Morton number

In fluid dynamics, the Morton number (Mo) is a dimensionless number used together with the Eötvös number or Bond number to characterize the shape of bubbles or drops moving in a surrounding fluid or continuous phase, c. The Morton number is defined as

where g is the acceleration of gravity, μ c is the viscosity of the surrounding fluid, ρ c the density of the surrounding fluid, Δ ρ the difference in density of the phases, and σ is the surface tension coefficient. For the case of a bubble with a negligible inner density the Morton number can be simplified to

The Morton number can also be expressed by using a combination of the Weber number, Froude number and Reynolds number,

The Froude number in the above expression is defined as

where V is a reference velocity and d is the equivalent diameter of the drop or bubble.