Morton number explained

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.^[1]

Definition

The Morton number is defined as

Mo=

	4
\mu
	c

\Delta\rho

	2
\rho		\sigma³
	c

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

Mo=

	4
g\mu
	c

\rho_c\sigma³

Relation to other parameters

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

Mo=

	We³
	Fr²Re⁴

The Froude number in the above expression is defined as

Fr²

	V²
	gd

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

Notes and References

Pfister . Michael . Hager . Willi H.. May 2014 . 10.1061/(asce)hy.1943-7900.0000870 . 5 . Journal of Hydraulic Engineering . 02514001 . History and significance of the Morton number in hydraulic engineering . 140.