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The mechanical behavior of spherical capsules and red blood cells in shear and confined pressure-driven flow of polymeric fluids was studied computationally. In particular, we study the effect of suspending fluid elasticity on the steady mechanical behavior of spherical capsules and red blood cells suspended in an Oldroyd-B fluid, in dilute shear and confined pressure-driven flow, as a model system for dilute suspensions of capsules in polymeric fluids. We investigate the effects of suspending fluid elasticity at fixed capillary number on the capsule deformation, membrane tensions, and effective viscosity for a range of capsule capillary numbers. For both spherical capsules and red blood cells, capsule deformation was found to decrease with increasing fluid elasticity in shear flow, and increase in confined pressure-driven flow. The average membrane tension for spherical capsules was found to follow the same trends: decreasing in shear and increasing in pressure-driven flow; however, the average membrane tension for red blood cells had a less pronounced trend with fluid elasticity, which we attribute to the reduced volume of the red blood cell. On the other hand, the effective viscosity of the suspension was found to be non-monotonic with an increase in suspending fluid elasticity for both flows and particle types. The underlying mechanisms for these trends were investigated by comparing these capsule simulations to results from rigid spherical particles. These results indicate that the mechanical behavior of these dilute capsule suspensions can be qualitatively understood by examining the disturbance flow created by the introduction of rigid spherical particles, and the subsequent stress induced in the polymeric fluid to these disturbances. • The effects of fluid elasticity in dilute capsule suspensions are investigated • At the particle level, elasticity affects capsule deformation and membrane tension • Elasticity also affects the bulk rheology (effective viscosity) of the suspension • Compared against rigid particle-fluid interactions in viscoelastic flow [ABSTRACT FROM AUTHOR]

This study numerically simulates the two-dimensional flow of Oldroyd-B fluid around an isosceles right-angled triangular cylinder with five orientations. The log-conformation reformulation is employed to stabilize the numerical simulations. By adjusting the triangular orientation angle (θ), three types of fluids development process can be observed: from steady to vortex shedding at θ = 0 and π , keeping the vortex shedding at θ = π 4 and 3 π 4 , and from vortex shedding to steady state at θ = π 2 . When the triangular cylinder faces the incoming stream with the inclined plane, the elastic effect acting on the cylinder is strong, otherwise it is weak. For θ = π 2 , the effects of the viscosity ratio (β), the Reynolds number (R e), and the Weissenberg number (W i) are further investigated. When the elasticity is reduced by changing the viscosity ratio (β) that ranged from 0 to 0.9, the final flow state will transition from stable to vortex shedding state, which indicates the restraining effect of elasticity on wake instability. In the high elastic Oldroyd-B fluid, the critical Reynolds number for vortex shedding is about 110 for W i = 1. Besides, the Weissenberg numbers (W i) ranged from 0.25 to 8 are discussed at R e = 100. With the increase of W i , four different flow states of the wake are observed: periodic vortex shedding at low Weissenberg number W i = 0. 25 , stabilizing for W i ranged from 0.5 to 1, semi-periodic strong vortex shedding for W i is about 2, and chaos when W i ≥ 4. The results indicate that excessively strong elastic effects may also lead to unstable flows. Finally, the flow states corresponding to each Reynolds number and Weissenberg number in a certain range (90 ≤ R e ≤ 120 and 0. 125 ≤ W i ≤ 4) are given in this study. • The strong elasticity mainly acts on the hypotenuse of the leading edge of the triangular cylinder. • The vortex shedding can be inhibited by the elasticity. • Inertial elastic instability is observed at high Weissenberg numbers. [ABSTRACT FROM AUTHOR]

A new theory is formulated for the description of the conformation state of the polymer chains in free turbulent shear flows of viscoelastic fluids. Using self-similarity arguments and new scaling relations for the turbulent flux of conformation tensor we show the existence of minimum and maximum solvent dissipation reduction asymptotes, and four different polymer deformation regimes. The similarities with the maximum drag reduction asymptote of turbulent pipe flow is discussed and new scaling laws are obtained for all components of the mean conformation tensor at each deformation regime. Analytical solutions for the self-similar transverse profiles of the conformation tensor components are also obtained, providing the complete solution for the mean flow problem at the far field. The analysis is developed for both planar jets and wakes and covers the two limits of shear flows, with large and small velocity differences, respectively. Comparisons of the new theoretical results with several direct numerical simulations employing the FENE-P rheological model show excellent agreement. • A new theory is developed for free turbulent shear flows of viscoelastic fluids. • There are four regimes of polymer deformation in free turbulent shear flows. • We show the existence of minimum and maximum dissipation reduction asymptotes. • Comparisons between the theory and DNS data show excellent agreement. [ABSTRACT FROM AUTHOR]

At low Reynolds numbers, "swirlers" – swimmers with an axisymmetric "head" and "tail" counterrotating about the axis of symmetry – generate no net propulsion in a Newtonian fluid as a consequence of the "scallop theorem". Viscoelasticity in the suspending fluid breaks the time-reversibility and allows swirlers to propel themselves, with the swim speed being a function of swimmer geometry, fluid elasticity, and swimming gait. Using analytical theory and numerical simulations, we study the unsteady motion of a freely-suspended self-propelled swirler though viscoelastic fluids described by the Giesekus model, allowing for general axisymmetric geometry and time-dependent tail rotation rate. We show the steady swim speed can be calculated for general arbitrary axisymmetric geometries at low Deborah number via the reciprocal theorem and the solution of two Newtonian flow problems. In this "weak flow" limit, we analytically determine the swim speed and its dependence on the parameters of the Giesekus fluid which in turn are related to the primary and secondary normal stress coefficients Ψ 1 and Ψ 2. Furthermore, at low De, we derive the unsteady swim speed as a function of a specified unsteady tail rotation rate and the material properties of the suspending fluid. We show that for a particular tail rotation rate, the unsteady swim speed can be analyzed to recover the spectrum of fluid relaxation times, analogous to small-amplitude oscillatory shear measurements on a benchtop rheometer. This study expands upon the design space for a "swimming rheometer" by increasing its functionality to make and interpret rheological measurements. • Normal stresses propel axisymmetric "swirlers" through complex fluids. • The swim speed for unsteady gaits is related to fluid viscoelasticity. • A method for designing swirler geometries for increased propulsion is proposed. [ABSTRACT FROM AUTHOR]

