Definitions

# 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. The Morton number is defined as

$mathit\left\{Mo\right\} = frac\left\{g mu_L^4 , Delta rho\right\}\left\{rho_L^2 sigma^3\right\},$

where g is the acceleration of gravity, $mu_L$ is the viscosity of the surrounding fluid, $rho_L$ 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

$mathit\left\{Mo\right\} = frac\left\{gmu_L^4\right\}\left\{rho_L sigma^3\right\}.$

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

$mathit\left\{Mo\right\} = frac\left\{mathit\left\{We\right\}^3\right\}\left\{mathit\left\{Fr\right\} mathit\left\{Re\right\}^4\right\}.$

The Froude number in the above expression is defined as

$mathit\left\{Fr\right\} = frac\left\{V^2\right\}\left\{gd\right\}$

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

## References

R. Clift, J. R. Grace, and M. E. Weber, Bubbles Drops and Particles, Academic Press New York, 1979.

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