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Complex fluids exist in nature and are continually engineered for specific applications involving the addition of macromolecules to a solvent, among other means. This imparts viscoelasticity to the fluid, a property responsible for various flow instabilities and major modifications to the fluid dynamics. Recent developments in the numerical methods for the simulation of viscoelastic fluid flows, described by continuum-level differential constitutive equations, are surveyed, with a particular emphasis on the finite-volume method. This method is briefly described, and the main benchmark flows currently used in computational rheology to assess the performance of numerical methods are presented. Outstanding issues in numerical methods and novel and challenging applications of viscoelastic fluids, some of which require further developments in numerical methods, are discussed.

Direct numerical simulations (DNS) of turbulent fronts spreading into an irrotational flow region are used to analyse the turbulent entrainment mechanism for viscoelastic fluids. The simulations use the FENE-P fluid model and are initiated from DNS of isotropic turbulence with Weissenberg and turbulence Reynolds numbers varying in the ranges $1.30 \le Wi \le 3.46$ and $206 \le Re_{\lambda }^{0} \le 404$, respectively. The enstrophy dynamics near the turbulent/non-turbulent interface (TNTI) layer, that separates regions of turbulent and irrotational flow, includes a new mechanism – the viscoelastic production – caused by the interaction between the vorticity field and the polymer stresses. This term can be a sink or a source of enstrophy in the turbulent core region of the flow, depending on the Weissenberg number, and contributes to the initial growth of the enstrophy in the viscous superlayer, together with the viscous diffusion, which is the only mechanism present for Newtonian fluids. For low and moderate Weissenberg numbers the scaling of the TNTI layer is similar to the scaling of TNTI layers for Newtonian fluids, but this is no longer the case at high Weissenberg numbers where the enstrophy tends to be concentrated into thin vortex sheets instead of vortex tubes. Finally, it is shown that the substantial decrease of the entrainment rates observed in turbulent flows of viscoelastic fluids, compared with Newtonian fluids, is caused by a reduction of the surface area and fractal dimension of the irrotational boundary, originated by the depletion of ‘active’ scales of motion in the fluid solvent caused by the viscoelasticity.

This work presents new semi-analytical solutions for the combined fully developed electro-osmotic pressure-driven flow in microchannels of viscoelastic fluids, described by the generalised Phan-Thien–Tanner model (gPTT) recently proposed by Ferrás et al. (Journal of Non-Newtonian Fluid Mechanics, 269:88–99, 2019). This generalised version of the PTT model presents a new function for the trace of the stress tensor—the Mittag–Leffler function—where one or two new fitting constants are considered in order to obtain additional fitting flexibility. The semi-analytical solution is obtained under sufficiently weak electric potential that allows the Debye–Hückel approximation for the electrokinetic fields and for thin electric double layers. Based on the solution, the effects of the various relevant dimensionless numbers are assessed and discussed, such as the influence of εWi2, of the parameters α and β of the gPTT model, and also of κ¯, the dimensionless Debye–Hückel parameter. We conclude that the new model characteristics enhance the effects of both εWi2 and κ¯ on the velocity distribution across the microchannels. The effects of a high zeta potential and of the finite size of ions are also studied numerically., A.M. Ribau would like to thank FCT - Fundacao para a Ciencia e a Tecnologia, for financial support through scholarship SFRH/BD/143950/2019. A.M. Ribau, A.M. Afonso, M.A. Alves and F.T Pinho also acknowledge FCT for financial support through projects UIDB/00532/2020 and UIDP/00532/2020 of CEFT (Centro de Estudos de Fenomenos de Transporte), and project PTDC/EMS-ENE/3362/2014-POCI-01-0145-FEDER-016665-funded by FEDER funds through COMPETE2020-Programa Operacional Competitividade e Internacionalizacao (POCI) and by national funds through FCT. L.L. Ferras would also like to thank FCT for financial support through scholarship SFRH/BPD/100353/2014 and projects UIDB/00013/2020 and UIDP/00013/2020. M.L. Morgado acknowledges funding by FCT through project UID/Multi/04621/2019 of CEMAT/IST-ID, Center for Computational and Stochastic Mathematics, Instituto Superior Tecnico, University of Lisbon. This work was partially supported by Fundacao para a Ciencia e a Tecnologia (Portuguese Foundation for Science and Technology) through project UIDB/00297/2020 (Centro deMatematica e Aplicacoes). The authors also acknowledge financial support from COST Action CA15225, a network supported by COST (European Cooperation in Science and Technology).

The effect of a spatially uniform magnetic field on the shear rheology of a dilute emulsion of monodispersed ferrofluid droplets, immersed in a non-magnetizable immiscible fluid, is investigated using direct numerical simulations. The direction of the applied magnetic field is normal to the shear flow direction. The droplets extra stress tensor arising from the presence of interfacial forces of magnetic nature is modeled on the basis of the seminal work of G. K. Batchelor, J. Fluid Mech., 41.3 (1970) under the assumptions of a linearly magnetizable ferrofluid phase and negligible inertia. The results show that even relatively small magnetic fields can have significant consequences on the rheological properties of the emulsion due to the magnetic forces that contribute to deform and orient the droplets towards the direction of the applied magnetic vector. In particular, we have observed an increase of the effective (bulk) viscosity and a reversal of the sign of the two normal stress differences with respect to the case without magnetic field for those conditions where the magnetic force prevails over the shearing force. Comparisons between the results of our model with a direct integration of the viscous stress have provided an indication of its reliability to predict the effective viscosity of the suspension. Moreover, this latter quantity has been found to behave as a monotonic increasing function of the applied magnetic field for constant shearing flows ("magneto-thickening" behaviour), which allowed us to infer a simple constitutive equation describing the emulsion viscosity., Peer-reviewed version: Added new arguments throughout the whole manuscript. Revised arguments in Section 5.2. Addition of a new section dedicated to the comparison with previous theoretical models (Sect. 5.3)