Lubricating oils are used to minimize the friction and wear of mechanical components by virtue of a thin lubricant film separating the sliding surfaces. The film's characteristics, under high pressure, can exhibit non-Newtonian effects, such as viscoelasticity and shear thinning. The strength of these effects are measured using the Weissenberg (Deborah) number W i (D e), i.e., the ratio of the polymer relaxation time to the shear (residence) time scale. Modeling these effects is computationally challenging, especially when relying on the direct numerical simulation (DNS) of the Cauchy momentum and the mass conservation equations. However, the viscoelastic Reynolds (VR) approach (Ahmed & Biancofiore, Journal of Non-Newtonian Fluid Mechanics, 292, 104524, 2021.) has been shown to be effective in modeling (i) the pressure distribution and (ii) the load carrying capacity of a viscoelastic lubricating film for mechanical contacts for the Oldroyd-B constitutive relation, since these contacts operate within the small D e limit (but no constraint in W i). In this work, we have extended the VR approach to the finitely extensible non-linear elastic (FENE) type constitutive relations that account for the (i) finite extension of the polymer chains and (ii) shear thinning. We have validated the VR approach against DNS, showing an excellent agreement over a wide range of the Weissenberg number W i , and finite extensibility parameter L , using FENE-CR and FENE-P models. Following a thorough validation, the pressure distribution and the load carrying capacity of a journal bearing, whose channel height is governed by the journal eccentricity ratio e , is considered. It is observed that the load carrying capacity of the film portrays a strongly non-linear dependence on W i , L and e : while it increases for small values of W i , limited greatly by the capacity of the polymer to stretch, a saturation and a subsequent decline is observed for high W i regimes. Additionally, a weakly (strongly) eccentric configuration plays an important role in promoting (hindering) the growth in load versus both W i and L. These effects are significant and have to be considered when modeling thin contacts lubricated with a strongly viscoelastic fluid. • For the first time non-linear stress constitutive equations are used to model viscoelastic lubricants. • The VR approach is able to reproduce DNS results but it is much more computationally efficient. • We cannot neglect the finite extensibility of the polymers and shear thinning in contacts lubricated by viscoelastic films. • In a journal bearing the viscoelastic effect strongly depends on the eccentricity ratio. [ABSTRACT FROM AUTHOR]

A new rheological formalism based on the ideas of recovery is presented. Our new formalism contains recoverable and unrecoverable contributions to arbitrary deformations. The introduction of the two displacement gradients leads to two distinct measures of strain and strain rates, which highlights the importance of performing recovery experiments. Having established the new formalism, we show the benefits of this way of thinking by performing transient step strain and startup shear recovery measurements in a wide range of shear strains and shear rates on a model viscoelastic solution. With recovery, we show clear similarities in the material behavior between the two test protocols. The resultant recovery material functions – recoverable modulus and flow viscosity – allow the development of a new constitutive model, which consists of nonlinear elastic and viscous functions, along with a retarded viscous term. The predictions of the model are compared favorably with the experimental data, including responses to extremely large step strains. These observations allow us to revisit the transient entanglement length, relaxation time, and damping function based on the idea of recovery rheology. The present findings suggest a clear correlation exists between microstructural evolution and recoverable and unrecoverable components and provide a new direction for the exploration of the relation between recovery material functions and material responses under different dynamic flows. • Acknowledgment that strain is composite affects how we study complex fluids. • Formal definitions affect how experiments should be carried out. • Recoverable and unrecoverable responses can be used to make new models. [ABSTRACT FROM AUTHOR]

Moving mesh finite element method (FEM) for simulating dynamics of viscoelastic droplets on inclined surfaces is proposed. Viscoelasticity is incorporated into the governing system employing the Oldroyd-B constitutive model. The supporting (inclined) surface is allowed to have non-homogeneous properties incorporated into the mathematical model through the generalized Navier boundary conditions (GNBC). The droplet motion (sliding and/or rolling) is handled by employing arbitrary Lagrangian Eulerian (ALE) framework. Energy balance is derived from the governing system and it is a starting point in the derivation of the numerical scheme. The overall numerical strategy is designed in such a way that a counterpart of the (continuous) energy balance holds on the discrete level. This ensures that no spurious energy is introduced into the discrete system which, in turn, guarantees the stability of the scheme in the energy norm. The framework proposed is very general and encapsulates both two and three dimensional scenarios. Numerical studies in this work focus primarily on the three dimensional scenarios since such are significantly more challenging and seem to be much scarcer in the literature. The newly proposed numerical strategy is validated on several examples to confirm the theoretical predictions. The role of viscoelasticity in the overall droplet dynamics is briefly investigated and the behaviors of Newtonian and non-Newtonian droplets are compared. • Energy stable arbitrary Lagrangian Eulerian finite element method for sliding and rolling viscoelastic droplets. • Dynamic contact line and non-homogeneous properties of supporting surface are incorporated. • Viscoelasticity is incorporated through Oldroyd-B constitutive model. [ABSTRACT FROM AUTHOR]

• Transient 3D finite element method to predict extrudate swell for complex domains. • The method is validated using a 2D axisymmetric problem. • Difficulties in convergence due to the singularity at the die exit are highlighted. • Swell results are shown for different complex 3D die. • Viscoelastic results are shown for extrudate swell out of a 3D square die. 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. [ABSTRACT FROM AUTHOR]

• The thermocapillary motion of a Newtonian drop in a viscoelastic fluid is investigated numerically. • Viscoelastic stresses concentrate at the rear stagnation point of the drop. • The drop is found to deform into a prolate ellipsoid. For sufficiently large Deborah numbers, a pointed end is also observed. • The drop migration speed is found to be affected by the presence of viscoelastic stresses. In this work we investigate the role played by viscoelasticity on the thermocapillary motion of a deformable Newtonian droplet embedded in an immiscible, otherwise quiescent non-Newtonian fluid. We consider a regime in which inertia and convective transport of energy are both negligible (represented by the limit condition of vanishingly small Reynolds and Marangoni numbers) and free from gravitational effects. A constant temperature gradient is maintained by keeping two opposite sides of the computational domain at different temperatures. Consequently the droplet experiences a motion driven by the mismatch of interfacial stresses induced by the non-uniform temperature distribution on its boundary. The departures from the Newtonian behaviour are quantified via the "thermal" Deborah number, De T and are accounted for by adopting either the Oldroyd-B model, for relatively small De T , or the FENE-CR constitutive law for a larger range of De T. In addition, the effects of model parameters, such as the concentration parameter c = 1 − β (where β is the viscoelastic viscosity ratio), or the extensibility parameter, L 2, have been studied numerically using a hybrid volume of fluid-level set method. The numerical results show that the steady-state droplet velocity behaves as a monotonically decreasing function of De T , whilst its shape deforms prolately. For increasing values of De T , the viscoelastic stresses show the tendency to be concentrated near the rear stagnation point, contributing to an increase in its local interface curvature. [ABSTRACT FROM AUTHOR]

