A.M. Afonso

Steady viscoelastic fluid flow between parallel plates under electro-osmotic forces: Phan-Thien-Tanner model.

The electro-osmotic flow of a viscoelastic fluid between parallel plates is investigated analytically. The rheology of the fluid is described by the Phan-Thien-Tanner model. This model uses the Gordon-Schowalter convected derivative, which leads to a non-zero second normal stress difference in pure shear flow. A nonlinear Poisson-Boltzmann equation governing the electrical double-layer field and a body force generated by the applied electrical potential field are included in the analysis. Results are presented for the velocity and stress component profiles in the microchannel for different parametric values that characterize this flow. Equations for the critical shear rates and maximum electrical potential that can be applied to maintain a steady fully developed flow are derived and discussed.

Dynamics of high-Deborah-number entry flows: a numerical study

A. M. AFONSO, P. J. OLIVEIRA, F. T. P INHO AND M. A. ALVES† Departamento de Engenharia Quı́mica, Centro de Estudos de Fenómenos de Transporte, Faculdade de Engenharia da Universidade do Porto, Rua Doutor Roberto Frias, 4200-465 Porto, Portugal Departamento de Engenharia Electromecânica, Unidade de Materiais Texteis e Papeleiros, Universidade da Beira Interior, 6201-001 Covilhã, Portugal Departamento de Engenharia Mecânica, Centro de Estudos de Fenómenos de Transporte, Faculdade de Engenharia da Universidade do Porto, Rua Doutor Roberto Frias, 4200-465 Porto, Portugal

Analytical solution of two-fluid electro-osmotic flows of viscoelastic fluids

This paper presents an analytical model that describes a two-fluid electro-osmotic flow of stratified fluids with Newtonian or viscoelastic rheological behavior. This is the principle of operation of an electro-osmotic two-fluid pump as proposed by Brask et al. [Tech. Proc. Nanotech., 1, 190-193, 2003], in which an electrically non-conducting fluid is transported by the interfacial dragging viscous force of a conducting fluid that is driven by electro-osmosis. The electric potential in the conducting fluid and the analytical steady flow solution of the two-fluid electro-osmotic stratified flow in a planar microchannel are presented by assuming a planar interface between the two immiscible fluids with Newtonian or viscoelastic rheological behavior. The effects of fluid rheology, shear viscosity ratio, holdup and interfacial zeta potential are analyzed to show the viability of this technique, where an enhancement of the flow rate is observed as the shear-thinning effects are increased.

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.

Laminar flow of a viscoelastic shear-thinning liquid over a backward-facing step preceded by a gradual contraction

Experimental observations and numerical simulations, based upon the Phan-Thien and Tanner model, are reported for the laminar flow of a series of viscoelastic liquids (0.05%, 0.1%, and 0.4% concentrations of a polyacrylamide) over a symmetrical, double backward-facing step geometry preceded by a short gradual contraction from a long (120 hydraulic diameters in length) square duct. Reynolds numbers are typically between 10 and 100 (i.e., inertia is not negligible) and Deborah numbers of order 100 for the experiments (based on a relaxation time determined from linear viscoelasticity measurements) and order 10 for the viscoelastic simulations. As the polymer concentration is increased, the combined effects of increased shear thinning and viscoelasticity are found to dramatically reduce the length of the recirculation region downstream of the step. The nature of the flow field within the contraction itself is found to be fundamentally different for the viscoelastic liquids to that for a comparable Newtonian f...

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...

A numerical study of the Kernel-conformation transformation for transient viscoelastic fluid flows

This work presents a numerical application of a generic conformation tensor transformation for simulating highly elastic flows of non-Newtonian fluids typically observed in computational rheology. In the Kernel-conformation framework 14, the conformation tensor constitutive law for a viscoelastic fluid is transformed introducing a generic tensor transformation function. The numerical stability of the application of the Kernel-conformation for highly elastic flows is ultimately related with the specific kernel function used in the matrix transformation, but also to the existence of singularities introduced either by flow geometry or by the characteristics of the constitutive equation. In this work, we implement this methodology in a free-surface Marker-And-Cell discretization methodology implemented in a finite differences method. The main contributions of this work are two fold: on one hand, we demonstrate the accuracy of this Kernel-conformation formulation using a finite differences method and free surfaces; on the other hand, we assess the numerical efficiency of specific kernel functions at high-Weissenberg number flows. The numerical study considers different viscoelastic fluid flow problems, including the Poiseuille flow in a channel, the lid-driven cavity flow and the die-swell free surface flow. The numerical results demonstrate the adequacy of this methodology for high Weissenberg number flows using the Oldroyd-B model. We analyze a generic conformation tensor transformation for simulating the HWNP.The numerical scheme is constructed in the context of finite differences.The numerical study considers transient benchmarks in Computational Rheology.Complex flows are solved, including the die-swell free surface problem.

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]

The finite-volume method in computational rheology

The finite volume method (FVM) is widely used in traditional computational fluid dynamics (CFD), and many commercial CFD codes are based on this technique which is typically less demanding in computational resources than finite element methods (FEM). However, for historical reasons, a large number of Computational Rheology codes are based on FEM. There is no clear reason why the FVM should not be as successful as finite element based techniques in Computational Rheology and its applications, such as polymer processing or, more recently, microfluidic systems using complex fluids. This chapter describes the major advances on this topic since its inception in the early 1990’s, and is organized as follows. In the next section, a review of the major contributions to computational rheology using finite volume techniques is carried out, followed by a detailed explanation of the methodology developed by the authors. This section includes recent developments and methodologies related to the description of the viscoelastic constitutive equations used to alleviate the high-Weissenberg number problem, such as the log-conformation formulation and the recent kernel-conformation technique. At the end, results of numerical calculations are presented for the well-known benchmark flow in a 4:1 planar contraction to ascertain the quality of the predictions by this method.

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 ...