Purely-elastic flow instabilities and elastic turbulence in microfluidic cross-slot devices.

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.

Purely elastic flow instabilities in microscale cross-slot devices.

We present an experimental investigation of viscoelastic fluid flow in a cross-slot microgeometry under low Reynolds number flow conditions. By using several viscoelastic fluids, we investigate the effects of the microchannel bounding walls and the polymer solution concentration on the flow patterns. We demonstrate that for concentrated polymer solutions, the flow undergoes a bifurcation above a critical Weissenberg number (Wi) at which the flow becomes asymmetric but remains steady. The appearance of this elastic instability depends on the channel aspect ratio, defined as the ratio between the depth and the width of the channels. At high aspect ratios, when bounding wall effects are reduced, two types of elastic instabilities were observed, one in which the flow becomes asymmetric and steady, followed by a second instability at higher Wi, in which the flow becomes time-dependent. When the aspect ratio decreases, the bounding walls have a stabilizing effect, preventing the occurrence of steady asymmetric flow and postponing the transition to unsteady flow to higher Wi. For less concentrated solutions, the first elastic instability to steady asymmetric flow is absent and only the time-dependent flow instability is observed.

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.

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.

Shear viscosity and nonlinear behavior 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.

Extensional flow of blood analog solutions in microfluidic devices.

In this study, we show the importance of extensional rheology, in addition to the shear rheology, in the choice of blood analog solutions intended to be used in vitro for mimicking the microcirculatory system. For this purpose, we compare the flow of a Newtonian fluid and two well-established viscoelastic blood analog polymer solutions through microfluidic channels containing both hyperbolic and abrupt contractions∕expansions. The hyperbolic shape was selected in order to impose a nearly constant strain rate at the centerline of the microchannels and achieve a quasihomogeneous and strong extensional flow often found in features of the human microcirculatory system such as stenoses. The two blood analog fluids used are aqueous solutions of a polyacrylamide (125 ppm w∕w) and of a xanthan gum (500 ppm w∕w), which were characterized rheologically in steady-shear flow using a rotational rheometer and in extension using a capillary breakup extensional rheometer (CaBER). Both blood analogs exhibit a shear-thinning behavior similar to that of whole human blood, but their relaxation times, obtained from CaBER experiments, are substantially different (by one order of magnitude). Visualizations of the flow patterns using streak photography, measurements of the velocity field using microparticle image velocimetry, and pressure-drop measurements were carried out experimentally for a wide range of flow rates. The experimental results were also compared with the numerical simulations of the flow of a Newtonian fluid and a generalized Newtonian fluid with shear-thinning behavior. Our results show that the flow patterns of the two blood analog solutions are considerably different, despite their similar shear rheology. Furthermore, we demonstrate that the elastic properties of the fluid have a major impact on the flow characteristics, with the polyacrylamide solution exhibiting a much stronger elastic character. As such, these properties must be taken into account in the choice or development of analog fluids that are adequate to replicate blood behavior at the microscale.

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.