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We report the design of a microcapillary rheometer (μCR) that allows to perform experiments rapidly and in a broad range of shear rates (i.e., from 0.1 to 1000 s−1), using small amounts of material (i.e., just few milligrams). Additionally, multiple measurement parallelization makes it suitable for High-Throughput Rheological Experimentation of polymer melts (HT-Rheo-E). The novel rheometer consists of a set of three cylindrical microcapillaries in which the fluid flows driven by a controlled pressure. A camera, placed at the capillary exit, records the fluid motion to measure its flow rate, from which the fluid viscosity can be determined. The optimization of the setup allowed for reliable and fast viscosity measurements using ca. 10 mg of material. The current work reports the design of the rheometer and validation measurements on several model fluids. The microfabricated μCR is of potential interest for applications in quality control and research where rapid and repeated measurements using limited milligrams of polymer are required, as well as for High-Throughput-Experimentation of complex fluids (e.g., biological systems).

The formation of equally-spaced structures (trains) of rigid, spherical particles suspended in a viscoelastic fluid flowing in a cylindrical microchannel is investigated by numerical simulations. Direct Numerical Simulations (DNS) have been employed to accurately compute the translational velocities of a system made by three particles aligned along a cylindrical channel for different interparticle distances. A shear-thinning, elastic fluid, modeled by the Giesekus costitutive equation, is considered. The DNS results are collected in a database used for simulating the dynamics of a multi-particle system. The evolution of the particle microstructure through the channel is presented in terms of interparticle distance distributions. The effects of the Deborah number (defined as the ratio between the fluid and flow characteristic times), the volume fraction, and the initial particle distribution on the train dynamics are investigated.

Viscoelastic polymer solutions have been widely employed as suspending liquids for a myriad of microfluidic applications including particle and cell focusing, sorting, and encapsulation. It has been recently shown that viscoelastic solutions can drive the formation of equally spaced particles called "particle trains" as a result of the viscoelasticity-mediated hydrodynamic interactions between adjacent particles. Despite their potential impact on applications such as droplet encapsulation and flow cytometry, only limited experimental studies on viscoelastic ordering are currently available. In this work, we demonstrate that a viscoelastic shear-thinning aqueous xanthan gum solution drives the self-assembly of particle trains on the centerline of a serpentine microfluidic device with a nearly circular cross section. After focusing, the flowing particles change their mutual distance and organize in aligned structures characterized by a preferential spacing, quantified in terms of distributions of the interparticle distance. We observe the occurrence of multi-particle strings, mainly doublets and triplets, that interrupt the continuity of the particle train. To account for the fluctuations in the number of flowing particles in the experimental window, we introduce the concept of local particle concentration, observing that an increase of the local particle concentration leads to an increase of doublets and triplets. We also demonstrate that using only a single tube to connect the sample to the microfluidic device results in a drastic reduction of doublets/triplets, thus leading to a more uniform particle train. Our findings establish the foundation for optimized applications such as deterministic droplet encapsulation in viscoelastic liquids and optimized flow cytometry.

The use of nanomaterials, thanks to their peculiar properties and versatility, is becoming central in an increasing number of scientific and engineering applications. At the same time, the growing concern towards environmental issues drives the seeking of alternative strategies for a safer and more sustainable production of nanoparticles. Here we focus on a low-energy, magnetically-driven wet milling technique for the synthesis of metal nanoparticles starting from a bulky solid. The proposed approach is simple, economical, sustainable, and provides numerous advantages, including the minimization of the nanoparticles air dispersion and a greater control over the final product. This process is investigated by experiments and discrete element method simulations to reproduce the movement of the grinding beads and study the collision dynamics. The effect of several parameters is analyzed, including the stirring bar velocity, its inclination, and the grinding bead size, to quantify the actual frequency, energy, and angle of collisions. Experiments reveal a non-monotonous effect of the stirring velocity on the abrasion efficiency, whereas numerical simulations highlight the prevalent tangential nature of collisions, which is only weakly affected by the stirring velocity. On the other hand, the stirring velocity affects the collision frequency and relative kinetic energy, suggesting the existence of an optimal parameters combination. Although a small variation of the stirring bar length does not significantly affect the collision dynamics, the use of grinding beads of different dimensions offers several tuning opportunities.

One of the critical issues encountered when particle suspensions are made to flow in microfluidic devices is the adhesion of the suspended particles on the channel surfaces. This process, known as fouling, may lead to a progressive growth of clusters attached to the walls and, possibly, to a complete clogging of the microchannel. In this work, we employ Computational Fluid Dynamics combined with Discrete Element Method to study the initial growth of a cluster at the wall of a slit microchannel. We consider a suspension of ‘soft’ microparticles in a Newtonian liquid under laminar flow conditions, with a well-known simple model to describe particle-particle adhesion. The cluster growth dynamics is quantified in terms of morphology and projected area onto the slit wall. A comparison with some experimental data is carried out, showing that the model captures several qualitative experimental features of the fouling process, e.g., cluster morphology, possibility of break-up and resuspension, and linear growth rate of the cluster projected area onto the channel wall.

Controlling the fate of particles and cells in microfluidic devices is critical in many biomedical applications, such as particle and cell alignment and separation. Recently, viscoelastic polymer solutions have been successfully used to promote transversal migration of particles and cells toward fixed positions in straight microchannels. When inertia is negligible, numerical simulations have shown that strongly shear-thinning polymer solutions (fluids with a shear viscosity that decreases with increasing flow rates) promote transversal migration of particles and cells toward the corners or toward the centerline in a straight microchannel with a square cross section, as a function of particle size, cell deformability, and channel height. However, no experimental evidence of such shifting in the positions for particles or cells suspended in strongly shear-thinning liquids has been presented so far. In this work, we demonstrate that particle positions over the channel cross section can be shifted "from the edge to the center" in a strongly shear-thinning liquid. We investigate the viscoelasticity-induced migration of both rigid particles and living cells (Jurkat cells and NIH 3T3 fibroblasts) in an aqueous 0.8 wt % hyaluronic acid solution. The combined effect of fluid elasticity, shear-thinning, geometric confinement, and cell deformability on the distribution of the particle/cell positions over the channel cross section is presented and discussed. In the same shear-thinning liquid, separation of 10 and 20 μm particles is also achieved in a straight microchannel with an abrupt expansion. Our results envisage further applications in viscoelasticity-based microfluidics, such as deformability-based cell separation and viscoelastic spacing of particles/cells.