Direct numerical simulations (DNS) of spatially evolving turbulent planar jets of viscoelastic fluids described by the FENE-P model, such as those consisting of a Newtonian fluid solvent carrying long chain polymer molecules, are carried out in order to develop a theory for the far field of turbulent jets of viscoelastic fluids. New evolution relations for the jet shear-layer thickness is the coordinate in the streamwise direction. It is shown that, compared with a classical (Newtonian) turbulent jet, the effect of the polymers is to reduce the spreading rate, centreline velocity decay, Reynolds stresses and viscous dissipation rate. The self-preserving character of the flow is analysed and it is shown that profiles of mean velocity, Reynolds stresses and polymer stresses are self-similar provided the proper scales are used in the normalisation of these quantities. A fundamental difference from the Newtonian jet in this regard is the necessity for two, instead of only one, different velocity and length scales to properly characterise the evolution of the turbulent flow. These extra velocity and length scales are directly related to a time scale associated with the characteristic fading memory property of viscoelastic fluids.

In this work, we present a systematic numerical investigation of the 1:4 planar expansion creeping flow under the influence of slip boundary conditions for Newtonian and viscoelastic fluids, the latter modeled by the simplified Phan-Thien-Tanner constitutive model. The linear and nonlinear Navier slip laws were considered with the dimensionless slip coefficient kl* varying in the range mml:mfenced close="]" open="["0,4500 mml:mfenced> and the slip exponents m = 0.5, 1, and 2. The simulations were carried out for a low Reynolds number, Re = 0.001, and for Deborah numbers (De) between 0 and 100. Convergence could not be achieved for higher values of the Deborah number and large values of the slip coefficient due to the large stress gradients near the singularity point (reentrant corner). The results obtained allow us to conclude that for all De, the increase in slip velocity leads to vortex suppression. The flow characteristics are described in detail for low values of the Deborah number, De, A. M. Afonso acknowledges the support of CEFT (Centro de Estudos de Fenomenos de Transporte) and through Project Nos. PTDC/EMS-ENE/3362/2014 and POCI-01-0145-FEDER-016665-funded by FEDER funds through COMPETE2020-Programa Operacional Competitividade e InternacionalizacAo (POCI) and by national funds through FCT-FundacAo para a Ciencia e a Tecnologia, I.P. A. M. Afonso, M. M. Alves, and F. T. Pinho are also grateful to FCT for funding through projects UIDB/00532/2020 and UIDP/00532/2020.The research of L. L. Ferras was partially financed by Portuguese Funds through FCT within the Project Nos. UIDB/00013/2020 and UIDP/00013/2020 and the scholarship Grant No. SFRH/BPD/100353/2014. J. M. Nobrega acknowledges the funding by FEDER funds through the COMPETE 2020 Program and National Funds through FCT-Portuguese Foundation for Science and Technology under the Project No. UID/05256/2020.

This work is concerned with time-dependent axisymmetric free surface flows of Oldroyd-B fluids for any value of β, the ratio of solvent to total viscosities. The Oldroyd-B constitutive equation is dealt with by employing a novel technique to calculate the conformation tensor while an EVSS transformation allows the solution of the momentum equations coupled with the free surface stress conditions: this avoids numerical instabilities that can arise when using small values of β. The convergence of this new methodology is verified on pipe flow and also by comparing results from the literature for the time-dependent impacting drop problem. This approach is then used to predict the time-dependent free surface flow after a viscoelastic drop impacts a solid surface for β values in the range [0, 1]. The impacting drop problem is investigated for polymer solutions containing a small solvent contribution ( β ⟶ 0 ) or without any solvent viscosity ( β = 0 ). In addition, a study of the bouncing drop problem for different values of β, Weissenberg and Reynolds numbers is undertaken.

The flows of two semi-dilute surfactant solutions (CTAB and CPyCl) through several micro contractions/expansions are experimentally investigated, following an extensive rheological characterization in both shear and extensional flows. The shear rheology of the solutions shows strong shear thinning and shear banding, whereas Small Amplitude Oscillatory Shear and Capillary Break-up Extensional Rheometry indicate that they have high shear and extensional elasticities. Flow visualizations and micro-particle image velocimetry measurements show that the surfactant solutions exhibit three established types of flow patterns in contraction flows: Newtonian-like, asymmetric and disordered. Newtonian-like flow occurs at low flow rates and is preceded by a long transient flow in experiments starting from rest, which seems to be related to shear banding and the alignment of wormlike micelles. The asymmetric flow regime occurs at moderate flow rates and is characterized by an asymmetric upstream central jet with two adjacent vortices, features that change non-periodically, but slowly, in time. This flow pattern seems to be related with the high elasticity of the semi-dilute solutions. The disordered flow pattern is similar to the asymmetric flow in terms of broad characteristics, but the flow asymmetry changes with time much faster than in the asymmetric flow regime, resembling a chaotic-like flow. The disordered flow seems to be related with the breakdown of micellar structures. We concluded also that the flows in both the asymmetric and disordered flow regimes are globally stable in terms of flow patterns, but locally unstable in terms of flow characteristics, with power spectra of the velocity fluctuations having slopes that differ from those typically encountered in elastic turbulence. [GRAPHICS] .

In this work we investigate the role played by viscoelasticity on the thermocapillary motion of a deformable Newtonian droplet embedded in an immiscible, otherwise quiescent non-Newtonian fluid. We consider a regime in which inertia and convective transport of energy are both negligible (represented by the limit condition of vanishingly small Reynolds and Marangoni numbers) and free from gravitational effects. A constant temperature gradient is maintained by keeping two opposite sides of the computational domain at different temperatures. Consequently the droplet experiences a motion driven by the mismatch of interfacial stresses induced by the non-uniform temperature distribution on its boundary. The departures from the Newtonian behaviour are quantified via the “thermal” Deborah number, De T , and are accounted for by adopting either the Oldroyd-B model, for relatively small De T , or the FENE-CR constitutive law for a larger range of De T . In addition, the effects of model parameters, such as the concentration parameter c = 1 − β (where β is the viscoelastic viscosity ratio), or the extensibility parameter, L 2 have been studied numerically using a hybrid volume of fluid-level set method. The numerical results show that the steady-state droplet velocity behaves as a monotonically decreasing function of De T , whilst its shape deforms prolately. For increasing values of De T , the viscoelastic stresses show the tendency to be concentrated near the rear stagnation point, contributing to an increase in its local interface curvature.

