Viscous Regime

In the viscous regime, dispersed droplets and bubbles behave in the same manner as solid spherical particles. Hence, the drag coefficient is well approximated by the Alexander-Morsi correlation:

(12–59)

Distorted Regime

In the distorted particle regime, the drag coefficient is approximately constant, independent of Reynolds number, but dependent on particle shape through the dimensionless group known as the Eotvos number, which measures the ratio between gravitational and surface tension forces:

(12–60)

where is the density difference between the phases, is the gravitational acceleration, and is the surface tension coefficient.

For the distorted regime, the Ishii-Zuber correlation gives:

(12–61)

Spherical Cap Regime

In the spherical cap regime, the drag coefficient is approximated by:

(12–62)

The bubble drag coefficient over a large particle Reynolds number range is computed as follows:

(12–63)

Viscous Regime

In the viscous regime, the drag coefficient is modeled in the same way as in Ishii-Zuber Drag Model (Equation 12–59).

Distorted Regime

The Grace drag model is formulated for flow past a single bubble. Here the drag coefficient in the distorted particle regime is given by:

(12–64)

where is the terminal velocity given by:

(12–65)

where is the Morton number calculated by:

and

with

Here, is the molecular viscosity of water at 25°C and 1 bar.

In the above equations, subscript refers to continuous phase.

Spherical Cap Regime

In the spherical cap regime, the drag coefficient is modeled in the same way as in Ishii-Zuber Drag Model (Equation 12–63).