A PHYSICALLY-BASED CORRELATION FOR THE EFFECTS OF POWER-LAW RHEOLOGY AND INCLINATION ON SLUG BUBBLE RISE VELOCITY

A study has been made of the motion of long bubbles in inclined pipes containing viscous Newtonian and non-Newtonian liquids. A semi-theoret ical expression for the rise velocity of air bubbles in water is deriv ed on the hypothesis that the dominant factor is the momentum exchange of the bubble underflow, i.e. the bubble nose shape. The correlation calls on empirical inputs from established literature on bubble rise s peeds at high Reynolds number. The effects of increasing Newtonian vis cosity are analysed with reference to the momentum exchange and it is shown how viscosity reduces the inclination dependence of the bubble F roude number. Results from an experimental survey in seven different n on-Newtonian liquids in three different diameter pipes are presented. These data are correlated so as to decouple the effects of surface ten sion and viscosity. An empirical relation is proposed for the effectiv e shear rate in the fluid travelling around the bubble nose. Our corre lation is compared to literature data from a broad range of Reynolds n umbers with excellent agreement except at shallow angles.