This work presents an analytical solution for electro-osmotic flow (EOF) in small amplitude oscillatory shear (SAOS) as a measuring tool suitable to characterize the linear viscoelastic properties of non-Newtonian fluids in microchannel flow. The flow in the straight microchannel is driven by applying oscillating sinusoidal electric potentials. Fourier series are used to derive an expression for the velocity field, under an externally imposed generic potential field aimed at the practical application of SAOS in characterizing the rheological properties of viscoelastic fluids. This extensive investigation covers a wide range of parameters and considers the multi-mode upper-convected Maxwell (UCM) model, which represents the rheology of viscoelastic fluids in the limit of small and slow deformations. Particular focus is given to two cases of practical interest: equal wall zeta potentials at both channel walls and negligible zeta potential at one of the walls. The results show that in flows with thin electric double layers (EDL), Reynolds numbers below 0.001, and Deborah numbers below 100, corresponding to a viscoelastic Mach number of 0.32, the velocity field outside the EDLs is linear and has a large enough amplitude of oscillation, which may allow the quantification of the storage and loss moduli in the linear regime. This technique requires the use of significantly smaller sample sizes than the traditional SAOS in a rotational rheometer.

Direct numerical simulations and large-eddy simulations of turbulent planar jets are used to assess the distortion similarity (DSIM) model, recently developed by Ferreira et al. ["Large-eddy simulations of forced isotropic turbulence with viscoelastic fluids described by the finitely extensible nonlinear elastic rheological model with Peterlin's closure model," Phys. Fluids 28, 125104 (2016)] for homogeneous turbulence, in the simulation of turbulent viscoelastic planar jets. Both a priori and a posteriori tests of the DSIM model are used and show that the several assumptions used in the development of the DSIM model hold well in inhomogeneous free turbulent viscoelastic flows, e.g., (i) the scale similarity of the subgrid-scale (SGS) polymer stretching and (ii) the local equilibrium of the elastic energy production and dissipation. The DSIM model for the SGS polymer stretching term, together with the dynamic Smagorinsky model, is able to reproduce well the flow structures and the classical one-point statistics of turbulent viscoelastic planar jets. The model should be equally able to simulate other free shear flows of viscoelastic fluids, e.g., wakes and mixing layers.

Direct numerical simulations (DNS) were carried out to investigate turbulent heat transfer in a channel flow of homogenous polymer solutions described by the Finitely Extensible Nonlinear Elastic-Peterlin (FENE-P) constitutive model at intermediate and high Prandtl numbers (Pr = 1.25 and 5). Time-averaged statistics of temperature fluctuations, turbulent heat fluxes, thermal turbulent diffusivity, and of budget terms of the temperature variance are reported and compared with those of the Newtonian fluid cases at the same Prandtl and Reynolds numbers. Moreover, twenty one sets of DNS data of fluid flow are utilized to improve existing k–e– v 2 ‾ –f models for FENE-P fluids to deal with turbulent flow of dilute polymer solutions up to the high drag reduction regime; specifically the dependency of closures on the wall friction velocity is removed. Furthermore, five sets of recent DNS data of fluid flow and heat transfer of FENE-P fluids were used to develop the first RANS model capable of predicting the heat transfer rates in viscoelastic turbulent flows. In this model, an existing closure for calculating the turbulent Prandtl number for Newtonian fluids is extended to deal with heat transfer in turbulent viscoelastic fluids. Predicted polymer stresses, velocity profiles, mean temperature profiles, and turbulent flow characteristics are all in good agreement with the DNS data, and show improvement over previous RANS models.

The laminar flat plate boundary-layer flow solution for finitely extensible nonlinear elastic model with Peterlin's closure fluids, originally derived by Olagunju [D. O. Olagunju, Appl. Math. Comput. 173, 593–602 (2006)], is revisited by relaxing some of the assumptions related to the conformation tensor. The ensuing simplification through an order of magnitude analysis and the use of similarity-like variables allows for a semi-analytical approximate similarity solution to be obtained. The proposed solution is more accurate than the original solution, and it tends to self-similar behavior only in the limit of low elasticity. Additionally, we provide a more extensive set of results, including profiles of polymer conformation tensor components, laws of decay for peak stresses and their location, as well as the streamwise variations of boundary layer thickness, displacement and momentum thicknesses. We also provide asymptotic laws for these quantities under low elasticity flow conditions. Comparisons with results from the numerical solution of the full set of governing equations show the approximate similarity solution to be valid up to a high local Weissenberg number ( W i x) between 0.2 and 0.3, corresponding to a local Weissenberg number based on the boundary layer thickness of about 10, for a wide range of values of dumbbell extensibility and solvent viscosity ratio. Above this critical condition, the semi-analytical solution is unable to describe the complex variations of the conformation tensor within the boundary layer, but it still remains accurate in its description of the velocity profiles, friction coefficient, and the variations of displacement, momentum, and boundary layer thicknesses for Weissenberg numbers at least one order of magnitude higher (within 5% up to W i x ≈ 5).

Electro-elastic instabilities in electro-osmotic contraction/expansion flows (EOF) of viscoelastic fluids are experimentally investigated in this work. Several microchannel configurations are used, including the cases with hyperbolic-shaped contractions followed by an abrupt expansion, or abrupt contractions followed by a hyperbolic-shaped expansion. Such cases were selected to assist in the understanding of the EOF instability mechanisms and at which conditions they occur. A reference Newtonian fluid was also used in the experiments, and a wide range of electric fields were imposed to drive the flow. Flow visualizations for a Newtonian fluid allowed to assess the impact of dielectrophoresis on the velocity field of the seeding particles. For each geometry, depending on the polymer concentration, the flow was found to be quasi-Newtonian below a critical electric potential difference, characterized by smooth parallel steady flow patterns in the upstream and downstream channels. Above the critical voltage difference two types of electro-elastic instabilities were found to occur, leading to an unsteady symmetric flow, and to time-dependent irregular flow.