• Concentrated stresses seen in simulations near swimmer tips in viscoelastic fluids. • Theoretical investigations probe the origin of these concentrated stresses. • Polymer stress: linear (small Wi) and exponential (high Wi) in oscillating extension. • Flow near tips of swimmers is oscillating extension. • High amplitude regime quantified, significant nonlinear feedback, higher stresses. Simulations of undulatory swimming in viscoelastic fluids with large amplitude gaits show concentration of polymer elastic stress at the tips of the swimmers. We use a series of related theoretical investigations to probe the origin of these concentrated stresses. First the polymer stress is computed analytically at a given oscillating extensional stagnation point in a viscoelastic fluid. The analysis identifies a Deborah number (De) dependent Weissenberg number (Wi) transition below which the stress is linear in Wi, and above which the stress grows exponentially in Wi. Next, stress and velocity are found from numerical simulations in an oscillating 4-roll mill geometry. The stress from these simulations is compared with the theoretical calculation of stress in the decoupled (given flow) case, and similar stress behavior is observed. The flow around tips of a time-reversible flexing filament in a viscoelastic fluid is shown to exhibit an oscillating extension along particle trajectories, and the stress response exhibits similar transitions. However in the high amplitude, high De regime the stress feedback on the flow leads to non time-reversible particle trajectories that experience asymmetric stretching and compression, and the stress grows more significantly in this regime. These results help explain past observations of large stress concentration for large amplitude swimmers and non-monotonic dependence on De of swimming speeds. [ABSTRACT FROM AUTHOR]

Highlights • Emphasized the applicability of the newly developed extensional rheometry technique. • Characterized low viscosity commercially used printing inks through extensional rheology. • Performed parametric study on the effect of binder concentration, polymer architecture, molecular weight and solution viscosity. • Characterized inks of relaxation time as low as λ = 160 μ s. • Distinguished jetted inks from non-jettable inks. Abstract In this manuscript, the capillary thinning dynamics of a series of solutions containing polymers commonly used in the coating industry as low-viscosity printing inks were studied. Four different polymer binders were studied in methyl-ethyl ketone. These included one acrylic polymer, one cellulose polymer and two vinyl polymers of different molecular weights. The dripping-onto-substrate capillary breakup extensional rheometry (CaBER-DoS) method was used to characterize the extensional rheology for solutions with viscosities as low as 3.5mPa.s. This technique is based on the measurement of the decay of a fluid filament under the influence of surface tension and has been shown to be capable of measuring relaxation times as low as 20 µs for weakly elastic liquids. The influence of the polymer concentration on the dynamics of filament breakup was investigated for each polymer solution and the results were compared to those obtained with different polymer binders. With an increase in polymer concentration, a critical polymer concentration was identified for the transition between the inertio-capillary, the visco-capillary and the elasto-capillary breakup regimes. With the onset of elasto-capillary breakup at moderate to high polymer concentrations, a delay in the filament breakup was observed due to an increase of the viscous and elastic stresses. This viscoelastic breakup delay would be detrimental to most ink jet printing applications. Within the elasto-capillary breakup regime, the transient extensional viscosity resulted in Trouton ratios ranging from just above the Newtonian limit of Tr = 3 to values close to Tr = 100. [ABSTRACT FROM AUTHOR]

Highlights • Relevance of 3D numerical simulations for slit die swell. • Interplay of viscous and elastic effects using the PTT constitutive model. • Model validation based on die pressure and real time experimental HD imaging. Abstract 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. [ABSTRACT FROM AUTHOR]

Highlights • Retraction of a viscoelastic liquid circular film after it has been stretched is studied by numerical simulations. • A parametric study is carried out at varying film stretching rate and fluid viscosity, elasticity, and inertia. • Different retraction behaviors can be identified depending on relative weight of the parameters. Abstract 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. [ABSTRACT FROM AUTHOR]

Highlights • A coupled numerical approach to compute the flow of viscoelastic fluids is proposed. • The Oldroyd-B Poiseuille, UCM lid-driven and LPTT 4:1 contraction flows are studied. • The new technique showed significant reduction in CPU time and number of iterations. • The benefits obtained generally increase with mesh resolution and Deborah number. • The code is implemented in the open-source computational library foam-extend. Abstract In this work, a block coupled algorithm for the solution of laminar, incompressible viscoelastic flow problems on collocated grids is presented. The inter-equation coupling of the incompressible Cauchy momentum equations and extra-stress tensor constitutive equation is obtained by deriving a pressure equation in a procedure similar to a SIMPLE algorithm with the Rhie-Chow interpolation technique, and a special treatment of the diffusion term in the momentum equations added by the improved both-sides diffusion (iBSD) technique, recently developed for the finite volume method. Additionally, the velocity field is considered implicitly in the extra-stress tensor constitutive equation by expanding the convective term with a second order Taylor series expansion. All the equations, comprising the continuity, momentum and extra-stress tensor constitutive equations are block-coupled into a single system of equations. The implicitly coupled system of equations is solved by an algebraic multigrid algorithm, which allows to accelerate the calculation process. The performance improvements obtained with the new solver are studied for three 2D viscoelastic flow case studies, and are quantified in terms of number of iterations and CPU time required to reach the predefined convergence criteria. The presented algorithm has been implemented into the open-source computational library foam-extend, a community driven fork of the OpenFOAM software. [ABSTRACT FROM AUTHOR]

Highlights • Proper Orthogonal Decomposition (POD) analysis of viscoelastic fluid dynamics. • Analysis of viscoelastic fluid instabilities at extensional points in Stokes limit. • Temporal transitions well-captured by a few temporal modes. • Dynamic modes ordered by total energy of system. Abstract 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. [ABSTRACT FROM AUTHOR]

