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

$\mathrm{M}\mathrm{o}=\frac{g{\mu }_c^4\mathrm{\Delta }\rho }{{\rho }_c^2{\sigma }^3},$

where g is the acceleration of gravity, ${\mu }_c$ is the viscosity of the surrounding fluid, ${\rho }_c$ the density of the surrounding fluid, $\mathrm{\Delta }\rho$ 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

$\mathrm{M}\mathrm{o}=\frac{g{\mu }_c^4}{{\rho }_c{\sigma }^3}.$

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

$\mathrm{M}\mathrm{o}=\frac{{\mathrm{W}\mathrm{e}}^3}{\mathrm{F}\mathrm{r}{\mathrm{R}\mathrm{e}}^4}.$

The Froude number in the above expression is defined as

$\mathrm{F}\mathrm{r}=\frac{V^2}{gd}$

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

References

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