Three local self-similar solutions are obtained for the laminar planar jet flow of viscoelastic fluids, described by the FENE-P constitutive equation, through an order of magnitude simplification of the governing equations. The more general solution is shown to be more accurate than two further simplified solutions, here called the delta and the Olagunju-type solutions, at least for the profiles of conformation tensor components. In the limit of vanishing viscoelasticity, all conformation tensor components reduce to the same low elasticity asymptotic behavior, and the polymer stresses become Newtonian-like. The general solution is then used to obtain the laws of the decay of the centerline velocity and of the growth of the jet half-width and to ascertain the effects of the Weissenberg number, maximum polymer extensibility parameter and the ratio of polymer to total viscosities upon the flow characteristics. The general local self-similar solution compares well with results of numerical simulations obtained by the RheoFoam module of the freeware OpenFoam code.

Made available in DSpace on 2018-12-11T16:54:16Z (GMT). No. of bitstreams: 0 Previous issue date: 2018-09-01 Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP) Fundació Catalana de Trasplantament In this work the fully-developed steady channel flow of the homogeneous polymer solution studied in [4] is revisited and a completely new analytical solution is proposed which is devoid of the limitations of the previous solution (β3ɛDeκ 2≤2/27), i.e., it is valid for the complete range of the rheological parameters. The viscoelastic fluid is described by the simplified Phan–Thien and Tanner model with linear stress coefficient function for the polymer contribution plus a Newtonian solvent. The solution is also valid if the polymer contribution is described by the finitely extensive non-linear elastic model with the Peterlin approximation for the average spring force (FENE-P model). Centro de Estudos de Fenómenos de Transporte Departamento de Engenharia Mecânica Faculdade de Engenharia da Universidade do Porto, Rua Dr. Roberto Frias s/n Centro de Matemática - UM Departamento de Matemática Universidade do Minho Institute for Polymers and Composites/I3N University of Minho, Campus de Azurém Departamento de Engenharia Mecânica Faculdade de Engenharia da Universidade do Porto, Rua Dr. Roberto Frias s/n Porto Universidade Estadual Paulista (Unesp) Instituto de Ciência e Tecnologia Universidade Estadual Paulista (Unesp) Instituto de Ciência e Tecnologia FAPESP: 2015/26842-3 Fundació Catalana de Trasplantament: PTDC/EMS-ENE/2390/2014 Fundació Catalana de Trasplantament: PTDC/EMS-ENE/3362/2014

Significant progress has been made over the years on the topic of hemorheology, not only in terms of the development of more accurate and sophisticated techniques, but also in terms of understanding the phenomena associated with blood components, their interactions and impact upon blood properties. The rheological properties of blood are strongly dependent on the interactions and mechanical properties of red blood cells, and a variation of these properties can bring further insight into the human health state and can be an important parameter in clinical diagnosis. In this article, we provide both a reference for hemorheological research and a resource regarding the fundamental concepts in hemorheology. This review is aimed at those starting in the field of hemodynamics, where blood rheology plays a significant role, but also at those in search of the most up-to-date findings (both qualitative and quantitative) in hemorheological measurements and novel techniques used in this context, including technical advances under more extreme conditions such as in large amplitude oscillatory shear flow or under extensional flow, which impose large deformations comparable to those found in the microcirculatory system and in diseased vessels. Given the impressive rate of increase in the available knowledge on blood flow, this review is also intended to identify areas where current knowledge is still incomplete, and which have the potential for new, exciting and useful research. We also discuss the most important parameters that can lead to an alteration of blood rheology, and which as a consequence can have a significant impact on the normal physiological behavior of blood.

Using a priori analyses of direct numerical simulation (DNS) data, a Reynolds stress model (RSM) is developed to account for the influence of polymer additives on turbulent flow over a wide range of flow conditions. The Finitely Extensible Nonlinear Elastic-Peterlin (FENE-P) rheological constitutive model is utilized to evaluate the polymer contribution to the stress tensor. Thirteen DNS data sets are used to analyze the budgets of elastic stress–velocity gradient correlations as well as Reynolds stress and dissipation transport. Closures are developed in the framework of the RSM model for all the required unknown and non-linear terms. The polymer stresses, velocity profiles, turbulent flow statistics and the percentage of friction drag reduction predicted by the RSM model are in good agreement with present and those obtained from independent DNS data over a wide range of rheological and flow parameters.

We present an investigation of the rheological behavior of whole human blood under uniaxial extensional flow. For that purpose, capillary breakup experiments were carried out by combining the slow retraction method, high-speed imaging techniques, and an immiscible oil bath. The use of the oil bath was aimed at reducing liquid loss by evaporation and to reduce light refraction effects, thus allowing the visualization of the blood cells during the filament thinning. Extensional relaxation times were measured in whole blood samples collected from a total of 13 healthy adult volunteers from both genders, with hematocrit levels between 38.7% and 46.3%. For this range of red blood cell concentrations, the variation of the extensional relaxation time is small, with the average extensional relaxation times measured in air and in oil being 114 +/- 30 and 259 +/- 47 mu s, respectively. An increase of the red blood cells concentration leads to an increase of the bulk viscosity of the sample, which delays the thinning of the filament and consequently the time to breakup. In addition, blood aging was found to reduce the relaxation time while the absence of anticoagulant increases it significantly. (C) 2018 The Society of Rheology.

