Gas Bubbles in Non-Newtonian Fluids

The velocity of the bubble in the gravitational field is related to the bubble volume by the following equation  

Oldshue (1966), by using the above equation, showed the various bubble sizes required to have various terminal velocities for fluids with a specific gravity of 1.0 and varying viscosities. If air bubbles are to rise from viscous fluids with any appreciable velocity, then they must have a reasonable size. For example in fluid of 10 poise viscosity, bubbles that are less than 0.76 mm in diameter will remain in the system, and only those that are 2.03 mm or larger will enter and pass out with any appreciable velocity. This, of course, causes much more difficulty in a small-scale fermenter than it would in a large-scale one. 

Astarita and Gianin (1965) have reviewed the available theoretical knowledge of the motion of gas bubbles in Newtonian liquids, and studied the possibility of extension to non-Newtonian liquids. 

In Stockes regime, the velocity-volume relationship is represented by the following equation. 

Q is the drag coefficient and is a modified Reynolds number. It is worthwhile pointing out that for pseudoplastic fluids (s l) the bubble velocity increases with increasing bubble volume more rapidly 

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