Approximate solutions for drag coefficient of bubbles moving in shear-thinning elastic fluids

Abstract

Abstract:The drag coefficient for bubbles with mobile or immobile interface rising in shear-thinning elastic fluids described by an Ellis or a Carreau model is discussed. Approximate solutions based on linearization of the equations of motion are presented for the highly elastic region of flow. These solutions are in reasonably good agreement with the theoretical predictions based on variational principles and with published experimental data.

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

“…The effect of the characteristic parameters A and n of the Carreau equation on the drag coefficient is shown in Figure 1 for a single bubble and in Figure 2 for a swarm of bubbles when gas holdup is equal to 0.2 or 0.4. Predictions of the appropriate expression of Kawase and Moo-Young (1985) (Equation (16) of their paper), also shown in Figure 1, are in reasonable agreement with the variational solution if the shear thinning behaviour is not pronounced; however the results differ more markedly for larger values of the characteristic time parameter A and lower values of n . In general, the values of the drag coefficient predicted by Kawase and Moo-Young expression for bubbles with mobile interface are lower than those obtained from the variational algorithm.…”

“…Later studies covered the creeping flow of an Ellis fluid past a Newtonian fluid sphere (Mohan and Venkateswarlu, 1976b;Mohan and Raghuraman, 1976) and multiple bubble motion in a power law fluid (Bhavaraju et al, 1978;Kawase and Ulbrecht, 1981a). The most recent investigations deal with slow flow of a Carreau fluid over a single rigid spherical particle (Chhabra and Uhlherr, 1980;Bush and Phan-Thien, 1984), over an assemblage of particles (Chhabra and Raguraman, 1984) and over gas bubbles (Kawase and Moo-Young, 1985). The latter problem is of potential interest in viscous fermentation problems.…”

“…Since their results were in close agreement with those of Chhabra and Uhlherr (1980) they concluded that the theoretical upper bound for the drag force is a good representation of the true solution. To obtain closed form expressions for the drag coefficient, Kawase and Moo-Young (1985) linearized the governing system of equations. However, due to linearization, predictions of the expressions are reasonably accurate only in regions of high values of the characteristic time parameter and when shear thinning is not pronounced.…”

The Slow Motion of a Spherical Particle in a Carreau Fluid

“…It can be seen that the effect of shear-thinning is more pronounced for a sphere than for a bubble. Kawase and Moo-Young (1985) obtained approximate expressions for the drag coefficient in the case of bubbles and spheres moving in a Carreau fluid. Their expressions for a sphere and a bubble are respectively:…”

Dynamic processes in a deformed drop rising through shear-thinning fluids

“…As is well-known, a large number of investigations concerning various aspects of the bubble or drop motion in shear-thinning fluids has been reported theoretically and experimentally (e.g., [1][2][3][4][5][6][7][8][9][10][11][12][13][14][15][16][17][18] for bubble motions and [19][20][21][22][23][24][25][26] for drop motions) in the past. Many of the most important results have been well summarized and reviewed by Chhabra [27].…”