No abstract

SUMMARYA high resolution scheme with improved iterative convergence properties was devised by incorporating total-variation diminishing constraints, appropriate for unsteady problems, into an implicit time-marching method used for steady ow problems. The new scheme, referred to as Convergent and Universally Bounded Interpolation Scheme for the Treatment of Advection (CUBISTA), has similar accuracy to the well-known SMART scheme, both being formally third-order accurate on uniform meshes for smooth ows. Three demonstration problems are considered: (1) advection of three scalar proÿles, a step, a sine-squared, and a semi-ellipse; (2) Newtonian ow over a backward-facing step; and (3) viscoelastic ow through a planar contraction and around a cylinder. For the case of the viscoelastic ows, in which the high resolution schemes are also used to represent the advective terms in the constitutive equation, it is shown that only the new scheme is able to provide a converged solution to the prescribed tolerance.

This paper reports the development and application of a finite-volume based methodology for the calculation of the flow of fluids which follow differential viscoelastic constitutive models. The novelty of the method lies on the use of the non-staggered grid arrangement, in which all dependent variables are located at the center of the control volumes, thus greatly simplifying the adoption of general curvilinear coordinates. The pressure -velocity -stress decoupling was removed by the development of a new interpolation technique inspired on that of Rhie and Chow, AIAA 82 (1982) 998. The differencing schemes are second order accurate and the resulting algebraic equations for each variable are solved in a segregated way (decoupled scheme). The numerical formulation especially designed for the interpolation of the stress field was found to work well and is shown to be indispensable for accurate results. Calculations have been carried out for two problems: the entry flow problem of Eggleton et al., J. Non-Newtonian Fluid Mech. 64 (1996) 269, with orthogonal and non-orthogonal meshes; and the bounded and unbounded flows around a circular cylinder. The results of the simulations compare favourably with those in the literature and iterative convergence has been attained for Deborah and Reynolds numbers similar to, or higher than, those reported for identical flow problems using other numerical methods. The application of the method with non-orthogonal coordinates is demonstrated. The entry flow problem is studied in more detail and for this case differences between Newtonian and viscoelastic fluids are identified and discussed. Viscoelasticity is shown to be responsible for the development of very intense normal stresses, which are tensile in the wall region. As a consequence, the viscoelastic fluid is more intensely decelerated in the wall region than the Newtonian fluid, thus reducing locally the shear rates and the role of viscosity in redeveloping the flow. A layer of high stress-gradients is formed at the wall leading edge and is convected below and away from the wall; its effect is to intensify the aforementioned deviation of elastic fluid from the wall.

No abstract

No abstract

Analytical expressions are derived for the velocity vector, the stress components and the viscosity function in fully developed channel and pipe flow of Phan-ThienTanner (PTT) fluids; both the linearized and the exponential forms of the PTT equation are considered. The solution shows that the wall shear stress of a PTT fluid is substantially smaller than the corresponding value for a Newtonian or upperconvected Maxwell fluid, with implications for comparing predicted and measured values in a non-dimensional form.

No abstract

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/w͒ and of a xanthan gum ͑500 ppm w/w͒, which were characterized rheologically in steady-shear flow using a rotational rheometer and in extension using a capillary breakup extensional rheometer ͑CaBER͒. 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 magnitude͒. 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.