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In this paper, we investigate the retraction of a circular viscoelastic liquid film with a hole initially present in its center by means of finite element numerical simulations. We study the whole retraction process, aiming at understanding the hole opening dynamics both when the hole does not feel any confinement and when it interacts with the solid wall bounding the film. The retraction behavior is also interpreted through a simple toy model, that highlights the physical mechanism underlying the process. We consider three different viscoelastic constitutive equations, namely, Oldroyd-B, Giesekus (Gsk), and Phan Thien-Tanner (PTT) models, and several system geometries, in terms of the film initial radius and thickness. For each given geometry, we investigate the effects of liquid inertia, elasticity, and flow-dependent viscosity on the dynamics of the hole opening. Depending on the relative strength of such parameters, qualitatively different features can appear in the retracting film shape and dynamics. When inertia is relevant, as far as the opening hole does not interact with the wall bounding the film, the influence of liquid elasticity is very moderate, and the retraction dynamics tends to the one of Newtonian sheets; when the hole starts to interact with the solid wall, hole radius/opening velocity oscillations are detected. Such oscillations enhance at increasing elasticity. From the morphological point of view, the formation of a rim at the edge of the retracting film is observed. If inertial forces become less relevant with respect to viscous forces, R-oscillations disappear, the hole opening velocity goes through a maximum and then monotonically decays to zero, and no rim forms during the film retraction. Geometrical changes have the effect of enlarging or reducing the portion of the retraction dynamics not influenced by the presence of the solid wall with respect to the one governed by the hole-wall

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.

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.

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 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 towards 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 flow alignment regime (bistability). A further range of De is found where flow alignment is attained differently for particles starting far 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.

The dynamic response of a viscoelastic suspension of spheres under small and large amplitude oscillatory shear is investigated by 3D direct numerical simulations. A sliding triperiodic domain is implemented whereby the computational domain is regarded as the bulk of an infinite suspen- sion. 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 semi-dilute and concentrated viscoelastic suspensions. To investigate on such discrepancies, the effect of aggre- gates 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 semi-dilute suspensions show that the de- crease of the moduli is more and more pronounced as the volume fraction is higher. Furthermore, an higher concentration of solid particles reduces the value of strain amplitude such that the non- linear behavior is observed. Simulations at higher frequencies also correctly capture the overshoot in the loss modulus for intermediate strain amplitudes. Fina

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 3D 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.