Clogging is the mechanism that interrupts the flow in confined geometries due to the complete blockage of the channel cross section. It represents a critical issue in the processing of particle suspensions for both industrial and biological applications, and it is particularly relevant in microfluidics and membrane technology due to the high particle confinement and the difficult device cleaning. Although numerous experimental and numerical studies have been carried out to understand the mechanism governing this complex multiscale phenomenon, the picture is not yet clear and many questions still remain, especially at the particle level. In this regard, the numerical simulations may represent a useful investigation tool since they provide a direct insight to quantities not easily accessible from experiments. In this work, a detailed computational fluid dynamics-discrete element method simulation study on the clogging mechanism in a microchannel with planar contraction is carried out. Both constant flow rate and constant pressure drop conditions are investigated, highlighting the effect of flow conditions, particle volume fraction, cohesion forces, and contraction angle. The onset of clogging conditions is discussed.

Laser powder bed fusion additive manufacturing is among the most used industrial processes, allowing for the production of customizable and geometrically complex parts at relatively low cost. Although different aspects of the powder spreading process have been investigated, questions remain on the process repeatability on the actual beam–powder bed interaction. Given the influence of the formed bed on the quality of the final part, understanding the spreading mechanism is crucial for process optimization. In this work, a Discrete Element Method (DEM) model of the spreading process is adopted to investigate the spreading process and underline the physical phenomena occurring. With parameters validated through ad hoc experiments, two spreading velocities, accounting for two different flow regimes, are simulated. The powder distribution in both the accumulation and deposition zone is investigated. Attention is placed on how density, effective layer thickness, and particle size distribution vary throughout the powder bed. The physical mechanism leading to the observed characteristics is discussed, effectively defining the window for the process parameters.

The aggregation/fragmentation dynamics of hard-gel microparticles suspended in a Newtonian liquid flowing through a straight channel is studied by numerical simulations. A one-way Discrete Element Method is employed to simulate the motion and the adhesion of the particles. The formation and fragmentation of aggregates, and their deposition at the channel walls are investigated by varying the Reynolds number and the strength of the adhesive force. A non-periodic channel is considered to simulate the start-up phase of aggregate formation till a ‘pseudo steady-state’ condition. Results in terms of microstructures, particle velocity profiles, and spatial and temporal evolution of aggregates in 2D and cylindrical (3D) channels are presented and discussed.

We address the effect of wall slip on the dynamics of a spherical particle suspended in an inertialess Newtonian or viscoelastic shear-thinning fluid under shear or Poiseuille flow. The study is performed through 3D direct finite element simulations by employing an Arbitrary Lagrangian-Eulerian method for the particle motion.In both shear and Poiseuille flows, wall slip reduces the difference between the particle translational velocity along the flow direction and the velocity of the unperturbed fluid, and slows down the particle rotational velocity. Remarkably, in a viscoelastic fluid, the presence of wall slip reverses the migration direction as compared to the no-slip case. Hence, for sufficiently high slip coefficients, all the particles migrate toward the channel midplane in shear flow and toward the channel centerline in Poiseuille flow, regardless of their initial position through the channel.

Solid&ndash, liquid separation is a key unit operation in the wastewater treatment, generally consisting of coagulation and flocculation steps to promote aggregation and increase the particle size, followed by sedimentation, where the particles settle due to the effect of gravity. The sedimentation efficiency is related to the hydrodynamic behavior of the suspended particles that, in turn, depends on the aggregate morphology. In addition, the non-Newtonian rheology of sludges strongly affects the drag coefficient of the suspended particles, leading to deviations from the known settling behavior in Newtonian fluids. In this work, we use direct numerical simulations to study the hydrodynamic drag of fractal-shaped particles suspended in a shear-thinning fluid modeled by the power-law constitutive equation. The fluid dynamics governing equations are solved for an applied force with different orientations uniformly distributed over the unit sphere. The resulting particle velocities are interpolated to compute the aggregate dynamics and the drag correction coefficient. A remarkable effect of the detailed microstructure of the aggregate on the sedimentation process is observed. The orientational dynamics shows a rich behavior characterized by steady-state, bistable, and periodic regimes. In qualitative agreement with spherical particles, shear-thinning increases the drag correction coefficient. Elongated aggregates sediment more slowly than sphere-like particles, with a lower terminal velocity as the aspect ratio increases.

In this work, we numerically investigate the dynamics of the growth and impingement of two gas bubbles in a Newtonian liquid in the presence of a rigid spherical particle. The computational analysis is carried out through 3D Arbitrary Lagrangian Eulerian (ALE) Finite Element Method (FEM) simulations. During their growth, as the bubbles start to ‘feel’ each other, they lose their spherical shape, with the side facing the other bubble becoming almost flat. In the liquid layer between the gas inclusions, an essentially biaxial extensional flow takes place. Depending on its initial position with respect to the bubbles, the solid particle can be ‘captured’ by the coalescing bubbles or ‘escape’ them. The effects of the physical and geometrical parameters of the system on such phenomenon are studied.

We study the dynamics of a slippery spherical particle suspended in an inertialess Newtonian or viscoelastic shear-thinning fluid, under shear or Poiseuille flow, by means of 3D direct numerical simulations. In particular, we investigate on the effect of particle slip on the cross-stream migration induced by fluid viscoelasticity. The governing equations are solved through the finite element method, by adopting an Arbitrary Lagrangian-Eulerian (ALE) formulation to handle the particle motion.In shear flow, the migration dynamics is qualitatively unchanged as compared to the no-slip case, i.e. the particle always moves towards the nearest wall regardless of the initial position. For increasing slip, the migration velocity first reaches a maximum, and then decreases to values lower than the no-slip one. Thus, a pronounced particle slip slows down the migration phenomenon.In Poiseuille flow, at variance with the no-slip case for a shear-thinning viscoelastic fluid, the tube wall becomes a `hydrodynamic repulsor' for high slip values, and all the particles migrate towards the channel centerline (`attractor'). In this sense, slippery particles are more easily aligned along the channel centerline than no-slip particles.

