheology of many industrial fluids at large extensional strain rates (100–1000 s-1) and influences many complex industrial processes such as jetting, coating and stamping.

Nonmodal analysis typically uses square-integrated quantities to characterize amplification of disturbances. However, such measures may be misleading in viscoelastic fluids, where polymer stresses can be strongly amplified over a small region. Here, we show that when using a localized measure of disturbance amplification, spanwise-constant polymer-stress fluctuations can be more amplified than streamwise-constant polymer-stress fluctuations, which is the opposite of what is observed when a square-integrated measure of disturbance amplification is used. To demonstrate this, we consider a model problem involving two-dimensional pressure-driven inertialess channel flow of an Oldroyd-B fluid subject to a localized time-periodic body force. Nonmodal analysis of the linearized governing equations is performed using recently developed well-conditioned spectral methods that are suitable for resolving sharp stress gradients. It is found that polymer-stress fluctuations can be amplified by an order of magnitude while there is only negligible amplification of velocity fluctuations. The large stress amplification arises from the continuous spectrum of the linearized problem, and may put the flow into a regime where nonlinear terms are no longer negligible, thereby triggering a transition to elastic turbulence. The results suggest an alternate mechanism that may be useful for understanding recent experimental observations of elastic turbulence in microchannel flows of viscoelastic fluids.

A rotating cylinder asymmetrically placed across a duct, with its axis perpendicular to the axis of the channel, has long established itself as a simple mechanism for the transport of Newtonian fluids in microfluidic channels. In the present study, the possibility of transporting viscoelastic fluids by this simple mechanism is numerically investigated using finite-volume method (FVM). For ease of analysis, we have relied on two-dimensional flow between two parallel plates for this purpose. To screen out the complicating effects of shear-dependent viscosity from the analysis, the viscoelastic fluid of interest is assumed to obey the Oldroyd-B model. Using finite-volume-method (RheoFoam solver) we have obtained converged creeping-flow results over a wide range of working parameters for Deborah numbers up to unity. Based on our obtained numerical results, it is concluded that a fluid's elasticity can negatively affect the performance of viscous micro-pumps. The drop in efficiency is predicted to increase the larger the Deborah number. At De = 1, the drop in efficiency is predicted to be around 30%, as compared with Newtonian fluids of the same viscosity. Since the drop in efficiency is not too excessive, viscous micropumps can be regarded as a viable option for the transport of moderately-elastic liquids, particularly in those microfluidic applications where efficiency is of secondary importance.

The sedimentation of a spherical solid particle in viscoelastic fluids was studied using a Giesekus model by development of a direct numerical simulation solver based on fully-resolved and immersed boundary methods to understand the complex non-Newtonian fluid flow and spherical particle dynamics. Two benchmark problems were modeled to evaluate the accuracy of the developed solver and excellent agreement with prior experimental and simulation results were obtained. In addition, the temporal and spatial order of convergence of the transient and advection discretization schemes were studied. The aim is to provide a clearer picture for the effect of confinement and rheology of the viscoelastic fluid on the sedimentation phenomenon of a spherical particle in a Giesekus fluid. We report that the negative wake occurs at Weissenberg number Wi ≥ 2.45 at all blockage ratios a ∕ R = 0 . 243 , 0.390, 0.464, and 0.538. At Wi = 1 . 00 , the negative wake occurs mainly at blockage ratio a ∕ R ≥ 0.390 when the effect of confinement is enhanced. There is a linear relationship between the sphere overshoot/steady-state velocity and blockage ratio due to shear-thinning effects. The oscillations in the sphere velocity were reported at all Wi for blockage ratios a ∕ R ≤ 0.464. The sphere velocity oscillations disappear at the highest blockage ratio a ∕ R = 0 . 538 except at Wi = 0 . 01 and 1.00. The viscoelastic fluid velocity oscillations were reported at Wi ≥ 1.00 at all blockage ratios. The viscoelastic fluid velocity oscillations become more damped with blockage ratio a ∕ R which the mutual effects of shear-thinning and wall effects become more dominant.

A theoretical investigation of the behavior of Newtonian and viscoelastic jets during centrifugal spinning (CS) is presented in this paper. We used a discretized model, which provides a numerical framework to solve complex continuum equations, to model the spinning behavior of the viscoelastic Boger fluid. The jet was modeled as a series of beads connected with massless springs. After defining the viscoelastic, surface tension and aerodynamic drag forces for each bead, we solve Newton's second law of motion to obtain the trajectory of the jet. We first compared the jet profile predictions of the Newtonian fluid from the bead-spring model with an asymptotic thin-fiber model and obtained consistent results. Finally, we performed a parameter study to understand the effects of various properties such as viscoelasticity, surface tension and process conditions on the behavior of the viscoelastic jet. We also compared the simulation results with the experimental observations of PIB/PB Boger fluids to validate the discretized model.

We consider the linear stability of channel flow of a shear-thinning viscoelastic fluid, replicating a instability recently discovered in experimental [1] and theoretical work [2]. We have extended the fluid model to allow for an inelastic shear-thinning stress component, and find that this additional contribution always has a stabilising influence on the instability. We conclude that, while shear-thinning is critical to the instability, the mechanism is primarily elastic.

International audience; When a polymer solution is sheared between concentric cylinders, with the inner rotating and the outer fixed, the torque on the inner cylinder is modified compared to a Newtonian fluid of the same viscosity revealing the di↵erent flow patterns that emerge above the linear stability threshold for circular Couette flow. Here, mixtures of relatively short and long linear polymers in dilute and semi-dilute concentrations were considered. Their shear viscosity and extensional relaxation time are quantified. The stability of the flow is monitored through torque measurements and flow visualisations for a constant rate of acceleration and deceleration of the inner cylinder in a wide range of polymer concentrations. The torque exhibits an hysteretic behaviour, typical of subcritical transition. For large concentrations, six di↵erent numbers of steady solitary pairs of vortices, called diwhirls, were observed depending on the deceleration rate and their torque contribution is reported.