Numerical solution of the eXtended Pom-Pom model for viscoelastic free surface flows

In this paper we present a finite difference method for solving two-dimensional viscoelastic unsteady free surface flows governed by the single equation version of the eXtended Pom-Pom (XPP) model. The momentum equations are solved by a projection method which uncouples the velocity and pressure fields. We are interested in low Reynolds number flows and, to enhance the stability of the numerical method, an implicit technique for computing the pressure condition on the free surface is employed. This strategy is invoked to solve the governing equations within a Marker-and-Cell type approach while simultaneously calculating the correct normal stress condition on the free surface. The numerical code is validated by performing mesh refinement on a two-dimensional channel flow. Numerical results include an investigation of the influence of the parameters of the XPP equation on the extrudate swelling ratio and the simulation of the Barus effect for XPP fluids. (C) 2010 Elsevier B.V. All rights reserved.

Numerical Solution of the Upper-Convected Maxwell Model for Three-Dimensional Free Surface Flows

This work presents a finite difference technique for simulating three-dimensional free surface flows governed by the Upper-Convected Maxwell (UCM) constitutive equation. A Marker-and-Cell approach is employed to represent the fluid free surface and formulations for calculating the non-Newtonian stress tensor on solid boundaries are developed. The complete free surface stress conditions are employed. The momentum equation is solved by an implicit technique while the UCM constitutive equation is integrated by the explicit Euler method. The resulting equations are solved by the finite difference method on a 3D-staggered grid. By using an exact solution for fully developed flow inside a pipe, validation and convergence results are provided. Numerical results include the simulation of the transient extrudate swell and the comparison between jet buckling of UCM and Newtonian fluids.

A Numerical Study of the FENE-CR Model Applied to a Jet Flow Problem

The FENE-CR model is investigated through a numerical algorithm to simulate the time-dependent moving free surface flow produced by a jet impinging on a flat surface. The objective is to demonstrate that by increasing the extensibility parameter L, the numerical solutions converge to the solutions obtained with the Oldroyd-B model. The governing equations are solved by an established free surface flow solver based on the finite difference and marker-and-cell methods. Numerical predictions of the extensional viscosity obtained with several values of the parameter L are presented. The results show that if the extensibility parameter L is sufficiently large then the extensional viscosities obtained with the FENE-CR model approximate the corresponding Oldroyd-B viscosity. Moreover, the flow from a jet impinging on a flat surface is simulated with various values of the extensibility parameter L and the fluid flow visualizations display convergence to the Oldroyd-B jet flow results.

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

This work presents numerical simulations of two fluid flow problems involving moving free surfaces: the impacting drop and fluid jet buckling. The viscoelastic model used in these simulations is the eXtended Pom-Pom (XPP) model. To validate the code, numerical predictions of the drop impact problem for Newtonian and Oldroyd-B fluids are presented and compared with other methods. In particular, a benchmark on numerical simulations for a XPP drop impacting on a rigid plate is performed for a wide range of the relevant parameters. Finally, to provide an additional application of free surface flows of XPP fluids, the viscous jet buckling problem is simulated and discussed. (C) 2011 Elsevier B.V. All rights reserved.

The Traceless Oldroyd viscoelastic model

In the traceless Oldroyd viscoelastic model, the viscoelastic extra stress tensor is decomposed into its traceless (deviatoric) and spherical parts, leading to a reformulation of the classical Oldroyd model. The equivalence of the two models is established comparing model predictions for simple test cases. The new model is validated using several 2D benchmark problems. The structure and behavior of the new model are discussed and the future use of the new model in envisioned, both on the theoretical and numerical perspectives.

A computational study of some rheological influences on the ""splashing experiment""

In various attempts to relate the behaviour of highly-elastic liquids in complex flows to their rheometrical behaviour, obvious candidates for study have been the variation of shear viscosity with shear rate, the two normal stress differences N(1) and N(2), especially N(1), the extensional viscosity, and the dynamic moduli G` and G ``. In this paper, we shall confine attention to `constant-viscosity` Boger fluids, and, accordingly, we shall limit attention to N(1), eta(E), G` and G ``. We shall concentrate on the ""splashing"" problem (particularly that which arises when a liquid drop falls onto the free surface of the same liquid). Modern numerical techniques are employed to provide the theoretical predictions. We show that high eta(E) can certainly reduce the height of the so-called Worthington jet, thus confirming earlier suggestions, but other rheometrical influences (steady and transient) can also have a role to play and the overall picture may not be as clear as it was once envisaged. We argue that this is due in the main to the fact that splashing is a manifestly unsteady flow. To confirm this proposition, we obtain numerical simulations for the linear Jeffreys model. (C) 2010 Elsevier B.V. All rights reserved.