Strong extensional flows of viscoelastic fluids generate purely-elastic instabilities and elastic turbulence at high Weissenberg numbers., We experimentally investigate the dynamics of viscoelastic fluid flows in cross-slot microgeometries under creeping flow conditions. We focus on the unsteady flow regime observed at high Weissenberg numbers (Wi) with the purpose of understanding the underlying flow signature of elastic turbulence. The effects of the device aspect ratio and fluid rheology on the unsteady flow state are investigated. Visualization of the flow patterns and time-resolved micro-particle image velocimetry were carried out to study the fluid flow behavior for a wide range of Weissenberg numbers. A periodic flow behavior is observed at low Weissenberg numbers followed by a more complex dynamics as Wi increases, eventually leading to the onset of elastic turbulence for very high Weissenberg numbers.

This work presents a numerical study of the 4:1 planar contraction flow of a viscoelastic fluid described by the simplified Phan-Thien–Tanner model under the influence of slip boundary conditions at the channel walls. The linear Navier slip law was considered with the dimensionless slip coefficient varying in the range ½0; 4500. The simulations were carried out for a small constant Reynolds number of 0.04 and Deborah numbers (De) varying between 0 and 5. Convergence could not be achieved for higher values of the Deborah number, especially for large values of the slip coefficient, due to the large stress gradients near the singularity of the reentrant corner. Increasing the slip coefficient leads to the formation of two vortices, a corner and a lip vortex. The lip vortex grows with increasing slip until it absorbs the corner vortex, creating a single large vortex that continues to increase in size and intensity. In the range De = 3–5 no lip vortex was formed. The flow is characterized in detail for De ¼ 1 as function of the slip coefficient, while for the remaining De only the main features are shown for specific values of the slip coefficient., The authors gratefully acknowledge funding by COMPETE, FEDER and Fundacao para a Ciencia e a Tecnologia (FCT) through projects PEst-C/CTM/LA0025/2013 (Strategic Project - LA 25 - 2013-2014, PTDC/EME-MFE/113988/2009 and PTDC/EME-MFE/114322/2009. AMA would also like to thank FCT for the financial support through the scholarship SFRH/BPD/75436/2010.

Many artificial and natural fluids contain macromolecules, particles or droplets that impart complex flow behavior to the fluid. This complex behavior results in a non-linear relationship between stress and deformation standing in between Newton’s law of viscosity for an ideal viscous liquid and Hooke’s law for an ideal elastic material. Such non-linear viscoelastic behavior breaks down flow reversibility under creeping flow conditions, as encountered at the micro-scale, and can lead to flow instabilities. These instabilities offer an alternative to the development of systems requiring unstable flows under conditions where chaotic advection is unfeasible. Flows of viscoelastic fluids are characterized by the Weissenberg (Wi) and Reynolds (Re) numbers, and at the micro-scale flow instabilities occur in regions in the Wi–Re space typically unreachable at the macro-scale, namely high Wi and low Re. In this paper, we review recent experimental work by the authors on the topic of elastic instabilities in flows having a strong extensional component, including: flow through a hyperbolic contraction followed by a sudden expansion; flow in a microfluidic diode and in a flow focusing device; flow around a confined cylinder; flow through porous media and simplified porous media analogs. These flows exhibit different types of flow transitions depending on geometry, Wi and Re, including: transition from a steady symmetric to a steady asymmetric flow, often followed by a second transition to unsteady flow at high Wi; direct transition between steady symmetric and unsteady flows.

The flow of viscoelastic fluids past a confined cylinder in a rectangular duct was investigated experimentally and numerically in order to assess the three-dimensional effects associated with cylinder aspect ratio (AR) and the fluid rheology. The blockage ratio was 50%, the cylinder aspect ratios were AR=16, 8 and 2, and the flow conditions tested varied from creeping flow conditions up to the onset of time-dependent flow. Three viscoelastic fluids were tested, namely a shear-thinning and two Boger fluids, and the results were compared against the numerical and experimental data for Newtonian fluids. For the shear-thinning fluid, and in the range of Deborah numbers (De) studied (0.025

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., COMPETE, FEDER and Fundação para a Ciência e a Tecnologia (FCT) through Projects PEst-C/CTM/LA0025/2013 (Strategic Project – LA 25-2013-2014), PTDC/EQU-FTT/113811/2009 and PDTC/EME-MFE/113988/2009. AMA would also like to thank FCT for financial support through the scholarship SFRH/BPD/75436/2010

A tensorially consistent near-wall four equation model is developed to model turbulent flow of dilute polymer solutions. The model is validated up to the maximum drag reduction limit, by utilizing the data obtained from direct numerical simulations using the finitely extensible nonlinear elastic-Peterlin (FENE-P) constitutive model. Eight sets of direct numerical simulation (DNS) data are used to analyze budgets of relevant physical quantities, such as the nonlinear terms in the FENE-P constitutive equation, the turbulent kinetic energy, the wall normal Reynolds stress and dissipation transport. Closures were developed in the framework of the k - e - v 2 ¯ - f model for the viscoelastic stress work, the viscoelastic destruction of the rate of dissipation, the viscoelastic turbulent viscosity, and the interactions between the fluctuating components of the conformation tensor and of the velocity gradient tensor terms. Predicted polymer stress, velocity profiles and turbulent flow characteristics are all in good agreement with the literature, from which six independent DNS data sets were used covering a wide range of rheological and flow parameters, including high Reynolds number flows, and showing significant improvements over the corresponding predictions of other existing models.

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.

