Drag force on bubbles

The ECtvCs number is determining the ratio between the gravitational—and surface tension forces (i, ethe Edtvds number is equal to the Bond number), and defined by  

Only three of these numbers are independent, since the Eotvos number can be expressed as  

Similarly, the Capillary number, Ca, determining the ratio between the viscous—and surface tension forces, is related to the Weber number. We, and particle Reynolds number. Rep. That is, the Capillary number can be expressed as, Ca = When the Reynolds, Morton and Eotvos numbers are determined, the shape of bubbles or drops falling or rising unhindered in a liquid can be determined from the shape regime map in Fig. 5.7. A similar map has been presented earlier by Grace et al. [47]. 

Notice that arr 0 on the surface of the bubble due to the prevailing free slip condition, in contrast to the rigid sphere case in which cr r vanishes on the surface due to the no-slip condition. 

A similar solution for creeping flow past a spherical droplet of fluid were derived independently by Hadamard [49] and Rybczynski [104], In this case the fluid stream has a velocity V at infinity and viscosity pf, while the droplet has a viscosity pp and a fixed interface. The boundary conditions at the droplet interface are (1) zero radial velocities and (2) equality of surface shear and tangential velocity on either side of the interface. 

Similarly, the Capillary number, Ca, determining the ratio between the viscous-and surface tension forces, is related to the Weber number, We, and particle Reynolds number, Rep. That is, the Capillary number can be expressed as. 

When the Reynolds, Morton and Eotvos numbers are determined, the shape of bubbles or drops falling or rising unhindered in a liquid can be determined from the shape regime map in Fig 5.7. A similar map has been presented earlier by Grace et al [53]. 

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E Distance of impeller to the bottom of the vessel Fo Drag force on bubble... 

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