Flow of a blood analogue solution through microfabricated hyperbolic contractions

The flow of a blood analogue solution past a microfabricated hyperbolic contraction followed by an abrupt expansion was investigated experimentally. The shape of the contraction was designed in order to impose a nearly constant strain rate to the fluid along the centerline of the microgeometry. The flow patterns of the blood analogue solution and of a Newtonian reference fluid (deionized water), captured using streak line imaging, are quite distinct and illustrate the complex behavior of the blood analogue solution flowing through the microgeometry. The flow of the blood analogue solution shows elastic-driven effects with vortical structures emerging upstream of the contraction, which are absent in Newtonian fluid flow. In both cases the flow also develops instabilities downstream of the expansion but these are inertia driven. Therefore, for the blood analogue solution at high flow rates the competing effects of inertia and elasticity lead to complex flow patterns and unstable flow develops

Divergent streamlines and free vortices in Newtonian fluid flows in microfluidic flow focusing devices

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

High performance microfluidic rectifiers for viscoelastic fluid flow

The flow of Newtonian and non-Newtonian fluids within microfluidic rectifiers with a hyperbolic shape was investigated to assess the effect of the bounding walls on the diodicity of the microfluidic device and achieve high flow anisotropy. Three microchannels were used, with different depths and the same geometrical configuration, which creates a strong extensional flow and generates high anisotropic flow resistance between the two flow directions. The Newtonian fluid, de-ionized water, was used as a reference fluid. The viscoelastic fluid used was an aqueous solution of polyethylene oxide (0.1% w/w) with high molecular weight. The flow patterns were visualized using streak photography and the velocity field was investigated using micro-particle image velocimetry. Moreover, pressure drop measurements were performed in order to compare the diodicity achieved in the microfluidic rectifiers. For the Newtonian fluid flow, the experimental results are compared with numerical predictions obtained using a finite-volume method and good agreement was found between both approaches. For the viscoelastic fluid, significant anisotropic flow resistance can be achieved. The effect of the bounding walls was analysed and found to be qualitatively similar for all microchannels. Nevertheless, in quantitative terms, the diodicity is enhanced when the wall effect is reduced, i.e. when the channels are deeper. A maximum diodicity above six was found for the deeper channel, a value well beyond those previously reported

Steady flow of power-law fluids in a 1:3 planar sudden expansion

The laminar flow of inelastic non-Newtonian fluids, obeying the power-law model, through a planar sudden expansion with a 1:3 expansion ratio was investigated numerically using a finite volume method. A broad range of power-law indices in the range 0.2 n 4 was considered. Shear-thinning, Newtonian and shear-thickening fluids are analyzed, with particular emphasis on the flow patterns and bifurcation phenomenon occurring at high Reynolds number laminar flows. The effect of the generalized Reynolds numbers (based on power-law index, n, and the in flow channel height, h) on the main vortex characteristics and Couette correction are examined in detail in the range varying from 0.01 Regen 600. Values for the critical generalized Reynolds number for the onset of steady flow asymmetry and the appearance of a third main vortex are also included. We found that the shear-thinning behavior increases the critical Regen, while shear-thickening has the opposite effect. Comparison with available literature and with predictions using a commercial software (FluentR 6.3.26) are also presented and discussed. It was found that both results are in good agreement, but that our code is able to achieve converged solution for a broader range of flow conditions, providing new benchmark quality data

Effect of the contraction ratio upon viscoelastic fluid flow in three-dimensional square-square contractions

In this work we investigate the laminar flow through square–square sudden contractions with various contraction ratios (CR¼2.4, 4,8and12), using a Newtonian fluid and a shear-thinning viscoelastic fluid. Visualizations of the flow patterns were carried out using streakline photography and detailed velocity field measurements were performed using particle image velocimetry. The experimental results are compared with numerical predictions obtained using a finite-volume method. For the Newtonian fluid, a corner vortex is found upstream of the contraction and increasing flow inertia leads to a reduction of the vortex size. Good agreement is observed between experiments and numerical simulations. For the shear-thinning fluid flow a corner vortex is also observed upstream of the contraction independently of the contraction ratio. Increasing the elasticity of the flow, while still maintaining low inertia flow conditions, leads to a strong increase of the vortex size, until an elastic instability sets in and the flow becomes time-dependent at DeE200, 300, 70 and 450 for CR¼2.4, 4, 8 and 12, respectively. At low contraction ratios, viscoelasticity brings out an anomalous divergent flow upstream of the contraction. For both fluids studied the flow presents a complex three-dimensional helical vortex structure which is well predicted by numerical simulations. However, for the viscoelastic fluid flow the maximum Deborah number achieved in the numerical simulations is about one order of magnitude lower than the critical Deborah number for the onset of the elastic instability found in the experiments

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

Flow of low viscosity Boger fluids through a microfluidic hyperbolic contraction

In this work we focus on the development of low viscosity Boger fluids and assess their elasticity analyzing the flow through a microfluidic hyperbolic contraction. Rheological tests in shear and extensional flows were carried out in order to evaluate the effect of the addition of a salt (NaCl) to dilute aqueous solutions of polyacrylamide at 400, 250, 125 and 50 ppm (w/w). The rheological data showed that when 1% (w/w) of NaCl was added, a significant decrease of the shear viscosity curve was observed, and a nearly constant shear viscosity was found for a wide range of shear rates, indicating Boger fluid behavior. The relaxation times, measured using a capillary break-up extensional rheometer (CaBER), decreased for lower polymer concentrations, and with the addition of NaCl. Visualizations of these Boger fluids flowing through a planar microfluidic geometry containing a hyperbolic contraction, which promotes a nearly uniform extension rate at the centerline of the geometry, was important to corroborate their degree of elasticity. Additionally, the quantification of the vortex growth upstream of the hyperbolic contraction was used with good accuracy and reproducibility to assess the relaxation time for the less concentrated Boger fluids, for which CaBER measurements are difficult to perform

Shear viscosity and nonlinear behaviour of whole blood under large amplitude oscillatory shear

We investigated experimentally the rheological behavior of whole human blood subjected to large amplitude oscillatory 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 demonstrated 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

Annular flow of viscoelastic fluids: Analytical and numerical solutions

This work provides analytical and numerical solutions for the linear, quadratic and exponential Phan–Thien–Tanner (PTT) viscoelastic models, for axial and helical annular fully-developed flows under no slip and slip boundary conditions, the latter given by the linear and nonlinear Navier slip laws. The rheology of the three PTT model functions is discussed together with the influence of the slip velocity upon the flow velocity and stress fields. For the linear PTT model, full analytical solutions for the inverse problem (unknown velocity) are devised for the linear Navier slip law and two different slip exponents. For the linear PTT model with other values of the slip exponent and for the quadratic PTT model, the polynomial equation for the radial location (β) of the null shear stress must be solved numerically. For both models, the solution of the direct problem is given by an iterative procedure involving three nonlinear equations, one for β, other for the pressure gradient and another for the torque per unit length. For the exponential PTT model we devise a numerical procedure that can easily compute the numerical solution of the pure axial flow problemCOMPETE, 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 PTDC/EME-MFE/113988/2009. LLF and AMA would also like to thank FCT for financial support through the scholarships SFRH/BD/37586/2007 and SFRH/BPD/75436/2010, respectively