The competing roles of extensional viscosity and normal stress differences in complex flows of elastic liquids

In various attempts to relate the behaviour of highly-elastic liquids in complex flows to their rheometrical behaviour, obvious candidates for study have been the variation of shear viscosity with shear rate, the two normal stress differences N(1) and N(2) especially N(1), and the extensional viscosity eta(E). In this paper, we shall be mainly interested in `constant-viscosity` Boger fluids, and, accordingly, we shall limit attention to N(1) and eta(E). We shall concentrate on two important flows - axisymmetric contraction flow and ""splashing"" (particularly that which arises when a liquid drop falls onto the free Surface of the same liquid). Modem numerical techniques are employed to provide the theoretical predictions. It is shown that the two obvious manifestations of viscoelastic rheometrical behaviour can sometimes be opposing influences in determining flow characteristics. Specifically, in an axisymmetric contraction flow, high eta(E) , can retard the flow, whereas high N(1) can have the opposite effect. In the splashing experiment, high eta(E) can certainly reduce the height of the so-called Worthington jet, thus confirming some early suggestions, but, again, other rheometrical influences can also have a role to play and the overall picture may not be as clear as it was once envisaged.

Numerical simulation of some viscoelastic fluids

Numerical simulation of the Oldroyd-B type viscoelastic fluids is a very challenging problem. rnThe well-known High Weissenberg Number Problem" has haunted the mathematicians, computer scientists, and rnengineers for more than 40 years. rnWhen the Weissenberg number, which represents the ratio of elasticity to viscosity, rnexceeds some limits, simulations done by standard methods break down exponentially fast in time. rnHowever, some approaches, such as the logarithm transformation technique can significantly improve rnthe limits of the Weissenberg number until which the simulations stay stable. rnrnWe should point out that the global existence of weak solutions for the Oldroyd-B model is still open. rnLet us note that in the evolution equation of the elastic stress tensor the terms describing diffusive rneffects are typically neglected in the modelling due to their smallness. However, when keeping rnthese diffusive terms in the constitutive law the global existence of weak solutions in two-space dimension rncan been shown. rnrnThis main part of the thesis is devoted to the stability study of the Oldroyd-B viscoelastic model. rnFirstly, we show that the free energy of the diffusive Oldroyd-B model as well as its rnlogarithm transformation are dissipative in time. rnFurther, we have developed free energy dissipative schemes based on the characteristic finite element and finite difference framework. rnIn addition, the global linear stability analysis of the diffusive Oldroyd-B model has also be discussed. rnThe next part of the thesis deals with the error estimates of the combined finite element rnand finite volume discretization of a special Oldroyd-B model which covers the limiting rncase of Weissenberg number going to infinity. Theoretical results are confirmed by a series of numerical rnexperiments, which are presented in the thesis, too.

Simulations of pendant drop formation of a viscoelastic liquid

A modified Volume-of-Fluid (VOF) numerical method is used to predict the dynamics of a liquid drop of a low viscosity dilute polymer solution, forming in air from a circular nozzle. Viscoelastic effects are represented using an Oldroyd-B model. Predicted drop shapes are compared with experimental observations. The main features, including the timing of the shape evolution and the bead-on-a-string effect, are well reproduced by the simulations. The results confirm published conclusions of the third author, that the deformation is effectively Newtonian until near the time of Newtonian pinch-off and that the elastic stress becomes large in the pinch region due to the higher extensional flow there.