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 in a classical benchmark problem in computational rheology, the viscoelastic fluid flow in a slip-stick geometry, aiming to identify the influence of slip intensity on the flow patterns, velocity, and stress growth at the singularity region. Published by AIP Publishing., The authors acknowledge funding from FEDER and Fundacao para a Ciencia e Tecnologia (FCT), Portugal, through Project Nos. PTDC/EMS-ENE/3362/2014, PTDC/EQU-FTT/113811/2009, and PTDC/EME-MFE/113988/2009 and FEDER, via FCT, under the Project No. UID/CTM/50025/2013. L.L.F. would like to thank FCT for the funding through the Scholarship No. SFRH/BPD/100353/2014., info:eu-repo/semantics/publishedVersion

Suspensions of healthy and pathological red blood cells (RBC) flowing in microfluidic devices are frequently used to performin vitroblood experiments for a better understanding of human microcirculation hemodynamic phenomena. This work reports the development of particulate viscoelastic analogue fluids able to mimic the rheological and hemorheological behavior of pathological RBC suspensions flowing in microfluidic systems. The pathological RBCs were obtained by an incubation of healthy RBCs at a high concentration of glucose, representing the pathological stage of hyperglycaemia in diabetic complications, and analyses of their deformability and aggregation were carried out. Overall, the developedin vitroanalogue fluids were composed of a suspension of semi-rigid microbeads in a carrier viscoelastic fluid made of dextran 40 and xanthan gum. All suspensions of healthy and pathological RBCs, as well as their particulate analogue fluids, were extensively characterized in steady shear flow, as well as in small and large amplitude oscillatory shear flow. In addition, the well-known cell-free layer (CFL) phenomenon occurring in microchannels was investigated in detail to provide comparisons between healthy and pathologicalin vitroRBC suspensions and their corresponding analogue fluids at different volume concentrations (5% and 20%). The experimental results have shown a similar rheological behavior between the samples containing a suspension of pathological RBCs and the proposed analogue fluids. Moreover, this work shows that the particulatein vitroanalogue fluids used have the ability to mimic well the CFL phenomenon occurring downstream of a microchannel contraction for pathological RBC suspensions. The proposed particulate fluids provide a more realistic behavior of the flow properties of suspended RBCs when compared with existing non-particulate blood analogues, and consequently, they are advantageous for detailed investigations of microcirculation., The authors acknowledge the financial support provided by Fundac¸~ao para a Ci^encia e a Tecnologia (FCT), COMPETE, and FEDER through the Ph.D. scholarship SFRH/BD/89077/2012, Grant IF/00148/2013, and project POCI-01–0145-FEDER-016861 (with associated reference PTDC/ QEQ-FTT/4287/2014) funded by COMPETE2020—Programa Operacional Competitividade e Internacionalizac¸~ao (POCI) with the financial support of FCT/MTES through national funds (PIDDAC) and by the project Nos. PTDC/EQU-FTT/118716/2010, EXPL/EMS-SIS/2215/2013, UID/EMS/00532/2013, and UID/EMS/04077/2013., info:eu-repo/semantics/publishedVersion

We investigated experimentally the rheological behavior of whole human blood subjected to large amplitude oscilla- tory shear under strain control to assess its nonlinear viscoelastic response. In these rheological tests, the shear stress response presented higher harmonic contributions, revealing the nonlinear behavior of human blood that is associated with changes in its internal microstructure. For the rheological conditions investigated, intra-cycle strain-stiffening and intra-cycle shear-thinning behavior of the human blood samples were observed and quantified based on the Lissajous-Bowditch plots. The results demon- strated that the dissipative nature of whole blood is more intense than its elastic component. We also assessed the effect of adding EDTA anticoagulant on the shear viscosity of whole blood subjected to steady shear flow. We found that the use of anticoagulant in appropriate concentrations did not influence the shear viscosity and that blood samples without anticoagulant preserved their rheological characteristics approximately for up to 8 minutes before coagulation became significant.

In this work, we explore two methods to simultaneously measure the electroosmotic mobility in microchannels and the electrophoretic mobility of micron-sized tracer particles. The first method is based on imposing a pulsed electric field, which allows to isolate electrophoresis and electroosmosis at the startup and shutdown of the pulse, respectively. In the second method, a sinusoidal electric field is generated and the mobilities are found by minimizing the difference between the measured velocity of tracer particles and the velocity computed from an analytical expression. Both methods produced consistent results using polydimethylsiloxane microchannels and polystyrene micro-particles, provided that the temporal resolution of the particle tracking velocimetry technique used to compute the velocity of the tracer particles is fast enough to resolve the diffusion time-scale based on the characteristic channel length scale. Additionally, we present results with the pulse method for viscoelastic fluids, which show a more complex transient response with significant velocity overshoots and undershoots after the start and the end of the applied electric pulse, respectively.

The non-Newtonian properties of blood are of great importance since they are closely related with incident cardiovascular diseases. A good understanding of the hemodynamics through the main vessels of the human circulatory system is thus fundamental in the detection and especially in the treatment of these diseases. Very often such studies take place in vitro for convenience and better flow control and these generally require blood analogue solutions that not only adequately mimic the viscoelastic properties of blood but also minimize undesirable optical distortions arising from vessel curvature that could interfere in flow visualizations or particle image velocimetry measurements. In this work, we present the viscoelastic moduli of whole human blood obtained by means of passive microrheology experiments. These results and existing shear and extensional rheological data for whole human blood in the literature enabled us to develop solutions with rheological behavior analogous to real whole blood and with a refractive index suited for PDMS (polydymethylsiloxane) micro-and milli-channels. In addition, these blood analogues can be modified in order to obtain a larger range of refractive indices from 1.38 to 1.43 to match the refractive index of several materials other than PDMS. (C) 2013 AIP Publishing LLC.

The authors acknowledge funding from COMPETE/FEDER and Fundacao para a Ciencia e a Tecnologia (FCT), Portugal, through project PTDC/EME-MFE/113988/2009, and FEDER, via FCT, under the PEst-C/CTM/LA0025/2011 (Strategic Project - LA 25 - 2011-2012). L.L.F. would like to thank FCT for financial support through the scholarship SFRH / BD / 37586 / 2007.

