Creeping motion of a carreau fluid past a newtonian fluid sphere

Abstract

Previous work on the slow motion of drops in non-Newtonian liquids has been reviewed. The variational principles have been employed to obtain approximate upper and lower bounds on drag force experienced by a fluid sphere moving slowly in Carreau model fluids. The paper is concluded by presenting a comparison with the appropriate experimental data available in the literature.On a fait I Ctude bibliographique sur les travaux portant sur le mouvement lent des gouttes dans des liquides non-newtonit . On a utilist les principes variationnels pour obtenir de maniere approximative les limites inftrieures et supkrieures 1,: la force de trainte d'une sphtre fluide se dtplaFant lentement dans les fluides qui obtissent au modtle de Carreau. On prisente en conclusion une comparaison avec les donnies exphnentales approprites publites.otion of liquid drops in non-Newtonian fluids is of

Drag on a single fluid sphere translating in power-law liquids at moderate Reynolds numbers

“…It is useful to recall here that this approach is not only restricted to the inertialess flow in shear-thinning fluids, but it yields true upper and lower bounds only for Newtonian and power-law fluids. In spite of this limitation, this approach has been used for Ellis (Mohan and Venkateswarlu, 1976) and Carreau model fluids (Chhabra andDhingra, 1986, 1988;Jarzebski and Malinowski, 1987b). However, this approach predicts a slight enhancement in the value of drag coefficient for a Newtonian droplet settling in a quiescent power-law medium (n < 1) as compared to that in a Newtonian continuous phase otherwise under identical conditions.…”

“…Consequently, only approximate analyses are available even in the zero-Reynolds number limit. Early analyses such as that of Nakano and Tien (1968), Mohan et al (1972), Mohan (1974), Mohan and Venkateswarlu (1976), Malinowski (1986, 1987a,b), Chhabra and Dhingra (1986), etc., are based on the use of the velocity and stress variational principles. This approach yields upper and lower bounds on the drag force (and hence on the terminal velocity); usually the two bounds diverge with the increasing degree of shear-thinning behaviour.…”

Drag of a Spherical Bubble Rising in Power Law Fluids at Intermediate Reynolds Numbers

“…This approach is applicable only to shear-thinning fluids. The works of Mohan 12 and Mohan and Venkateswarlu 13 exemplify this approach, which has also been extended to swarms of drops and bubbles, where the results in the limit of vanishingly small values of the gas volume fraction and of the viscosity ratio also reduce to the single bubble case (see refs [14][15][16][17][18]. Finally, it is appropriate to note here that both these approaches are restricted to the creeping flow regime and for shear-thinning behavior.…”

The Slow Motion of a Spherical Particle in a Carreau Fluid

“…In this particular case, an analytical solution could be derived for the drag coefficent. Chhabra and Dhingra (1986) and Jarzebski and Malinowski (1987) both used variational principles to approximate the upper and lower bounds on the drag force for fluids that can be represented by a Carreau equation. Comparisons were made with the solutions for power-law fluids and with experimental data from earlier works.…”