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.

Search another word or see Morton_numberon Dictionary | Thesaurus |Spanish