The appearance of divergent streamlines and subsequent formation of free vortices in Newtonian fluid flows through microfluidic flow-focusing geometries is discussed in this work. The micro-geometries are shaped like a cross-slot but comprise three entrances and one exit. The divergent flow and subsequent symmetric vortical structures arising near the centreline of the main inlet channel are promoted even under creeping flow conditions, and are observed experimentally and predicted numerically above a critical value of the ratio of inlet velocities (VR). As VR is further increased these free vortices continue to grow until a maximum size is reached due to geometrical constraints. The numerical calculations are in good agreement with the experimental observations and we probe numerically the effects of the geometric parameters and of inertia on the flow patterns. In particular, we observe that the appearance of the central recirculations depends non-monotonically on the relative width of the entrance branches and we show that inertia enhances the appearance of the free vortices. On the contrary, the presence of the walls in three-dimensional geometries has a stabilizing effect for low Reynolds numbers, delaying the onset of these secondary flows to higher VR. The linearity of the governing equations for creeping flow of Newtonian fluids was invoked to determine the flow field for any VR as a linear combination of the results of three other independent solutions in the same geometry.

An experimental and numerical investigation was carried out to characterize the isothermal laminar flow of a liquid impinging jet confined by inclined plane walls and emanating from a rectangular duct, where the flow was allowed to become fully-developed. The rectangular duct has an aspect ratio of 13, the plane walls opposite to the impinging jet have an inclination of 12° and the nozzle-to-plate distance ( D ) is very short, D / H = 0.8. The presence of the impact plate is felt upstream the nozzle, inside the rectangular duct, up to x/H = −0.4. The flow in the cell is symmetric relative to the x-y and x-z center planes and near the inclined walls the flow separates for Reynolds numbers higher than 208, except close to the side walls where the flow remains attached. The length of the separated flow region, L R , measured along the inclined wall, is constant in the central portion of the channel with L R / H = 0.35 for Re = 275 and dropping to zero before reaching the side walls. The recirculation length increases with the Reynolds number and with the thickness of the outlet channel. There is a three-dimensional effect associated with the finite slenderness of the geometry. It consists of spiraling secondary motions away from the central symmetry plane and toward the side walls, where the fluid merges with the main flow creating a local wall jet, as is discussed in detail.

This work presents a finite volume method used to solve the relevant coupled equations for general electro-osmotic flows of viscoelastic fluids, using the upper-convected Maxwell and the simplified Phan-Thien–Tanner models. Three different implementations of the electro-osmosis physical models were carried out, which depend on the required level of approximation. In the first implementation, the Poisson–Nernst–Planck equations were incorporated into the code and the electric charge distribution required to quantify the electric field forcing of the momentum equation is calculated from these fundamental equations. The second implementation is an approximation in which a stable Boltzmann distribution of ions is assumed to occur in the electric double layer, represented by the Poisson–Boltzmann equations. Finally, the so-called Debye–Huckel approximation was also implemented in the Poisson–Boltzmann–Debye–Huckel model, which is valid for cases with a stable Boltzmann distribution of ions characterized by a small ratio of electrical to thermal energies. Numerical simulations were undertaken in a cross-slot geometry, to investigate the possible appearance of purely electro-elastic flow instabilities, by considering the effect of the electric field. For pure electro-osmotic flow, i.e., in the absence of an imposed pressure gradient, we were able to capture the onset of an unsteady asymmetric flow above a critical Weissenberg number, which is lower than the corresponding value for pressure-driven viscoelastic flow. Additionally, we derive analytically the fully-developed electro-osmosis driven channel flow of polymer solutions described by the FENE-P and PTT models with a Newtonian solvent and assuming a thin electric double layer.

A new low-Reynolds-number k–e turbulence model is developed for flows of viscoelastic fluids described by the finitely extensible nonlinear elastic rheological constitutive equation with Peterlin approximation (FENE-P model). The model is validated against direct numerical simulations in the low and intermediate drag reduction (DR) regimes (DR up to 50%). The results obtained represent an improvement over the low DR model of Pinho et al. (2008) [A low Reynolds number k–e turbulence model for FENE-P viscoelastic fluids, Journal of Non-Newtonian Fluid Mechanics, 154, 89–108]. In extending the range of application to higher values of drag reduction, three main improvements were incorporated: a modified eddy viscosity closure, the inclusion of direct viscoelastic contributions into the transport equations for turbulent kinetic energy (k) and its dissipation rate, and a new closure for the cross-correlations between the fluctuating components of the polymer conformation and rate of strain tensors (NLTij). The NLTij appears in the Reynolds-averaged evolution equation for the conformation tensor (RACE), which is required to calculate the average polymer stress, and in the viscoelastic stress work in the transport equation of k. It is shown that the predictions of mean velocity, turbulent kinetic energy, its rate of dissipation by the Newtonian solvent, conformation tensor and polymer and Reynolds shear stresses are improved compared to those obtained from the earlier model.

The flow of viscoelastic fluids between parallel plates under the combined influence of electro-osmotic and pressure gradient forcings with asymmetric boundary conditions, by considering different zeta potentials at the walls, is investigated. The fluids are z-z symmetric electrolytes. The analytic solutions of the electrical potential, velocity distributions and streaming potential are based on the Debye-Huckel approximation for weak potential. The viscoelastic fluids used are modelled by the simplified Phan-Thien-Tanner constitutive equation, with linear kernel for the stress coefficient function, and the Finitely Extensible Nonlinear Elastic dumbbells model with a Peterlin approximation for the average spring force. The combined effects of fluid rheology, electrical double- layer thickness, ratio of the wall zeta potentials and ratio between the applied streamwise gradients of electrostatic potential and pressure on the fluid velocity and stress distributions are discussed.

