Luís Jorge Lima Ferrás

Analytical and numerical study of the electro-osmotic annular flow of viscoelastic fluids

In this work we present semi-analytical solutions for the electro-osmotic annular flow of viscoelastic fluids modeled by the Linear and Exponential PTT models. The viscoelastic fluid flows in the axial direction between two concentric cylinders under the combined influences of electrokinetic and pressure forcings. The analysis invokes the Debye-Hückel approximation and includes the limit case of pure electro-osmotic flow. The solution is valid for both no slip and slip velocity at the walls and the chosen slip boundary condition is the linear Navier slip velocity model. The combined effects of fluid rheology, electro-osmotic and pressure gradient forcings on the fluid velocity distribution are also discussed.

Electro-osmotic and pressure-driven flow of viscoelastic fluids in microchannels: Analytical and semi-analytical solutions

In this work, we present a series of solutions for combined electro-osmotic and pressure-driven flows of viscoelastic fluids in microchannels. The solutions are semi-analytical, a feature made possible by the use of the Debye–Huckel approximation for the electrokinetic fields, thus restricted to cases with small electric double-layers, in which the distance between the microfluidic device walls is at least one order of magnitude larger than the electric double-layer thickness. To describe the complex fluid rheology, several viscoelastic differential constitutive models were used, namely, the simplified Phan-Thien–Tanner model with linear, quadratic or exponential kernel for the stress coefficient function, the Johnson-Segalman model, and the Giesekus model. The results obtained illustrate the effects of the Weissenberg number, the Johnson-Segalman slip parameter, the Giesekus mobility parameter, and the relative strengths of the electro-osmotic and pressure gradient-driven forcings on the dynamics of thes...

Fractional pennes' bioheat equation: theoretical and numerical studies

Abstract In this work we provide a new mathematical model for the Pennes’ bioheat equation, assuming a fractional time derivative of single order. Alternative versions of the bioheat equation are studied and discussed, to take into account the temperature-dependent variability in the tissue perfusion, and both finite and infinite speed of heat propagation. The proposed bioheat model is solved numerically using an implicit finite difference scheme that we prove to be convergent and stable. The numerical method proposed can be applied to general reaction diffusion equations, with a variable diffusion coefficient. The results obtained with the single order fractional model, are compared with the original models that use classical derivatives.

A Numerical Method for the Solution of the Time-Fractional Diffusion Equation

In this work we provide a new numerical scheme for the solution of the fractional sub-diffusion equation. This new scheme is based on a combination of a recently proposed non-polynomial collocation method for fractional ordinary differential equations and the method of lines. A comparison of the numerical results obtained with known analytical solutions is carried out, using different values of the order of the fractional derivative and several time and space stepsizes, and we conclude that, as in the fractional ordinary differential equation case, the convergence order of the method is independent of the order of the time derivative and does not decrease when dealing with certain nonsmooth solutions.

Development Length in Planar Channel Flows of Newtonian Fluids Under the Influence of Wall Slip

ðÞ , varying in the range 0 < kl � 1. The simulations were carried out for low Reynolds number flows in the range 0 < Re � 100, making use of a rigorous mesh refinement with an accuracy error below 1%. The development length is found to be a nonmonotonic function of the slip velocity coefficient, increasing up to kl � 0:1 � 0:4 (depending on Re) and decreasing for higher kl. We present a new nonlinear relationship between L, Re, and kl that can accurately predict the development length for Newtonian fluid flows with slip velocity at the wall for Re of up to 100 and kl up to 1. [DOI: 10.1115/1.4007383]

Design Guidelines to Balance the Flow Distribution in Complex Profile Extrusion Dies

Abstract In this work a novel methodology to balance the flow distribution in complex extrusion dies is proposed. For this purpose, the profile cross section geometry is divided into simpler geometries (L and T shaped profiles), which are balanced with a surrogate model obtained by a detailed numerical study. The numerical simulations are performed considering the non-isothermal flow of Bird-Carreau inelastic fluids, and the numerical computations are performed with a solver implemented in OpenFOAM computational library. The proposed methodology is assessed with some case studies.

A numerical and theoretical study on viscoelastic fluid slip flows

This work describes a theoretical and numerical investigation of viscoelastic fluid flows, considering slip boundary conditions. The viscoelastic fluid is described by the simplified Phan-Thien-Tanner model, and the governing equations with slip boundary conditions are solved by a finite volume method using (1) a recently proposed methodology to control the growth of the slip velocity along the iterative process (named the SIMPLE-slip method) where some simplifications are assumed at the wall, and also (2) a slip formulation where the complete stress tensor at the wall is taken into account. Analytical and semi-analytical solutions are also provided for the fully developed flow between parallel plates of viscoelastic fluids, assuming Thomson and Troian and Lau and Schowalter non-linear wall slip models. For verification purposes, the numerical results were compared with the analytical solution for fully developed slip-flow in a planar channel using two non-linear slip models. Simulations were carried out ...

Effect of polymer melt wall slip on the flow balance of profile extrusion dies

This work describes the implementation of the wall slip boundary condition in an in-house developed 3D numerical code based on the Finite Volume Method. For this purpose, several phenomenological models relating the velocity and the shear stress at the wall were implemented. This new feature is verified using a simple case study, by comparing the numerical results with those obtained through the corresponding analytical solution. Then, the potentialities of the new code are illustrated performing flow simulations of a polymer melt in a complex flow channel. The results obtained show that the slip at the wall influences the flow distribution at the die flow channel outlet. Therefore, and to assess the relevance of slippage in the optimal die geometry, the automatic optimization of a die flow channel, required for the production of a specific thermoplastic profile, is performed using both the no-slip and slip boundary conditions, together with two alternative optimization strategies. It is shown that slip f...

Guidelines for balancing the flow in extrusion dies: the influence of the material rheology

Abstract In this work we present improved design guidelines to support the die designer activity, when searching for the flow channel geometry that allows the achievement of a balanced flow distribution, in complex profile extrusion dies. The proposed methodology relies on surrogate models, obtained through a detailed and extensive numerical study, carried out with the open source computational library OpenFOAM®, in which an appropriate numerical solver for the problems under study was implemented. The main contribution of this work is to further enlarge the applicability of the simplified design methodology (Rajkumar A, Ferrás LL, Fernandes C, Carneiro OS, Becker M, Nóbrega JM. Int. Polym. Proc. 2017, 32, 58–71.) previously proposed by this group for similar purposes, by considering the effect of processing parameters and material rheology. The sensitivity analyses performed showed that, among the studied parameters, the power-law exponent was the only one that affected the system behavior. Thus, the previous proposed surrogate models were modified to include the effect of this parameter. Verification studies performed for three geometries and different rheological and process parameters evidenced the effectiveness of the proposed simplified design methodology.

An Open-Source Framework for the Computer Aided Design of Complex Profile Extrusion Dies

Abstract This work presents a new design procedure for improving the flow distribution in complex profile extrusion dies. The proposed approach is based on open source software and aims to motivate both academics and industrials to consider numerical methodologies in their future developments. A new solver was implemented in OpenFOAM computational library in order to model the steady non-isothermal flow of inelastic fluids. The developed code was verified with the Method of Manufactured Solutions. The capability of the proposed design procedure was experimentally assessed with an industrial case study, and the results obtained suggest that the computational based design aid is an excellent alternative to the usual experimental trial-and-error procedure used in industry.