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. It is named after Rose Morton, who described it with W. L. Haberman in 1953.

Definition
The Morton number is defined as


 * $$\mathrm{Mo} = \frac{g \mu_c^4 \, \Delta \rho}{\rho_c^2 \sigma^3}, $$

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


 * $$\mathrm{Mo} = \frac{g\mu_c^4}{\rho_c \sigma^3}.$$

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


 * $$\mathrm{Mo} = \frac{\mathrm{We}^3}{\mathrm{Fr}^2\, \mathrm{Re}^4}.$$

The Froude number in the above expression is defined as


 * $$\mathrm{Fr^2} = \frac{V^2}{g d}$$

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