Flow of non-Newtonian polymeric solutions through fibrous media

Abstract

ABSTRACT:The equations of motion (continuity and momentum) describing the steady flow of incompressible power law liquids in a model porous medium consisting of an assemblage of long cylinders have been solved numerically using the finite difference method. The field equations as well as the pertinent boundary conditions have been re-cast in terms of the stream function and vorticity. The inter-cylinder interactions have been simulated using a simple "concentric cylinders" cell model. Extensive information on the detailed structure of the flow field in terms of the surface vorticity distribution, streamlines, and viscosity distribution on the surface of the solid cylinder as well as on the values of the pressure and friction drag coefficients under wide ranges of physical (0.4 Յ ⑀ Յ 0.95; 1 Ն n Ն 0.4) and kinematic (0.01 Յ Re Յ 10) conditions have been obtained. The numerical results presented herein have been validated using the experimental results for the flow of Newtonian and power law fluids available in the literature; the match between the present predictions and the experiments was found to be satisfactory.

Convective heat transfer for power law fluids in packed and fluidised beds of spheres

“…), su ce it to add here that within the framework of the submerged object model, the simple free surface cell model has been shown to yield satisfactory predictions of macroscopic uid mechanical parameters in a variety of settings. Thus, for instance, the values of drag coe cient and Nusselt number for the ow of Newtonian and inelastic non-Newtonian media over the bundles of circular cylinders (Ishimi et al, 1987;Satheesh et al, 1999;Vijaysri et al, 1999;Dhotkar et al, 2000;Chhabra et al, 2000;Shibu et al, 2001;Mandhani et al, 2002), in beds of spheres (Jaiswal et al, 1991(Jaiswal et al, , 1992(Jaiswal et al, , 1993Kawase and Ulbrecht, 1981;Satish and Zhu, 1992, etc. ) and for the free rise/fall of uid particles (Gummalam and Chhabra, 1987;Gummalam et al, 1988;Jarzebski and Malinowski, 1986;Chhabra, 1998;Zhu, 2001, etc.).…”

Interaction between two circular cylinders in slow flow of Bingham viscoplastic fluid

“…To our knowledge, work carried out on interactions between cylindrical obstacles in non-Newtonian fluid flows have usually considered shear-thinning and viscoelastic fluids [6][7][8][9][10]. In the case of viscoplastic fluids, regardless of the type of obstacle, studies have concerned mainly drag (or pressure drop in the case of rows of obstacles) [2,4,5,11,12].…”

Steady Two-Dimensional Non-Newtonian Flow Past an Array of Long Circular Cylinders up to Reynolds number 500: A Numerical Study

“…elucidate the effect of these features on the fl ow process (Vossoughi and Seyer, 1974;Barboza et al, 1979;Chmielewski et al, 1990;Chhabra, 1993). In spite of its practical importance, even the purely viscous non-Newtonian fl ow across arrays of long cylinders has received limited attention, and the majority of these studies have been limited to the so-called creeping fl ow of shear-thinning (n < 1) power-law fl uids (Tripathi and Chhabra, 1992;Bruschke and Advani, 1993;Dhotkar et al, 2000;Vijaysri et al, 1999), with the sole exception of Shibu et al (2001) who reported limited drag coeffi cient values up to Reynolds number of 500. On the other hand, there has been a growing interest in the behaviour of shear-thickening (n > 1) fl uids, largely motivated by the need to understand the processing mechanisms of highly concentrated suspensions, pastes and of sewage sludge to optimise water treatment processes (Barnes, 1989;Chhabra and Richardson, 1999).…”

“…Bruschke and Advani (1993) used the zero vorticity cell model (Kuwabara, 1959) to study analytically the shearthinning behaviour in creeping fl ow conditions in sparse systems and for weakly shear-thinning liquids. Dhotkar et al (2000) used the free surface cell model and Vijaysri et al (1999) used the zero vorticity cell model to approximate the inter-cylinder interactions, and numerically solved the equations of motion for the fl ow of shear-thinning fl uids across cylinder arrays at Reynolds numbers (Re) in the range 0.01-10. Shibu et al (2001) extended these results up to Re = 500, and Chhabra et al (2000) carried out a similar analysis for shear-thickening fl uids at Re = 0.01-10.…”