Highlights • Surface charge diminishes the interval of Ohnesorge number for oscillations. • Surface charge and finite conductivity induce new bifurcations • The Rayleigh limit is the same as that for a perfectly conducting inviscid droplet. • High-order modes become dominant at sufficiently large electric fields. Abstract 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. [ABSTRACT FROM AUTHOR]

Highlights • The Frenet-Serret frame is the natural way to analyze material responses. • The motion of an instantaneous phase angle is used to track the yielding transition. • The yielding of soft materials is a gradual transition. • Yielding can be time-resolved within a period of oscillation using this approach. • The yield state of a Carbopol microgel is mapped in deformation and period time. Abstract 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. [ABSTRACT FROM AUTHOR]

Highlights • A viscoelastic model for CNF suspensions using a population balance equation. • The population balance equation for fiber floc aggregation-breakage. • The present model describes shear thinning in viscosity. • Viscoelastic stress growth in step shear, depending on the relaxation time. • Fiber floc aggregation-breakage in flows of CNF suspensions through a circular tube. Abstract 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. [ABSTRACT FROM AUTHOR]

Highlights • A VoF-time-splitting technique is described and released (http://www.basilisk.fr). • The splashing of viscoelastic droplets on solid and liquid substrates is studied. • Viscoelastic bulk effects are negligible in splashing on hard substrate. • On liquid substrate viscoelastic stresses alter the dynamic of the vortex shedding. Graphical abstract Abstract We propose an adaptive numerical solver for the study of viscoelastic 2D two-phase flows using the volume-of-fluid method. The scheme uses the robust log conformation tensor technique of Fattal and Kupferman (2004, 2005) [1,2] combined with the time-split scheme proposed by Hao and Pan (2007) [3]. The use of such a time-split scheme has been proven to increase the stability of the numerical computation of two-phase flows. We show that the adaptive computational technique can be used to simulate viscoelastic flows efficiently. The solver is coded using the open-source libraries provided by the Basilisk (Popinet, 2018 [4]) platform. In particular, the method is implemented for Oldroyd-B type viscoelastic fluids and related models (FENE-P and FENE-CR). The numerical scheme is then used to study the splashing of weakly viscoelastic drops. The solvers and tests of this work are freely available on the Basilisk (Popinet, 2018 [4]) web site (Lopez-Herrera, 2018 [5]). [ABSTRACT FROM AUTHOR]

Highlights • Planar and axisymmetric linear stability analysis of thin liquid sheets. • Planar and axisymmetric non-linear model for viscoelastic liquid sheet breakup. • Effect of viscoelasticity on the breakup time of thin liquid sheets. Abstract 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. [ABSTRACT FROM AUTHOR]

Highlights • The dynamics of a spheroid in a viscoelastic liquid in a wide-slit channel is studied. • The study is performed by 3D ALE finite element simulations. • Fluid viscoelasticity induces a migration prevalently towards the centerplane. • Wall attraction is possible, but limited to a narrow set of initial configurations. • The particle tends to slowly align along the flow direction. Abstract The translational and orientational dynamics of a spheroid suspended in a viscoelastic liquid flowing in a wide-slit microchannel is studied by 3D finite element simulations. An Arbitrary Lagrangian-Eulerian formulation is adopted to handle particle motion. The particle dynamics, with specific interest on the migration phenomenon and on the long-time orientation, is studied by computing the trajectories of the spheroid and the orbits described by its orientation vector. The effects of the initial distance from the channel centerplane and of the initial orientation on the particle motion is investigated, for low and moderate Weissenberg numbers. A 'migration state diagram' giving the long-time equilibrium positions of the particle for all possible initial configurations is derived: in most cases, the particle goes to the centerplane, but there are circumstances where also the wall is an attractor. [ABSTRACT FROM AUTHOR]

Highlights • Pure shear thinning reduces the drag, the vortex formation length, the separation angle, increases the shedding frequency. • Pure elasticity increases the drag coefficient, the vortex formation length, and reduces the shedding frequency, the separation angle. • Drag reduction in shear thinning fluids is mainly due to reduction in friction drag. • Anisotropic effects decrease the drag, the vortex formation length, and increases the shedding frequency. • Extensibility of polymer molecules increases the drag, the vortex formation length, and decreases the shedding frequency. Abstract This study focuses on the parametrical investigation and comparison of different non-Newtonian effects due to polymer/surfactant additives on the flow structure around a circular cylinder in periodic vortex shedding regime. For this purpose, inelastic power-law and viscoelastic Oldroyd-B, Giesekus and FENE-P models are adopted in the constitutive formulation. The range of the Reynolds number is 80 ≤ Re ≤ 300, the power-law index range is 0.6 ≤ n ≤ 1.2 and the Weissenberg number range is 0 ≤ Wi ≤ 1.2. A finite-element based solver is used in the two-dimensional flow simulations. The resulting flow structure is compared and discussed in terms of the variation in drag and lift coefficients, vortex shedding frequency, vortex formation length, separation angle and the critical Reynolds number for the onset of vortex shedding. Drag reduction is observed for shear thinning fluids as also observed in previous studies with inelastic models; moreover, the vortex shedding frequency increases, and both the vortex formation length and separation angle decrease under shear thinning. Drag reduction in shear thinning fluids is mainly due to reduction in friction drag. Fluid elasticity leads to an increase in the drag coefficient and vortex formation length, and a decrease in the vortex shedding frequency and separation angle. Also, anisotropy effects through the mobility factor decrease the drag, the vortex formation length, and increases the shedding frequency. The extensibility of polymer molecules increases the drag, the vortex formation length, and decreases the shedding frequency. It is also observed that weakly elastic effects have almost no impact on the onset of periodic vortex shedding. [ABSTRACT FROM AUTHOR]