The flow of Newtonian and viscoelastic fluids in a mixing-separating geometry that consists of two opposed channel flows interacting through a gap in the common separating wall is investigated. The flow in this type of geometry was studied experimentally by Cochrane et al. (Philos Trans R Soc Lond A301:163-181, 1981) using Newtonian and viscoelastic fluids at low Reynolds numbers (Re < 50). In this numerical study, by use of a finite-volume method, the effects of Deborah (De) and Reynolds numbers and gap size on the two-dimensional flow dynamics are assessed. The normalized gap size varies between 0 and 5, Re varies between 0 and 50 and De varies between 0 and the maximum attainable value. Due to the anti-symmetry of the fully developed inlet conditions and the symmetry of the flow geometry, the Newtonian creeping flow is anti-symmetric. Increasing the gap size of the separating walls leads to an increase of the reversed flow-rate ratio (R (r) ), which is defined as the ratio of the reversed and the total flow rate. For creeping flow of viscoelastic fluids, here described by the upper-convected Maxwell model, two distinct flow patterns are observed. Below a critical gap size, the reversed flow is slightly enhanced when the Deborah number increases. Further increase of De leads to a subsequent decrease in R (r) towards zero. For a supercritical gap size, increasing the Deborah number leads to a monotonic increase in R (r) .

In this work we propose a new type of microfluidic rectifier, which is able to operate efficiently under creeping flow conditions. The flow of Newtonian and non-Newtonian fluids was investigated experimentally in different microchannels with triangular (nozzle/diffuser) and hyperbolic shapes in order to achieve high anisotropic flow resistance between the two flow directions. The Newtonian fluid used was de-ionized water and the viscoelastic fluids were aqueous solutions of polyacrylamide and polyethylene oxide with different molecular weights. Pressure drop measurements were performed in addition to visualizations of the flow patterns by streak line photography for a wide range of flow rates. For the Newtonian flows, inertia leads to the appearance of recirculations for both flow directions, but no significant rectification effects appear. For the viscoelastic fluids, two distinct behaviors are identified: at low flow rates, the pressure drops are similar in both flow directions; above a critical flow rate (or Deborah number), the flow patterns become quite different, leading to different flow rates in the forward and backward flow directions for the same pressure drop, i.e., rectification effects emerge. In particular, the viscoelastic fluid flow becomes unsteady in the forward direction, due to the presence of elastic instabilities, which leads to a significant increase in the flow resistance. Flow resistance ratios greater than three were achieved for the hyperbolic rectifier, clearly in excess of the value for the triangular-shaped rectifier and for other geometries proposed in the literature for operation in creeping flow conditions. This high diodicity is associated with the distinct nature of the extensional flows in the forward and backward directions of the hyperbolic-type microgeometry.

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 PTT 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 ɛ and ξ on the extrudate swell and jet buckling problems is reported.

A systematic numerical investigation on creeping flows in planar sudden expansions of viscoelastic fluids obeying the upper-convected Maxwell model is carried out to assess the combined effects of viscoelasticity, through the Deborah number, and expansion ratio (ER), which was varied between 1.25 and 32. At large expansion ratios (ER ≥ 4) the flow becomes dominated by the downstream duct size and appropriately normalized quantities tend to be independent of ER. The recirculation size and strength become decreasing functions of De, whereas the Couette correction (the normalized entry pressure drop due to the presence of the expansion) increases. At small ER (ER ≤ 3), however, no simple scaling laws are found and there is a complex interaction between De and ER leading to non-monotonic variations, with an initial decrease in the recirculation length at low Deborah numbers, followed by an enhancement as De increases.

The flow of a viscoelastic fluid through a microfluidic flow-focusing device is investigated numerically with a finite-volume code using the upper-convected Maxwell (UCM) and Phan-Thien–Tanner (PTT) models. The conceived device is shaped much like a conventional planar “cross-slot” except for comprising three inlets and one exit arm. Strong viscoelastic effects are observed as a consequence of the high deformation rates. In fact, purely elastic instabilities that are entirely absent in the corresponding Newtonian fluid flow are seen to occur as the Deborah number (De) is increased above a critical threshold. From two-dimensional numerical simulations we are able to distinguish two types of instability, one in which the flow becomes asymmetric but remains steady, and a subsequent instability at higher De in which the flow becomes unsteady, oscillating in time. For the UCM model, the effects of the geometric parameters of the device (e.g. the relative width of the entrance branches, WR) and of the ratio of inlet average velocities (VR) on the onset of asymmetry are systematically examined. We observe that for high velocity ratios, the critical Deborah number is independent of VR (e.g. Dec ≈ 0.33 for WR = 1), but depends non-monotonically on the relative width of the entrance branches. Using the PTT model we are able to demonstrate that the extensional viscosity and the corresponding very large stresses are decisive for the onset of the steady-flow asymmetry.

The log-conformation formulation, proposed by Fattal and Kupferman [J. Non-Newt. Fluid Mech. 123 (2004) 281], has helped to provide further insights into the High-Weissenberg Number Problem. In this work, we investigate the performance of the log-conformation formulation in the Finite Volume Method (FVM) framework for creeping flows of viscoelastic fluids in steady and unsteady flows around a confined cylinder. The Oldroyd-B and Phan-Thien-Tanner (PTT) constitutive equations were used to assess the effect of different theological behaviour on the flow patterns and solution stability. The calculation of the polymer stress contribution is carried out with both the standard technique and with the log-conformation methodology. For all test cases, up to the critical conditions when both methods converge to a steady solution, the use of the log-conformation technique provides solutions with similar accuracy as the standard approach. In terms of stability the log-conformation formulation is found to be significantly more robust, and Solutions could be obtained at higher Deborah number flows.

An analytical solution is derived for the time-dependent flow of an infinite pool of fluid described by the viscoelastic upper convected Maxwell (UCM) model driven by an oscillating porous plate in the presence of cross flow. Whereas for a Newtonian fluid there is a solution regardless of the amount of suction or blowing, for viscoelastic fluids the solution breaks down under certain conditions. When the suction velocity exceeds the elastic shear wave speed there is no solution. For sub-critical blowing through the plate the stream-wise velocity profiles are periodic, but when the blowing speed exceeds the elastic shear wave speed non-periodic chaotic-like waves appear under certain conditions, which are characterized. The flow characteristics are properly scaled by the reciprocal square root of the Reynolds number with and without cross flow. Generally speaking, the flow properties are controlled by the cross flow and by the fluid elasticity at low and high Deborah numbers, respectively.