Morton number

For Morton number in number theory, see Morton number (number theory).

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

\[\mathit{Mo} = \frac{g \mu_c^4 \, \Delta \rho}{\rho_c^2 \sigma^3}, \]

where g is the acceleration of gravity, \( \mu_c\) is the viscosity of the surrounding fluid, \(\rho_c\) the density of the surrounding fluid, \( \Delta \rho\) the difference in density of the phases, and \(\sigma\) is the surface tension coefficient. For the case of a bubble with a negligible inner density the Morton number can be simplified to

\[\mathit{Mo} = \frac{g\mu_c^4}{\rho_c \sigma^3}.\]

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

\[\mathit{Mo} = \frac{\mathit{We}^3}{\mathit{Fr} \mathit{Re}^4}.\]

The Froude number in the above expression is defined as

\[\mathit{Fr} = \frac{V^2}{gd}\]

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

References

bs:Mortonov broj