Drag and mass transfer in a creeping flow of a carreau fluid over drops or bubbles

Abstract

Estimates for the upper bound on the drag coefficient for a single drop or bubble or a swarm of drops or bubbles translating in a Carreau fluid are obtained using variational principles. The effects of a wide range of shear thinning properties, holdup and viscosity ratios on drag and mass transfer rate are discussed. Recently published predictions of approximate analytical solutions are verified and found to be reasonable if shear thinning behaviour is not pronounced.

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.…”

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.…”

A New Solution of Drag for Newtonian Fluid Droplets in a Power-Law Fluid

“…Among them, many studies have adopted the free surface model originally proposed by Happel [11] as a conceptualized representation of flow problems over multiple particles, droplets, or bubbles to simplify the interacting effects among them. The free surface cell model was used in combination with variational principles to obtain the upper and lower bounds on the drag coefficient of a swarm of Newtonian fluid drops in a power-law fluid [12] and in a Carreau fluid [13]. Similarly, the combination of free surface cell model and variational principles was adopted to predict the rising velocity of spherical bubbles in a Carreau fluid [14] and in a powerlaw fluid [15].…”