# 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*.[1]
It is named after Rose Morton, who described it with W. L. Haberman in 1953.[2][3]

## Definition

The Morton number is defined as

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

## Relation to other parameters

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.

## References

- Clift, R.; Grace, J. R.; Weber, M. E. (1978),
*Bubbles Drops and Particles*, New York: Academic Press, ISBN 978-0-12-176950-5 - Haberman, W. L.; Morton, R. K. (1953),
*An experimental investigation of the drag and shape of air bubbles rising in various liquids*, Report 802, Navy Department: The David W. Taylor Model Basin - Pfister, Michael; Hager, Willi H. (May 2014). "History and significance of the Morton number in hydraulic engineering".
*Journal of Hydraulic Engineering*.**140**(5): 02514001. doi:10.1061/(asce)hy.1943-7900.0000870.