In this paper, we present a finite element implementation of fluctuating hydrodynamics with a moving boundary fitted mesh for treating the suspended particles. The thermal fluctuations are incorporated into the continuum equations using the Landau and Lifshitz approach [1]. The proposed implementation fulfills the fluctuation-dissipation theorem exactly at the discrete level. Since we restrict the equations to the creeping flow case, this takes the form of a relation between the diffusion coefficient matrix and friction matrix both at the particle and nodal level of the finite elements. Brownian motion of arbitrarily shaped particles in complex confinements can be considered within the present formulation. A multi-step time integration scheme is developed to correctly capture the drift term required in the stochastic differential equation (SDE) describing the evolution of the positions of the particles.The proposed approach is validated by simulating the Brownian motion of a sphere between two parallel plates and the motion of a spherical particle in a cylindrical cavity. The time integration algorithm and the fluctuating hydrodynamics implementation are then applied to study the diffusion and the equilibrium probability distribution of a confined circle under an external harmonic potential.

Strings of equally spaced particles (particle train) are tremendously important in a variety of microflu- idic applications. By using inertial microfluidics, particle trains can be formed near the channel walls. However, the high particle rotation and large local shear gradient near the microchannel walls can lead to blurred images and cell damage, thus negatively affecting applications related to flow cytometry. To address this challenge, we demonstrate that adding a tiny amount of hyaluronic acid biopolymer to an aqueous suspension drives self-assembly of a particle train on the centerline of a square-shaped straight microchannel, with a throughput up to approximately 2400 particles/s. The fraction of equally spaced par- ticles increases by increasing the volumetric flow rate and the distance from the channel inlet. Numerical simulations corroborate the experimental observations and, together with a simple qualitative argument on the particle train stability, shed insights on the underlying mechanism leading to particle ordering.

The effect of fluid rheology on particle migration induced by fluid viscoelasticity in a square-shaped microchannel is reported. Three water polymer solutions of PolyEthylene Oxyde at different concentrations, corresponding to different elasticity and degree of shear thinning, are prepared and rheologically characterized. Experiments are carried out for a wide range of flow rates, and the particle distributions over the channel cross section are reconstructed by combining particle tracking measurements and numerical simulations of the fluid velocity profile. The particle distributions show that the migration direction strongly depends on the fluid rheology. Specifically, when particles explore the constant viscosity region of the suspending liquids, they are focused around the channel centerline. Such an effect is more and more pronounced as the flow rate increases. On the other hand, for particles suspended in a shear-thinning fluid, a different scenario appears: At low flow rates, i.e., in the constant viscosity region, particles still migrate toward the channel centerline, while at high flow rates, i.e., in the shear thinning region, the migration reverts direction and the particles are driven toward the corners of the channel cross section. Those experimental observations elucidate the relevant and competing role of elasticity and shear thinning, with obvious implications in designing microfluidic devices for particle manipulation. Finally, our results highlight the weak effect of inertia on particle migration as compared to viscoelastic effects, even for low elastic suspending liquids.

Systems made by particles in viscoelastic liquids are ubiquitous in a variety of industrial and biological applications. Much work has been done in the last half-century in understanding the effect of non-Newtonian properties on the dynamics of the suspended particles. Theoretical predictions, experimental observations and numerical simulations highlighted peculiar phenomena induced by fluid elasticity that dramatically affect the particle motion and patterning. In this review, the existing literature on the dynamics of non-Brownian particles in viscoelastic fluids is discussed. The main part is focused on the dynamics of rigid particles passively transported in flowing viscoelastic liquids. The available results are classified by increasing level of complexity in terms of hydrodynamic interactions (single-particle problems, binary interactions, multi-body systems) and according to the flow field. Recent results on soft and active viscoelastic suspensions are also discussed.

The dynamics of a stick-slip “Janus” spherical particle suspended in a Newtonian fluid flowing in a cylindrical microchannel is studied by direct numerical simulations. Partial slip is imposed on half of the particle surface, whereas the no-slip boundary condition is present on the other half. The finite element method is used to solve the balance equations under creeping flow conditions. The translational and rotational velocities of the particle are evaluated at several orientations and distances from the tube centerline. The trajectories are then reconstructed by solving the kinematic equations where the velocities are taken by interpolating the simulation data. The particle dynamics is investigated by varying the initial position and orientation, the slip parameter, and the confinement ratio. The results, presented in terms of particle trajectories and phase portraits, highlight the existence of two relevant regimes: a periodic oscillation or a migration toward the tube axis for particle positions sufficiently far from or near the centerline, respectively. The basin of attraction of the tube axis grows with particle confinement and slip coefficient although the dynamics is qualitatively unaffected.The dynamics of a stick-slip “Janus” spherical particle suspended in a Newtonian fluid flowing in a cylindrical microchannel is studied by direct numerical simulations. Partial slip is imposed on half of the particle surface, whereas the no-slip boundary condition is present on the other half. The finite element method is used to solve the balance equations under creeping flow conditions. The translational and rotational velocities of the particle are evaluated at several orientations and distances from the tube centerline. The trajectories are then reconstructed by solving the kinematic equations where the velocities are taken by interpolating the simulation data. The particle dynamics is investigated by varying the initial position and orientation, the slip parameter, and the confinement ratio. The results, presented in terms of particle trajectories and phase portraits, highlight the existence of two relevant regimes: a periodic oscillation or a migration toward the tube axis for particle positions suf...

Migration and chaining of noncolloidal spheres in a worm-like micellar, viscoelastic solution under shear flow have been studied both experimentally and by numerical simulations. The microstructure dynamics have been experimentally investigated in the flow-gradient and in the flow-vorticity planes. 20 simulations in the flow-gradient plane have been performed for the same geometry, and with a proper selection for the constitutive equation of the suspending liquid. Experimental results show the formation of particle chains in the bulk, along with migration of a considerable fraction of spheres to the walls. At long times, chains in the bulk are stable, and cross-flow migration of individual spheres is suppressed. Numerical simulations with a standard viscoelastic constitutive equation (Giesekus fluid) reproduce the same phenomena observed experimentally, both in terms of fast particle migration to the wall and bulk chain stability. No alignment is, instead, found in simulations with a constant-viscosity, elastic fluid (Oldroyd-B model), in agreement with previous experimental results with Boger fluids. (C) 2013 Elsevier B.V. All rights reserved.

