Mapping cone (homological algebra)

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

$\mathrm {Fr} ={\frac {V^{2}}{gd}}$

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

References

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