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

Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)

Numerical solution of the PTT constitutive equation for unsteady three-dimensional free surface flows

This work deals with the development of a numerical technique for simulating three-dimensional viscoelastic free surface flows using the PTT (Phan-Thien-Tanner) nonlinear constitutive equation. In particular, we are interested in flows possessing moving free surfaces. The equations describing the numerical technique are solved by the finite difference method on a staggered grid. The fluid is modelled by a Marker-and-Cell type method and an accurate representation of the fluid surface is employed. The full free surface stress conditions are considered. The PTT equation is solved by a high order method, which requires the calculation of the extra-stress tensor on the mesh contours. To validate the numerical technique developed in this work flow predictions for fully developed pipe flow are compared with an analytic solution from the literature. Then, results of complex free surface flows using the FIT equation such as the transient extrudate swell problem and a jet flowing onto a rigid plate are presented. An investigation of the effects of the parameters epsilon and xi on the extrudate swell and jet buckling problems is reported. (C) 2010 Elsevier B.V. All rights reserved.

Numerical assessment of mass conservation on a MAC-type method for viscoelastic free surface flows

A numerical study of mass conservation of MAC-type methods is presented, for viscoelastic free-surface flows. We use an implicit formulation which allows for greater time steps, and therefore time marching schemes for advecting the free surface marker particles have to be accurate in order to preserve the good mass conservation properties of this methodology. We then present an improvement by using a Runge-Kutta scheme coupled with a local linear extrapolation on the free surface. A thorough study of the viscoelastic impacting drop problem, for both Oldroyd-B and XPP fluid models, is presented, investigating the influence of timestep, grid spacing and other model parameters to the overall mass conservation of the method. Furthermore, an unsteady fountain flow is also simulated to illustrate the low mass conservation error obtained.

Desenvolvimento de uma metodologia numérica para escoamentos viscoelásticos não-isotérmicos

Pós-graduação em Matematica Aplicada e Computacional - FCT

Application of the log-conformation tensor to three-dimensional time-dependent free surface flows

The numerical simulation of flows of highly elastic fluids has been the subject of intense research over the past decades with important industrial applications. Therefore, many efforts have been made to improve the convergence capabilities of the numerical methods employed to simulate viscoelastic fluid flows. An important contribution for the solution of the High-Weissenberg Number Problem has been presented by Fattal and Kupferman [J. Non-Newton. Fluid. Mech. 123 (2004) 281-285] who developed the matrix-logarithm of the conformation tensor technique, henceforth called log-conformation tensor. Its advantage is a better approximation of the large growth of the stress tensor that occur in some regions of the flow and it is doubly beneficial in that it ensures physically correct stress fields, allowing converged computations at high Weissenberg number flows. In this work we investigate the application of the log-conformation tensor to three-dimensional unsteady free surface flows. The log-conformation tensor formulation was applied to solve the Upper-Convected Maxwell (UCM) constitutive equation while the momentum equation was solved using a finite difference Marker-and-Cell type method. The resulting developed code is validated by comparing the log-conformation results with the analytic solution for fully developed pipe flows. To illustrate the stability of the log-conformation tensor approach in solving three-dimensional free surface flows, results from the simulation of the extrudate swell and jet buckling phenomena of UCM fluids at high Weissenberg numbers are presented. (C) 2012 Elsevier B.V. All rights reserved.

Stable and high-level production of recombinant Factor IX in human hepatic cell line

Hemophilia B is a genetic disease of the coagulation system that affects one in 30,000 males worldwide. Recombinant human Factor IX (rhFIX) has been used for hemophilia B treatment, but the amount of active protein generated by these systems is inefficient, resulting in a high-cost production of rhFIX. In this study, we developed an alternative for rhFIX production. We used a retrovirus system to obtain two recombinant cell lines. We first tested rhFIX production in the human embryonic kidney 293 cells (293). Next, we tested a hepatic cell line (HepG2) because FIX is primarily expressed in the liver. Our results reveal that intracellular rhFIX expression was more efficient in HepG2/rhFIX (46%) than in 293/rhFIX (21%). The activated partial thromboplastin time test showed that HepG2/rhFIX expressed biologically active rhFIX 1.5 times higher than 293/rhFIX (P = 0.016). Recovery of rhFIX from the HepG2 by reversed-phase chromatography was straightforward. We found that rhFIX has a pharmacokinetic profile similar to that of FIX purified from human plasma when tested in hemophilic B model. HepG2/rhFIX cell line produced the highest levels of rhFIX, representing an efficient in vitro expression system. This work opens up the possibility of significantly reducing the costs of rhFIX production, with implications for expanding hemophilia B treatment in developing countries.