The dynamics of pairs and triplets of particles suspended in a viscoelastic fluid flowing along the centerline of a cylindrical channel is studied by numerical simulations. The governing equations are solved by the finite element method by employing an ALE formulation to handle the particle motion. For a pair of particles, at variance with the Newtonian case, the viscoelastic nature of the suspending medium alters the interparticle distance during the flow. For low and moderate Deborah numbers, the particles can approach or separate depending on the initial distance. For high Deborah numbers, the approaching dynamics disappears. Different fluid rheology and confinement ratio only quantitatively alter such a scenario. The three-particle dynamics is more complex. In a Newtonian liquid, the leftmost particle of the triplet approaches and slows down the middle one. Consequently, the rightmost particle separates, giving rise to a pair and an isolated particle. A similar scenario occurs for a viscoelastic liquid. In this case, however, depending on the initial configuration and the Deborah number, the particles forming the pair can subsequently approach or separate. In the latter case, the final configuration is the formation of three isolated particles.

The viscoelasticity-induced migration of a sphere in pressure-driven flow in a square-shaped microchannel is investigated under inertialess conditions. The effects of fluid rheology, i.e. of shear thinning and normal stresses, is studied by means of 3D finite element simulations. Two constitutive models are selected, in order to highlight differences due to rheological properties. A strong influence of the suspending fluid rheology on the migration phenomenon is shown, by particle trajectory analysis. When the second normal stress difference is negligible and, as a consequence, no secondary flows appear, the particle migrates towards the channel centerline or the closest corner, depending on its initial position. As shear thinning is increased, the center-attractive region is reduced, and the migration rate is faster. On the other hand, the existence of secondary flows, linked to the existence of a second normal stress difference, alters the migration scenario. The competition between the particle-wall hydrodynamic interactions, promoting the migration mechanism, and the secondary flow velocity components gives rise to further ‘equilibrium’ positions within the channel cross-section. Particles driven towards such positions trace out a spiral trajectory, following the vortex structure of the secondary flows. However, as the particle dimension is increased or the Deborah number is reduced, the cross-streamline migration velocity overcomes the secondary flow velocity. In this case, most of the particles are driven towards the channel centerline, i.e. a strong flow-focusing effect results.

In this work, we study the dynamics of an elastic particle suspended in an inertialess Newtonian fluid flowing through a channel with an orthogonal side branch (asymmetric T-shaped bifurcation) by means of 2D Arbitrary Lagrangian Eulerian (ALE) Finite Element Method (FEM) direct numerical simulations. The simulations show that, when the fluid is equally partitioned in the two downstream branches and the particle starts from the inflow channel centerline, a sufficiently deformable particle is deviated into the ‘side’ branch, at variance with a rigid particle, which remains in the ‘main’ outlet. The effects of the elastic capillary number and the confinement ratio on the particle trajectory and deformation near the bifurcation are investigated. We discuss how this device can be exploited for separating particles based on their elasticity.

The cross-streamline migration of a spherical particle in a viscoelastic fluid flowing in a wide slit microdevice is here investigated through 3D finite element simulations. The study is performed by neglecting both fluid and particle inertia, which is a common assumption in microfluidic systems. In order to highlight the role of the suspending liquid rheology, two viscoelastic constitutive equations were chosen, i.e. the Giesekus and the Phan Thien–Tanner models. Because of the large cross-section aspect ratio, the influence of the lateral walls can be neglected, and the migration is unidirectional, along the gap (small) height. For small confinement ratios, i.e. for small particle-gap dimensions ratios, a multistable dynamics is found whereby the particle is driven towards the channel centerplane or the closest wall depending on its initial position through the gap, thus leading to the existence of an unstable separatrix. The position of such a separatrix is strongly influenced by the fluid rheology. For the Giesekus suspending liquid, the centerplane attractive region is always found to be wider than the wall attractive zone, independently of the flow rate. On the other hand, for the Phan Thien–Tanner liquid, large flow rates drastically move the separatrix towards the channel center. Beyond a critical particle size, the multistable behavior disappears and the separatrix collapses on the centerplane or the wall depending on the second normal stress difference. Finally, the calculated particle distributions along the channel gap at different distances from the inlet show that the migration is faster for large particles, higher flow rates, and more shear thinning fluids.

Low Pressure Cold Spray process is a relatively new additive technique allowing to create high quality metallic coatings, through the high velocity spraying of particles, on both metallic and non-metallic substrates. The adhesion mechanism of the particles is, to date, not fully understood and the phenomena occurring during long depositions (which are the more interesting for industrial processes) are not known and studied in details. Aiming to fulfill this lack of knowledge, the phenomena occurring during long deposition were studied through both careful experimental evaluations and numerical approach. Particular attention was paid at the working conditions of the De Laval nozzle system which accelerates the particles, a computational fluid dynamics model focusing on both geometrical features and spray behavior was proposed. Micron-sized aluminum powders and compressed air as carrier gas were used in this experimentation, numerical simulations are performed to predict the gas flow regime. It has been found that the deposition efficiency tends to decrease due to the critical phenomena occur into the spray nozzle during long time depositions. The sprayed particles tend to stick to the walls of the nozzle and, moreover, shock waves occur inside the nozzle further promoting the particles stick phenomena, making the system inefficient.

Particle migration is a relevant transport mechanism whenever suspensions flow in channels with gap size comparable to particle dimensions (e.g. microfluidic devices). Several theoretical as well as experimental studies have been performed on this topic, showing that the occurring of this phenomenon and the migration direction are related to particle size, flow rate, and the nature of the suspending liquid. In this work we perform a systematic analysis on the migration of a single particle in a sheared viscoelastic fluid through 2D finite element simulations in a Couette planar geometry. To focus on the effects of viscoelasticity alone, inertia is neglected. The suspending medium is modeled as a Giesekus fluid. An ALE particle mover is combined with a DEVSS/SUPG formulation with a log-representation of the conformation tensor giving stable and convergent results up to high flow rates. To optimize the computational effort and reduce the remeshing and projection steps, needed as soon as the mesh becomes too distorted, a ‘backprojection’ of the flow fields is performed, through which the particle in fact moves along the cross-streamline direction only, and the mesh distortion is hence drastically reduced. Our results, in agreement with recent experimental data, show a migration towards the closest walls, regardless of the fluid and geometrical parameters. The phenomenon is enhanced by the fluid elasticity, the shear thinning and strong confinements. The migration velocity trends show the existence of a master curve governing the particle dynamics in the whole channel. Three different regimes experienced by the particle are recognized, related to the particle-wall distance. The existence of a unique migration behavior and its qualitative aspects do not change by varying the fluid parameters or the particle size.

