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

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

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

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

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

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

The Froude number in the above expression is defined as

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

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

References

• Clift, R.; Grace, J. R.; Weber, M. E. (1978). Bubbles Drops and Particles. New York: Academic Press. ISBN 0-12-176950-X.