Morton number

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For Morton number in number theory, see Morton number.

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

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

\mathit{Mo} = \frac{g\mu_L^4}{\rho_L \sigma^3}.

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

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

The Froude number in the above expression is defined as

\mathit{Fr} = \frac{V^2}{gd}

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

[edit] References

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

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