The motion of a single, inertialess, non-Brownian sphere immersed in a suspending fluid is studied in a confined geometry. A simple shear flow is imposed as external flow field and the impact of the gap between the particle and the wall on the flow fields is investigated. The suspending fluid is considered both Newtonian and viscoelastic, using for the latter case two different constitutive equations in order to separately highlight the influence of typical non-linear phenomena of non-Newtonian fluids. The rotation rate of the sphere is investigated for different Deborah numbers and gap sizes, with the sphere always at the cell center. The study is carried out through full 3D numerical simulations. We solve the balance equations by means of a finite element method. The particle rigid-body motion is imposed through constraints on the sphere surface. Therefore, the unknown particle rotation is recovered by solving the full system of equations. Simulations for a Newtonian suspending liquid show a slowing down of the particle if the gap decreases, in quantitative agreement with other numerical results in literature. For a viscoelastic matrix, this effect is even more pronounced since the nature of the fluid leads itself to a slower rotation, even in unconfined geometries. Finally, the streamlines around the particle show the existence of a recirculation zone even in Newtonian suspending fluids. Such a zone is larger and closer to the sphere as the viscoelasticity of the suspending fluid increases.

In this paper we study, by means of numerical simulation, planar elongational flow of concentrated, inertialess, non-Brownian rigid particle suspensions in a viscoelastic fluid. The simulation is 2D and follows the approach presented in our previous work [G. D’Avino, P.L. Maffettone, M.A. Hulsen, G.W.M. Peters, A numerical method for simulating concentrated rigid particle suspensions in an elongational flow using a fixed grid, J. Comput. Phys. 226 (2007) 688–711]. A small computational domain is obtained by considering a three-layer domain. The innermost part is used to calculate the suspension response, the outermost is used to set the elongational flow boundary conditions far from the particles, and an intermediate region is mandatory to allow the developing of viscoelastic stress fields around the particle before entering the innermost layer. This scheme allows to achieve steady state (in a statistical sense). A time-independent fixed grid is used to avoid difficulties due to deforming meshes and remeshing of the domain. A fictitious domain has been implemented in order to easily manage the rigid-body motion. The particles are described by their boundaries only (rigid-ring description) and the rigid-body motion is imposed through Lagrange multipliers. A DEVSS-G/SUPG finite element formulation is implemented, and the log-conformation representation of the constitutive equation is used in order to improve the numerical stability of the method. The suspending liquid is treated as a Giesekus fluid. The bulk properties are determined by using an averaging procedure. Bulk calculations show that the extensional viscosity increases, with respect to the unfilled fluid, with the particle area fraction as well as with the Weissenberg number. The strain hardening parameter is predicted to decrease with increasing particle area fraction. The relative increase of the strain hardening parameter with increasing Weissenberg numbers is greatly reduced for larger particle area fraction. The predicted reduction of strain hardening agrees with experimental evidence. © 2007 Elsevier B.V. All rights reserved.

We investigate the dynamic response of industrial rubbers (styrene-butadiene random copolymers, SBR) in torsion and compare against common small amplitude oscillatory shear measurements by using a torsion rectangular fixture, a modified torsion cylindrical fixture, and a conventional parallel plate fixture, respectively, in two different rheometers (ARES 2kFRTN1 from TA Instruments, USA and MCR 702 from Anton Paar-Physica, Austria). The effects of specimen geometry (length-to-width aspect ratio) on storage modulus and level of clamping are investigated. For cylindrical specimens undergoing torsional deformation, we find that geometry and clamping barely affect the shear moduli, and the measurements essentially coincide with those using parallel plates. In contrast, a clear dependence of the storage modulus on the aspect ratio is detected for specimens having rectangular cross section. The empirical correction used routinely in this test is based on geometrical factors and can account for clamping effects, but works only for aspect ratios above a threshold value of 1.4. By employing a finite element analysis, we perform a parametric study of the effects of the aspect ratio in the cross-sectional stress distribution and the linear viscoelastic torsional response. We propose a new, improved empirical equation for obtaining accurate moduli values in torsion at different aspect ratios, whose general validity is demonstrated in both rheometers. These results should provide a guideline for measurements with different elastomers, for which comparison with dynamic oscillatory tests may not be possible due to wall slip issues.

The stress tensor for a dilute suspension of buoyancy free, inertialess, nonBrownian, rigid spheres immersed in a viscoelastic liquid is determined via a perturbative expansion. The perturbation parameter is the Deborah number De, giving the ratio between the characteristic time of the liquid and the characteristic time of the imposed flow. The theoretical predictions upto order De are validated through numerical simulations of continuity and momentum equations for the single sphere problem. The analytic expressions for the local fields of velocity, pressure, and stresses are successfully compared with the results obtained with finite element calculations. Bulk rheological quantities from theory and simulations also show an excellent agreement with each other. Good agreement is found with respect to experimental data from the literature, e.g., on bulk normal stresses for dilute suspensions in shear flow. © 2007 Elsevier B.V. All rights reserved

In this work a new numerical method for concentrated inertialess rigid particle suspensions in a planar elongational flow using a fixed mesh is presented. The main concept is to randomly relocate a particle on an inflow section of the domain when it crosses the outflow boundaries. A three-layer domain is considered in order to: (i) develop a small computational domain as the representative sample of the whole suspension, (ii) impose the elongational flow boundary conditions far from the particles, (iii) achieve a steady state (in a statistical meaning). Our scheme uses a time-independent fixed grid avoiding the difficulties involved in deforming meshes and remeshing of the domain. In this way, computations can proceed indefinitely and micro-structural fluctuations around a steady state can be studied. A fictitious domain is implemented in order to easily manage the rigid-body motion. The particles are described by their boundaries only (rigid-ring description) and the rigid-body motion is imposed through Lagrange multipliers. The bulk properties are recovered by using an averaging procedure where the traction forces on the particle surface are recovered by the Lagrange multipliers. The scheme has been combined with a standard velocity–pressure finite element formulation and 2D simulations of a large number (150 and 225) of particles in a Newtonian medium are performed. Local as well as bulk properties are evaluated and discussed. The results show very good agreement with dilute theory as well as with other numerical simulations in the literature for higher concentrations. Our formulation is well suited for viscoelastic suspensions and can be easily extended to 3D simulations.