Highlights • A mathematical model based on co-injection molding is proposed. • Rolie–Poly constitutive equation is used to describe viscoelastic flows. • "V" shape pattern in injection molding is successfully predicted. • Molecular orientation, extension and deformation of polystyrenes are shown. • Velocity, molecular weight are main factors that affecting the "V" shape pattern. Abstract The feature of the flow front for polystyrene melts in injection molding is investigated in detail in this article. To explore the generation and evolution processes of "V"-shape pattern in the skin areas for polymer melt, a mathematical model based on the co-injection molding is proposed in which the evolution of material line is traced by level set method, and viscoelastic behavior of polystyrenes is described by Rolie–Poly constitutive equation; the molecular orientation, extension and deformation of polystyrenes are also studied in this article. The capabilities of Rolie–Poly constitutive equation is validated by simulating the principal stress difference(PSD) for both an entry-exit slit flow and a cross-slot geometry for polystyrenes melt; then the mold filling process has been analyzed by finite volume method to solve the continuity, momentum, constitutive equation together with level set equation. The numerical results for the evolution processes of "V"-shape pattern shows good agreement with available numerical results and experiments results obtained by injection machine. Furthermore, three main factors that include inlet velocity, molecular weight of polymer and temperature that affecting the formation and form of "V"-shape pattern were discussed, and molecular conformation of polystyrenes melt are also presented. [ABSTRACT FROM AUTHOR]

Highlights • Complex local flow around a tiny bubble surface under pressure-oscillating field. • 2D flow birefringence profile captured by the latest high-speed polarization camera. • A negative wake generated cyclically at the tail of bubble due to rapid deformation. Abstract 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. [ABSTRACT FROM AUTHOR]

Highlights • Modeling of isothermal viscoelastic droplet impingement on hydrophilic surfaces. • Local projection stabilized finite element scheme for viscoelastic free-surface flows. • Arbitrary Lagrangian Eulerian (ALE) approach for tracking the free-surface. • Parametric study to analyze effects of viscoelasticity on the drop spreading dynamics. Abstract 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. [ABSTRACT FROM AUTHOR]

Highlights • Low- (LDR) and high-extent drag reduction (HDR) are qualitatively different stages. • Sharp changes in flow statistics are established between LDR and HDR. • Drag-reducing polymers affect different wall regions between LDR and HDR. • Turbulent structures become clustered and localized during the LDR–HDR transition. • A mechanism is proposed based on the changing vortex re-generation dynamics. Abstract Flexible polymer additives are known to reduce the energy dissipation and friction drag in turbulent flows. As the fluid elasticity increases, the flow undergoes several stages of transitions. Much attention in the area has been focused on the onset of drag reduction (DR) and the eventual convergence to the maximum drag reduction (MDR) asymptote. Between the onset and MDR, recent experimental and numerical observations prompted the need to further distinguish the low- and high-extent drag reduction (LDR and HDR). Fundamental knowledge of this transition will be important for understanding turbulent dynamics in the presence of polymers, as well as for inspiring new flow control strategies for efficient friction reduction. We use direct numerical simulation (DNS) to explore all these transitions in the parameter space and, in particular, demonstrate that the LDR–HDR transition is not merely a quantitative effect of the level of drag reduction, but a qualitative transition into a different stage of turbulence. A number of sharp changes in flow statistics are found to accompany the transition and at HDR, turbulence becomes localized with vortices forming clusters. These observations suggest that polymer-induced drag reduction follows two distinct stages. The first starts at the onset of drag reduction, where the coil-stretch transition of polymers causes an overall suppression of turbulent fluctuations. The second starts at the LDR–HDR transition, where flow statistics become fundamentally changed in the log-law layer and turbulence localization is observed. A mechanism is then proposed for the latter based on the changing vortex regeneration dynamics between LDR and HDR. [ABSTRACT FROM AUTHOR]

Highlights • Critical conditions of the inertial instability are modified due to elasticity • At high Re, first normal-stress difference peaks exist off the geometrical centre • Complex 3D flow due to instability leads to the generation of extra stagnation points • The inertial instability is modified due to elastic stresses at stagnation points Abstract 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. [ABSTRACT FROM AUTHOR]

Highlights • We have improved numerical stability of the deformation fields method for memory integral models. • The new stabilization techniques have been implemented using the finite element method. • Problems studied include time-dependent shear flow and flow around a cylinder. • Numerical stability is shown to be similar to state-of-the-art implementations for differential models. Abstract The implementation of the deformation fields method for integral models within a finite element context [1,2] has been updated with various techniques to have a numerical stability that is comparable to state-of-the-art implementations of differential models. In particular, the time-dependent stability in shear flow, decoupled schemes for zero or small solvent viscosities and the log-conformation representation now have counterparts in the numerical implementation of integral models leading to similar numerical stability. The new techniques have been tested in transient shear flow and the flow around a cylinder confined between two plates for the integral version of upper-convected Maxwell model and for integral models having a non-constant damping function. [ABSTRACT FROM AUTHOR]

Highlights • The VCM model can replicate the steady asymmetry observed in WLM cross-slot flow. • Onset of asymmetric instability due to stretching of micelles. • Elimination of steady and unsteady asymmetric instability due to chain scission. • Formation of lip vortex due to chain breakage and shear thinning. • Decrease in lip vortex size due to enhanced chain scission/degree of shear thinning. Abstract In this work, we focus on modeling the flow of wormlike micellar solutions in a cross-slot device. In particular, we investigate the role that the breakage of wormlike micelles plays in the formation of lip vortices and the development of an asymmetric elastic instability. The cross-slot induces a planar elongational flow field around the stagnation point in the center of the geometry, and a shear-dominated flow in the inlet and outlet arms. The extensional flow can induce the emergence of a bifurcation, in which the symmetric flow undergoes an instability and becomes asymmetric at sufficiently large flow rates. We further show that this instability can be completely suppressed by creating micelles that are easier to break under imposed stretching. Furthermore, at larger flow rates, unlike comparable simulations of polymer solutions, the asymmetric flow remains steady in agreement with experiments. In addition, the shear flow can induce the formation of a recirculation region in the inlet arm along the channel wall directly upstream of the corner. In particular, we reveal the possibility of controlling the vortex regions via flow-induced breakage; as the chains become easier to break, the degree of shear thinning increases and the size of the vortices decreases. Ultimately, our predictions show that chain scission plays an important role in altering fluid flow. [ABSTRACT FROM AUTHOR]

Highlights • Particle migration in Giesekus viscoelastic rectangular channel flow is studied. • Particle migrates toward channel centerline or corner at low Reynolds numbers. • Particles migrate toward face centers of shorter walls by elasto-inertial effect. • Particle migration trajectories are significantly affected by the secondary flow. Abstract 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. [ABSTRACT FROM AUTHOR]

