Morton number

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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.{{citation |first1=R. |last1=Clift |first2=J. R. |last2=Grace |first3=M. E. |last3=Weber |title=Bubbles Drops and Particles |location=New York |publisher=Academic Press |year=1978 |isbn=978-0-12-176950-5 }}

It is named after Rose Morton, who described it with W. L. Haberman in 1953.{{citation|first1=W. L.|last1=Haberman|first2=R. K.|last2=Morton|title=An experimental investigation of the drag and shape of air bubbles rising in various liquids|url=https://archive.org/details/experimentalinve00habe|series=Report 802|publisher=Navy Department: The David W. Taylor Model Basin|year=1953}}{{cite journal | last1 = Pfister | first1 = Michael | last2 = Hager | first2 = Willi H.| date = May 2014 | doi = 10.1061/(asce)hy.1943-7900.0000870 | issue = 5 | journal = Journal of Hydraulic Engineering | page = 02514001 | title = History and significance of the Morton number in hydraulic engineering | volume = 140| url = http://infoscience.epfl.ch/record/198760/files/2014_971_Pfister_Hager_history_and_significance_Morton_number_in_hydraulic_engineering.pdf }}

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.

References

Category:Bubbles (physics)

Category:Dimensionless numbers of fluid mechanics

Category:Fluid dynamics