We investigate through numerical simulations the dynamics of a neo-Hookean elastic prolate spheroid suspended in a Newtonian fluid under shear flow. Both initial orientations of the particle within and outside the shear plane and both unbounded and confined flow geometries are considered. In unbounded flow, when the particle starts on the shear plane, two stable regimes of motion are found, i.e., trembling (TR), where the particle shape periodically elongates and compresses in the shear plane and the angle between its major semiaxis and the flow direction oscillates around a positive mean value, and tumbling (TU), where the particle shape periodically changes and its major axis performs complete revolutions around the vorticity axis. When the particle is initially oriented out of the shear plane, more complex dynamics arise. Geometric confinement of the particle between the moving walls also influences its deformation and regime of motion. In addition, when the particle is initially located in an asymmetric position with respect to the moving walls, particle lateral migration is detected. The effects on the particle dynamics of the geometric and physical parameters that rule the system are investigated.

In this work, we study in detail the hydrodynamics and the Brownian motions of a spheroidal particle suspended in a Newtonian fluid near a flat rigid wall. We employ 3D Finite Element Method (FEM) simulations to compute how the mobility tensor of the spheroid varies with both the particle-wall separation distance and the particle orientation. We then study the Brownian motion of the spheroid by means of a discretized Langevin equation. We specifically focus on the additional drift terms arising from the position and orientational dependence of the mobility matrix. In this respect, we also propose a numerically convenient approximation of the orientational divergence of the mobility matrix that is required in the solution of the Langevin equation. Our results illustrate that both hydrodynamics and Brownian motions of a spheroidal particle near a confining wall display novel features from those of a sphere in the same type of confinement.

The deflection of magnetic beads in a microfluidic channel through magnetophoresis can be improved if the particles are somehow focused along the same streamline in the device. We design and fabricate a microfluidic device made of two modules, each one performing a unit operation. A suspension of magnetic beads in a viscoelastic medium is fed to the first module, which is a straight rectangular-shaped channel. Here, the magnetic particles are focused by exploiting fluid viscoelasticity. Such a channel is one inlet of the second module, which is a H-shaped channel, where a buffer stream is injected in the second inlet. A permanent magnet is used to displace the magnetic beads from the original to the buffer stream. Experiments with a Newtonian suspending fluid, where no focusing occurs, are carried out for comparison. When viscoelastic focusing and magnetophoresis are combined, magnetic particles can be deterministically separated from the original streamflow to the buffer, thus leading to a high deflection efficiency (up to ~96%) in a wide range of flow rates. The effect of the focusing length on the deflection of particles is also investigated. Finally, the proposed modular device is tested to separate magnetic and non-magnetic beads.

In this work, we present 2D numerical simulations on the migration of a particle suspended in a viscoelastic fluid under Poiseuille flow at finite Reynolds numbers, in order to clarify the simultaneous effects of viscoelasticity and inertia on the lateral particle motion. The governing equations are solved through the finite element method by adopting an Arbitrary Lagrangian-Eulerian (ALE) formulation to handle the particle motion. The high accuracy provided by such a method even for very small particle-wall distances, combined with proper stabilization techniques for viscoelastic fluids, allow obtaining convergent solutions at relatively large flow rates, as compared to previous works. As a result, the detailed non-linear dynamics of the migration phenomenon in a significant range of Reynolds and Deborah numbers is presented. The simulations show that, in agreement with the previous literature, a mastercurve relating the migration velocity of the particle to its vertical position completely describes the phenomenon. Remarkably, we found that, for comparable values of the Deborah and Reynolds numbers, inertial effects are negligible: migration is in practice driven by fluid viscoelasticity only. At moderate Reynolds numbers (20

The rheology of a dilute viscoelastic suspension of spheroids subjected to unconfined shear flow is studied by numerical simulations. To highlight the effect of the suspending fluid rheology, two viscoelastic constitutive equations, i.e., the Giesekus and the Phan-Thien-Tanner models, have been selected. Simulations are performed for a spheroid with two aspect ratios (4 and 8). The spherical particle case is also investigated for comparison. The Deborah number D e is varied between 0 and 4. The particle contribution to the viscosity is weakly affected by the particle shape and orientation. In contrast, spheroids oriented with major axis out of the vorticity direction significantly reduce the particle contribution to the first and second normal stress difference. The maximum reduction is found in the flow-alignment regime. Simulations of the transient dynamics of the suspension show that the initial distribution of the particle orientation has a remarkable influence on the evolution of the stress coefficients. The time needed to obtain steady-state rheological properties is at least one order of magnitude higher than the fluid characteristic time.

Background: The flow of suspensions through bifurcations is encountered in several applications. It is known that the partitioning of particles at a bifurcation is different from the partitioning of the suspending fluid, which allows particle separation and fractionation. Previous works have mainly investigated the dynamics of particles sus- pended in Newtonian liquids. Methods: In this work, we study through 2D direct numerical simulations the par- titioning of particles suspended in non-Newtonian fluids flowing in a T-junction. We adopt a flow configuration such that the two outlets are orthogonal, and their flow rates can be tuned. A fictitious domain method combined with a grid deformation procedure is used. The effect of fluid rheology on the partitioning of particles between the two outlets is investigated by selecting different constitutive equations to model the suspending liquid. Specifically, an inelastic shear-thinning (Bird-Carreau) and a viscoelastic shear-thinning (Giesekus) models have been chosen; the results are also compared with the case of a Newtonian suspending liquid. Results: Simulations are carried out by varying the confinement, the inlet flow rate and the relative weight of the two outlet flow rates. For each condition, the fluxes of particles through the two outflow channels are computed. The results show that shear- thinning does not have a relevant effect as compared to the equivalent Newtonian case, i.e., with the same choice of the relative outlet flow rates. On the other hand, fluid elasticity strongly alters the fraction of particles exiting the two outlets as compared to the inlet. Such effect is more pronounced for larger particles and inlet flow rates. Conclusions: The results illustrated here show the feasibility to efficiently separate/ fractionate particles by size, through the use of viscoelastic suspending liquids.

The flow behavior of suspensions is the subject of a huge amount of literature due to the obvious implications in several biological and industrial applications. The motion of non-Brownian rigid particles suspended in fluids flowing in some kind of geometry depends on several factors such as flow field, suspending liquid rheology, confinement, particle shape and concentration.

A novel method to estimate the relaxation time of viscoelastic fluids, down to milliseconds, is here proposed. The adopted technique is based on the particle migration phenomenon occurring when the suspending viscoelastic fluid flows in microfluidic channels. The method is applied to measure the fluid relaxation times of two water-glycerol polymer solutions in an ample range of concentrations. A remarkable improvement in the accuracy of the measure of the relaxation time is found, as compared with experimental data obtained from shear or elongational experiments available in the literature. Good agreement with available theoretical predictions is also found. The proposed method is reliable, handy and does not need a calibration curve, opening an effective way to measure relaxation times of viscoelastic fluids otherwise not easily detectable by conventional techniques.