Highlights • Velocity and Velocity gradient data from DNS of a turbulent viscoelastic channel flow are used. • A statistical analysis is offered on the tails of the PDFs fitted to a power law (Pareto). • The fitted power law exponents are offered at different locations in channel. • Smaller exponents correspond to more non‐Gaussian, fatter tail distributions. • The viscoelastic results are compared against the Newtonian showing much fatter tails. Abstract Direct numerical simulations (DNS) of Newtonian and drag-reducing viscoelastic turbulent channel flows generate crucial data to analyze and understand the nature of turbulence and its modification due to viscoelasticity. Such an understanding is necessary to enable better drag reduction technologies. Previously (Samanta et al., Phys. Fluids, 21, 115106, 2009) we have shown that viscoelasticity can significantly alter the non-Gaussian character of the probability density functions (PDFs) of many of the turbulent statistics in the flow. In this work, we investigate further the non-Gaussian characteristics of the PDFs generated in viscoelastic turbulence by focusing on their tail behavior. In particular, we show that many of the tails of the PDFs of the velocity and its derivatives obey a power law, as opposed to an exponential one exhibited by Gaussian PDFs, with power law indices that sometimes, for viscoelastic flows, are low enough to imply unbounded fourth- (kurtosis), or even third-(skewness) moments of the distribution, what we can call "strong fat tails" behavior. We use Hill's estimator to evaluate the power law index of the tails, as well as statistical inference methods to perform hypothesis testing for the appropriateness of the power law fit. We have found that fat tails corresponding to power law tail distribution behavior are observed in the PDFs for both Newtonian and viscoelastic cases. However, viscoelasticity leads to PDFs that exhibit consistently fatter tails than the Newtonian ones and it is only in the presence of viscoelasticity that turbulence leads to "strong fat tails" as defined above. We infer that drag-reducing viscoelastic turbulence involves more infrequent and more correlated and more extreme events which makes DNS of viscoelastic turbulent flows much more computationally demanding than Newtonian DNS, requiring finer spatial resolutions, longer integration times, and larger computational domain sizes. [ABSTRACT FROM AUTHOR]

Highlights • The capillary flow and a full rheological characterization of a commercial ionomer melt studied experimentally and numerically. • The excess pressure drop due to entry, the effect of pressure on viscosity and the possible slip effects on the capillary data analysis studied. • The effect of ionic interactions on the pressure drop and rheology have been studied and compared to the results of LDPE (parent polymer of this ionomer). Abstract The capillary flow of a commercial ionomer melt was studied both experimentally and numerically. The excess pressure drop due to entry, the effect of pressure on viscosity and the possible slip effects on the capillary data analysis have been examined. Using a parallel-plate rheometer equipped with a partitioned plate, and a capillary rheometer with a series of capillary dies having different diameters, D , and length-to-diameter L/D ratios, a full rheological characterization has been carried out. The experimental rheological data have been fitted to a viscoelastic (K-BKZ) model. Particular emphasis has been placed on the pressure-dependence of viscosity, with a pressure-dependent coefficient β p. For the viscoelastic K-BKZ simulations, the time-temperature shifting concept has been used for the non-isothermal calculations, while the time-pressure shifting concept has been used to shift the relaxation moduli for the pressure-dependence effect. It was found that these viscoelastic simulations were capable of reproducing the experimental data well with significant effects resulting from the effect of pressure on viscosity, a parameter which cannot be neglected for this class of polymers. Moreover the effect of ionic interactions on the pressure drop has been assessed by comparing the results with those of a linear density polyethylene (LDPE) (parent polymer of this ionomer). Although the ionomer has a slightly smaller viscosity, its entry pressure drop is almost double than that of LDPE with vortices stronger and larger. These observations signify the effect of ionic interactions in flows that are presented for the first time in the literature. [ABSTRACT FROM AUTHOR]

Highlights • The elasticity of the external medium has a stabilizing effect on a liquid thread. • If two fluids with equal elasticity the system behaves as if it were Newtonian. • The most unstable combination: inner viscoelastic outer Newtonian fluid. Abstract 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. [ABSTRACT FROM AUTHOR]

Highlights • We propose a method to build models for thixo-elasto-viscoplastic materials. • A model for a Laponite suspension is developed as an example. • The model is composed of one tensorial and one scalar differential equation. • The structuring level is given by the fluidity, and no structure parameter is needed. • The evolution equation is developed based on rheological measurement data. Abstract 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. [ABSTRACT FROM AUTHOR]

Highlights • We use the Bautista–Manero–Puig model to investigate channel flow instabilities. • Instability is seen when viscoelastic effects dominate; thixotropy is stabilising. • Very unstable flows have the low to high shear transition point near the wall. • The thixotropic structure recovery rate determines the growth rate of instability. • We predict a critical wall shear stress that is in agreement with experiments. Abstract 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. [ABSTRACT FROM AUTHOR]

Highlights • Viscoelastoplastic predictions in circular sharp-cornered contraction-expansion flow. • Plastic & viscoelastic regimes analysed under a flow-rate increase protocol. • Highly-dynamic vortex-activity registered, with coexistent lip and corner vortices. • Correlation of vortex-structures with N 1 & extensional viscosity trends. • Thixo-viscoelastoplasticity reflects growth of solid-like features and asymmetry. Abstract 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+_τ p , which reflects a bounded extensional viscosity response and an N 1 Shear -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 < 10−1) and viscoelastic flow (larger- Q > 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. [ABSTRACT FROM AUTHOR]

Highlights • Material forms at interface when aqueous surfactant solution is injected into oleic acid oil. • Interfacial rheology shows material to be viscoelastic. • Morphologies include droplets and tubes, depending on flow rate and surfactant concentration. Abstract We present an experimental investigation of instabilities due to the formation of interfacial micellar material around a flowing liquid column. By injecting an aqueous surfactant solution (cetylpyridinium chloride) into a reservoir of organic oil (oleic acid), we observe a wide variety of morphological states, dependent on the imposed flow rate and surfactant concentration. Interfacial rheology measurements show that this material is viscoelastic. The states observed include connected and disconnected falling droplets, a moving pipelike column with various surface wave instabilities, and a straight cylindrical pipe which undergoes a buckling instability. These states result from the competition between surface tension type effects, the geometry of the flow, and the growth of the micellar material at the interface. [ABSTRACT FROM AUTHOR]

