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# Morton number

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 Title: Morton number Author: World Heritage Encyclopedia Language: English Subject: Collection: Publisher: World Heritage Encyclopedia Publication Date:

### 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.