The motion of an ellipsoidal particle in a viscoelastic liquid subjected to an unconfined shear flow is addressed by numerical simulations. A complex dynamics is found with different transients and long-time regimes depending on the Deborah number De (De is the product of the viscoelastic liquid intrinsic time times the applied shear rate). Spiraling orbits toward a log-rolling motion around the vorticity are observed for low Deborah numbers, whereas the particle aligns with its major axis near to the flow direction at high Deborah numbers. The transition from vorticity to flow alignment is characterized by a periodic regime with small amplitude oscillations around orientations progressively shifting from vorticity to flow direction by increasing De. A range of Deborah numbers is detected such that the periodic solution coexists with the flow alignment regime (bistability). A further range of De is found where flow alignment is attained differently for particles starting far from or next to the shear plane: in the latter case, very long transients are found; hence an effective bistability (metabistability) is predicted to occur in a large time lapse before reaching the fully aligned state. Finally, the computed Deborah number values for flow alignment favorably compare with available experimental data. © 2014 American Physical Society.

We demonstrate the possibility to achieve 3D particle focusing in a straight microchannel with a square cross-section by exploiting purely viscoelastic effects. Experiments are carried out by considering an elastic, constant-viscosity aqueous solution of PVP (polyvinylpyrrolidone) as the suspending liquid. Several flow rates and two channel dimensions (with a fixed particle size to channel dimension ratio) are investigated. A novel technique combining particle tracking measurements and numerical simulations is used to reconstruct the position of the flowing particles over the channel cross-section. The results show that, for all the investigated experimental conditions, particles migrate towards the channel centerline. Flow-focusing is enhanced by higher flow rates. The measured particle fractions can be rescaled according to a single dimensionless parameter, as already reported in the literature for the case of cylindrical channels. The so-obtained master curve can be used as a guide to predict the required focusing length. The effect of the entrance on the focusing channel length is also addressed. Finally, analogies and discrepancies with similar previous works are discussed.

Particles suspended in non-Newtonian liquids flowing in channels may migrate transversally to the main flow direction as a result of normal stress gradients. Viscoelasticity-induced migration has proven to be an efficient mechanism to promote 3D flow-focusing in cylindrical microchannels, avoiding the need for complex and expensive apparati. In this work, we demonstrate the existence of a single dimensionless number (Theta) that governs the migration dynamics of particles in viscoelastic liquids flowing in micropipes at low Deborah numbers (Deborah number is the ratio of fluid and flow characteristic times). The definition of Theta in terms of the relevant fluid, flow and geometrical quantities is obtained by generalizing the particle migration velocity expression given in previous asymptotic analytical theories through numerical simulations. An extensive experimental investigation quantitatively confirms the novel predictions: the experimental particle distributions along the channel axial direction collapse on a single curve when rescaled in terms of the proposed dimensionless number. The results reported in this work give a simple and general way to define the flow-focusing conditions promoted by viscoelastic effects

Deterministic lateral displacement devices have been proved to be an efficient way to perform continuous particle separation in microfluidic applications (Huang et al. Science 304:987–990, 2004). On the basis of their size, particles traveling through an array of obstacles follow different paths and can be separated in outflow. One limitation of such a technique is that each device works for a specific critical size to achieve particle separation, and a new device with different geometrical properties needs to be fabricated, as the dimensions of the particles to be separated change. In this work, we demonstrate the possibility to tune the critical particle size in a deterministic lateral displacement device by using non-Newtonian fluids as suspending liquid. The analysis is carried out by extending the theory developed for a Newtonian constitutive law (Inglis et al. Lab Chip 6:655–658, 2006) to account for fluid shear-thinning. 3-D finite element simulations are performed to compute the dynamics of a spherical particle flowing through the deterministic ratchet. The results show that fluid shear-thinning, by altering the flow field between the obstacles, contributes to decrease the critical particle diameter as compared to the Newtonian case. Numerical simulations demonstrate that tunability of the critical separation size can be achieved by using the flow rate as control parameter. A design formula, relating the separation diameter to the fluid rheology and the relevant geometrical parameters of the device, is derived. Such a formula, originally developed for a power-law model, is proved to work for non-Newtonian liquids with a general viscosity trend.

The dynamic response of a viscoelastic suspension of spheres under small and large amplitude oscillatory shear is investigated by three-dimensional direct numerical simulations. A sliding triperiodic domain is implemented whereby the computational domain is regarded as the bulk of an infinite suspension. A fictitious domain method is used to manage the particle motion. After the stress field is computed, the bulk properties are recovered by an averaging procedure. The numerical method is validated by comparing the computed linear viscoelastic response of Newtonian and non-Newtonian suspensions with previous theories and simulations. The numerical predictions are in very good quantitative agreement with experimental data for the Newtonian case, whereas deviations are found with respect to some sets of experiments for semidilute and concentrated viscoelastic suspensions. To investigate on such discrepancies, the effect of aggregates in the bulk of the suspension is examined. The simulations show that the presence of structures significantly alters the loss modulus. Such an effect is more pronounced as the volume fraction increases. In this light, the above mentioned disagreement between simulations and data (and among experimental data themselves) can be rationalized, as its origin can be attributed to inhomogeneous particle configurations. For increasing strain amplitudes, both loss and storage moduli depart from the linear viscoelastic values. Although the deviations are qualitatively similar to the large amplitude response of the unfilled suspending matrix, our results for dilute and semidilute suspensions show that the decrease of the moduli is more and more pronounced as the volume fraction is higher. Furthermore, a higher concentration of solid particles reduces the value of strain amplitude such that the nonlinear behavior is observed. Simulations at higher frequencies also correctly capture the overshoot in the loss modulus for intermediate strain amplitudes. Finally, the effect of fluid elasticity on the particle motion is analyzed. The particles are found to move away from their starting positions and the average distance, computed at the beginning of each cycle with respect to the initial configuration, linearly increases with the number of cycles. The change in the microstructure is attributed to the long-range hydrodynamic interactions mediated by fluid viscoelasticity.