Highlights • The accuracy of the Oldroyd-B model is examined experimentally. • The model drastically overestimates the damping rate of an oscillating drop. • Possible causes of this failure are discussed. Abstract 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. [ABSTRACT FROM AUTHOR]

Highlights • Interactions between viscoelastic fluid and rigid disks or ellipsoids are addressed. • A method for the direct simulation of viscoelastic suspensions is proposed. • The numerical method is built upon a fictitious domain approach. • The fluid-structure issue is solved with a splitting scheme and penalty methods. • Numerical results are presented for both dilute and dense regimes. Abstract In this paper, we present a numerical method which performs the direct simulation of 2D viscoelastic suspensions. Objectives. Interactions between viscoelastic fluids of Oldroyd type, including inertial effects, and a large number of rigid disks or ellipsoids are addressed. Method. The numerical method is built upon a fictitious domain approach which consists in defining the fluid-structure problem over the whole domain (fluid+solid), see e.g. [1]. In the Newtonian case [2, 3], the resulting variational formulation, although classical, uses non-standard functional spaces which include the rigidity constraints. From the numerical point of view, these constraints can be addressed by penalty methods, leading to the possible use of standard finite elements solvers with fixed structured meshes. We show how this approach can be adapted to viscoelastic fluids of Oldroyd type. Results. Two types of configurations are investigated in dilute and dense regimes: sedimentation of circular particles and shear flows with ellipsoidal particles. [ABSTRACT FROM AUTHOR]

In this work the fully-developed steady channel flow of the homogeneous polymer solution studied in [4] is revisited and a completely new analytical solution is proposed which is devoid of the limitations of the previous solution ( β 3 ɛ D e κ 2 ≤ 2 / 27 ), i.e., it is valid for the complete range of the rheological parameters. The viscoelastic fluid is described by the simplified Phan–Thien and Tanner model with linear stress coefficient function for the polymer contribution plus a Newtonian solvent. The solution is also valid if the polymer contribution is described by the finitely extensive non-linear elastic model with the Peterlin approximation for the average spring force (FENE-P model). [ABSTRACT FROM AUTHOR]

Purely-elastic flow instabilities have been extensively investigated in pressure-driven systems, but little attention has been paid to electrically-driven systems. This work attempts to fill this gap by investigating the electroosmotic flow of viscoelastic fluids in cross-slot and flow-focusing micro-devices, with a special focus on the onset of elastic instabilities. Relying on the visualization of dye patterns, the onset of electro-elastic instabilities for dilute and semi-dilute polyacrylamide solutions was observed at a low bulk Weissenberg number, O (10 −2 ), through a direct transition from a steady symmetric flow to a time-dependent asymmetric flow. Time-series analysis of the dye interface patterns revealed a broad range of excitation frequencies with a power-law decay. The elastic instabilities observed seem not to improve significantly the mixing efficiency, contrarily to what has been previously reported for unstable pressure-driven flows. Numerical simulations of the electroosmotic flows were also carried out with a finite-volume method, showing that the observed electro-elastic instabilities can be predicted numerically. Both the experimental and numerical results suggest that the large stresses developed inside the electric double layer, coupled with the streamline curvature around the geometry corners, play a fundamental role in the onset and in the dynamics of the observed electro-elastic instabilities. However, further research is needed to clarify the mechanism of electro-elastic instabilities, and, in general, to improve our understanding of the complex behavior of polymeric fluids in electroosmotic flows. [ABSTRACT FROM AUTHOR]

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. [ABSTRACT FROM AUTHOR]

The finite volume method is used to numerically simulate the dynamics of cylindrical particles in the contraction flow of a second-order fluid. The effects of Stokes number, Deborah number, particle aspect ratio and contraction ratio on the spatial and orientation distributions of cylindrical particles are analyzed. Some numerical results are compared with the available experimental results in the contraction flow of Newtonian fluids. The results show that the spatial and orientation distributions of the particles are dependent on the competition among the inertia, viscoelasticity and effect of confined wall. The result of competition is responsible for the force and torque inducing a cross-streamline migration and rotation of particles. Along the flow direction, the particle spatial distribution in the cross section changes non-monotonically. The particle orientation distribution changes monotonically and particles gradually align themselves with the flow direction, and this phenomenon is more obvious than the case of the Newtonian fluid under the same conditions. High shear rate makes the particles align with their major axis near to the flow direction. With the increase of the Stokes number, the particle spatial distribution becomes more uniform, and orientation distribution function of particles becomes flatter and wider. With the increase of Deborah number and the contraction ratio, the particle spatial distribution becomes more non-uniform, in the meantime, more particles tend to align themselves with the flow direction. With the increases of the particle aspect ratio, the particle spatial distribution in the cross section becomes more uniform, and more particles align with their major axis near to the flow direction. In the parameter region studied here, the particle aspect ratio has a weaker effect on the spatial and orientation distributions of particles than Stokes number, Deborah number and contraction ratio. [ABSTRACT FROM AUTHOR]

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. [ABSTRACT FROM AUTHOR]

The smaller the scales on which complex fluids are studied, the more fluctuations become relevant, e.g. in microrheology and nanofluidics. In this paper, a general approach is presented for including fluctuations in conformation-tensor based models for viscoelasticity, in accordance with the fluctuation-dissipation theorem. It is advocated to do this not for the conformation tensor itself, but rather for its so-called contravariant decomposition, in order to circumvent two major numerical complications. These are potential violation of the positive semi-definiteness of the conformation tensor, and numerical instabilities that occur even in the absence of fluctuations. Using the general procedure, fluctuating versions are derived for the upper-convected Maxwell model, the FENE-P model, and the Giesekus model. Finally, it is shown that the fluctuating viscoelasticity proposed here naturally reduces to the fluctuating Newtonian fluid dynamics of Landau and Lifshitz [L. D. Landau and E. M. Lifshitz, Fluid Mechanics, Vol. 6 of Course of Theoretical Physics, Pergamon Press, Oxford, 1959], in the limit of vanishingly small relaxation time. [ABSTRACT FROM AUTHOR]