We perform 3D numerical simulations, heuristic modeling and microfluidic experiments to demonstrate, for the first time, the presence of a bistability scenario for transversal migration of particles suspended in a viscoelastic liquid flowing in a pipe. Our results show that particle migration, either at the centerline or at the wall, can be controlled by the rheological properties of the suspending liquid and by the relative dimensions of the particle and tube. Proper selection of these parameters can promote strict aligning of particles on a line, i.e., 3-D focusing. Simple design rules are given to rationally control particle focusing under flow in micropipes.

The intrinsically coupled effects of the curvature of the flow-field and of the viscoelastic nature of suspending medium on the cross-stream lateral migration of a single non-Brownian sphere in wide-gap Couette flow are studied. Quantitative videomicroscopy experiments using a counterrotating device are compared to the results of 3D finite element simulations. To evaluate the effects of differences in rheological properties of the suspending media, fluids have been selected which highlight specific constitutive features, including a reference Newtonian fluid, a single relaxation time wormlike micellar surfactant solution, a broad spectrum shear-thinning elastic polymer solution and a constant viscosity, highly elastic Boger fluid. As expected for conditions corresponding to Stokes flow, migration is absent in the Newtonian fluid. In the wormlike micellar solution and the shear-thinning polymer solution, spheres are observed to migrate in the direction of decreasing shear rate gradient, i.e. the outer cylinder, except when the sphere is initially released close to the inner cylinder, in which case the migration is towards it. The migration is enhanced by faster relative angular velocities of the cylinders. Shear-thinning reduces the migration velocity, showing an opposite behavior as compared to previous results in planar shear flow. In the Boger fluid, within experimental error no migration could be observed, likely due to the large solvent contribution to the overall viscosity. For small Deborah numbers the migration results are well described by an heuristic argument based on a local stress balance.

Solid–liquid disperse systems are complex fluids, extensively used for a variety of applications. The flow behavior of such materials is strongly dependent on the matrix rheological properties: when the suspending fluid shows viscoelastic behavior, isolated suspended particles in confined flow fields tend to migrate across the streamlines. In this work, we carry out a detailed experimental investigation of such migration phenomenon for a rigid, spherical particle in planar shear flow, and compare the experimental findings with 3D numerical simulations based on finite elements. A highly elastic non-Newtonian fluid is chosen as the suspending medium. The migration is studied by varying the confinement, the external shear rate and the fluid normal stresses. The particle is always found to move towards the closest wall, regardless of its initial position. For a fixed set of geometrical and flow parameters, the trajectories from different initial positions can be shifted in time to overlap on a single curve. Migration dynamics is governed by an exponential law as the particle is in the region around the midgap. Stronger confinements, higher shear rates and higher levels of normal stresses all enhance the migration speed. We found qualitative agreement between predictions from numerical simulations and experimental results.

When particles are dispersed in viscoelastic rather than Newtonian media, the hydrodynamics will be changed entailing differences in suspension rheology. The disturbance velocity profiles and stress distributions around the particle will depend on the viscoelastic material functions. Even in inertialess flows, changes in particle rotation and migration will occur. The problem of the rotation of a single spherical particle in simple shear flow in viscoelastic fluids was recently studied to understand the effects of changes in the rheological properties with both numerical simulations [D’Avino et al., J. Rheol. 52 (2008) 1331–1346] and experiments [Snijkers et al., J. Rheol. 53 (2009) 459–480]. In the simulations, different constitutive models were used to demonstrate the effects of different rheological behavior. In the experiments, fluids with different constitutive properties were chosen. In both studies a slowing down of the rotation speed of the particles was found, when compared to the Newtonian case, as elasticity increases. Surprisingly, the extent of the slowing down of the rotation rate did not depend strongly on the details of the fluid rheology, but primarily on the Weissenberg number defined as the ratio between the first normal stress difference and the shear stress. In the present work, a quantitative comparison between the experimental measurements and novel simulation results is made by considering more realistic constitutive equations as compared to the model fluids used in previous numerical simulations [D’Avino et al., J. Rheol. 52 (2008) 1331–1346]. A multimode Giesekus model with Newtonian solvent as constitutive equation is fitted to the experimentally obtained linear and nonlinear fluid properties and used to simulate the rotation of a torque-free sphere in a range of Weissenberg numbers similar to those in the experiments. A good agreement between the experimental and numerical results is obtained. The local torque and pressure distributions on the particle surface calculated by simulations are shown.

Dilute suspensions of spheres in a viscoelastic liquid under oscillatory shear flow are studied via numerical simulations. In linear viscoelastic regime, the 3D finite element simulation results agree with the analytical results from Palierne (1990). The analysis is extended to Large Amplitude Oscillations (LAOS). The rotation rate of the sphere as well as the bulk rheology are investigated. The moduli increase when particles are added into the fluid, in agreement with experimental findings. In the nonlinear range both moduli are found to be decreasing functions of the forcing amplitude. The non-linear response of the material is also illustrated by performing a Fourier analysis of the bulk shear stress signal which shows the appearance of higher harmonic contributions.

The effect of the viscoelastic nature of the suspending medium on the rotation of spherical particles in a simple shear flow is studied experimentally using a counter-rotating device. To evaluate the effect of variations in rheological properties of the suspending media, fluids have been selected which highlight specific constitutive features. These include a reference Newtonian fluid, a constant viscosity, high elasticity Boger fluid, a single relaxation time wormlike micellar surfactant solution, and a broad spectrum shear-thinning elastic polymer solution. It is shown that particle rotation slows down, when compared to the Newtonian case, as elasticity increases, in qualitative agreement with computer simulation studies. Despite the variation in constitutive properties and the wide range of time scales of the fluids, it is found that the Weissenberg number suffices to scale the data: the dimensionless rotation speed of the spheres in the different fluids scales onto a single master curve as a function of the Weissenberg number. This indicates that the slowing down in rotation finds its main origin in (indirect) normal stress effects. ©2009 The Society of Rheology

In inertialess suspensions of rigid particles, the rotational motion of each particle is governed by the so-called freely rotating condition, whereby the total torque acting on the particle must be zero. In this work, we study the effect of viscoelasticity of the suspending liquid on the rotation period of a sphere by means of three-dimensional finite element simulations, for conditions corresponding to a macroscopic shear flow. The simulation results capture the slowing down of the rotation, relative to the Newtonian case, which was recently observed in experiments. It is shown that such a phenomenon depends on the specific constitutive equation adopted for the viscoelastic liquid. Analysis of transients shows a clear correlation between rotation rate and the development of first normal stress difference.