• A multi-chain slip-link model was modified for friction and Brownian force. • Simulations were performed by switching the fluctuation-dissipation relation on/off. • Both results agreed with experiments for entangled polystyrene under fast flows. Description of the elongational rheology of concentrated polymers appears to require that in fast flows the friction coefficient decreases with respect to its equilibrium value. However, the proposed models typically maintain the validity of the fluctuation-dissipation theorem (FDT) out of equilibrium. On the other hand, FDT is routed in local equilibrium, the latter being clearly violated by the flow-induced monomer coalignment that induces friction change. A recent analysis by Watanabe et al. [Macromolecules, 54, 3700 (2021)] of unentangled polystyrene (PS) melts, based on a nonlinear extension of the Rouse model, indicates that FDT is indeed violated in fast flows. According to their analysis, the Brownian force intensity remains almost independent of the flow rate, even though the friction coefficient drastically decreases. A different violation of FDT is shown by previous nonequilibrium molecular dynamics simulations of PS oligomers [Ianniruberto et al., Macromolecules, 45, 8058 (2012)] where the diffusion coefficient grows more than the inverse friction coefficient. In this paper, Brownian simulations using a multi-chain sliplink model (the so-called primitive chain network model) are reported for two monodisperse entangled PS melts, for which nonlinear shear and elongational data were published. Two different friction reduction models are examined, and the effect of switching FDT on and off is tested. Results demonstrate that, irrespective of FDT, both friction models can reasonably well reproduce the behavior shown by the data. This result lends support to models that retain FDT since its violation appears not to significantly affect predictions of nonlinear rheology. [ABSTRACT FROM AUTHOR]

We analyze the steady non-Newtonian fluid–structure interaction between the flow of an Oldroyd-B fluid and a deformable channel. Specifically, we provide a theoretical framework for calculating the leading-order effect of the fluid's viscoelasticity on the flow rate–pressure drop relation and on the deformation of the channel's elastic wall. We first identify the characteristic scales and dimensionless parameters governing the fluid–structure interaction in slender and shallow channels. Applying the lubrication approximation for the flow and employing a perturbation expansion in powers of the Deborah number D e , we derive a closed-form expression for the pressure as a function of the non-uniform shape of the channel in the weakly viscoelastic limit up to O (D e). Coupling the hydrodynamic pressure to the elastic deformation, we provide the leading-order effect of the interplay between the viscoelasticity of the fluid and the compliance of the channel on the pressure and deformation fields, as well as on the flow rate–pressure drop relation. For the flow-rate-controlled regime and in the weakly viscoelastic limit, we show analytically that both the compliance of the deforming top wall and the viscoelasticity of the fluid decrease the pressure drop. Furthermore, we reveal a trade-off between the influence of compliance of the channel and the fluid's viscoelasticity on the deformation. While the channel's compliance increases the deformation, the fluid's viscoelasticity decreases it. • Analysis of flow of weakly viscoelastic Oldroyd-B fluid in a deformable channel. • Analytical expression shows leading-order effects of viscoelasticity and compliance. • Demonstration of trade-off between viscoelasticity and compliance on pressure drop. [ABSTRACT FROM AUTHOR]

In this work, effect of the second to first normal stress difference ratio at the die exit, −N 2 /N 1 , uniaxial extensional strain hardening, η E , U , m a x 3 η 0 , planar-to-uniaxial extensional viscosity ratio, η E , P η E , U , and Deborah number, De , has been investigated via viscoelastic isothermal modeling utilizing 1D membrane model and a single-mode modified Leonov model as the constitutive equation. Based on the performed parametric study, it was found that there exists a threshold value for De and η E , U , m a x 3 η 0 , above which, the neck-in starts to be strongly dependent on −N 2 /N 1 . It was found that such critical De decreases if −N 2 /N 1 , η E , U , m a x 3 η 0 increases and/or η E , P η E , U decreases. Numerical solutions of the utilized model were successfully approximated by a dimensionless analytical equation relating the normalized maximum attainable neck-in with η E , U , m a x 3 η 0 , η E , P η E , U , −N 2 /N 1 and De . Suggested equation was tested by using literature experimental data considering that −N 2 /N 1 depends on die exit shear rate, temperature and utilized constitutive model parameters for given polymer melt. It was found that approximate model predictions are in a very good agreement with the corresponding experimental data for low as well as very high Deborah numbers, at which neck-in strongly depends on −N 2 /N 1 . It is believed that the obtained knowledge together with the suggested simple model can be used for optimization of the extrusion die design (influencing flow history and thus die exit stress state), molecular architecture of polymer melts and processing conditions to suppress neck-in phenomenon in production of very thin polymeric flat films. [ABSTRACT FROM AUTHOR]

The linear stability analysis is carried out for the straight jet of a polymer melt in an electrospinning process. The stability of axisymmetric disturbances is examined in order to comprehend the onset of fiber morphology with diametric variations or bead formation along the fiber under non-isothermal electrospinning conditions. As the polymeric fluid (polylactic acid melt) is a low conductivity fluid with unentangled polymer molecules, the viscoelasticity is described using the non-linear rheological Giesekus constitutive model assuming very small axial conduction current. The non-periodic axisymmetric disturbances are imposed on the non-uniform radius jet, obtained as the solution of the 1-D slender filament governing equations and the eigenspectrum for the disturbance growth rate is constructed under the realistic melt electrospinning conditions. The growth rate corresponding to the leading mode in the eigenspectrum is found to increase with increasing surface tension forces and decrease with the enhanced external electric field. Thus, the leading growth rate behavior suggests that the classical Rayleigh–Plateau instability dominates over the conducting mode of instability for melt electrospinning. Further, the role of non-isothermal conditions in the stability behavior is examined. The convective heat transfer from electrified jet to the cooling ambiance leads to thicker fibers with greater stability to axisymmetric disturbances. The stabilizing effect of heat transfer is attributed mainly to the temperature sensitive fluid rheology. In particular, the enhancement in polymer viscosity in the jet propagation direction is responsible for the build up of stabilizing viscoelastic stress. The fluid elasticity, denoted by the flow Deborah number, also tends to stabilize the electrified jet as temperature drop along the flow increases the relaxation time of the polymer chains leading to high polymeric stress associated with the stretched chains. As crystallization of polymeric chains under non-isothermal condition is not considered, the analysis holds for either amorphous polymers or polymers with slow crystallization kinetics compared to the short residence time during the spinning flow. [ABSTRACT FROM AUTHOR]

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  > 300 r 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  > 50 r 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. [ABSTRACT FROM AUTHOR]