: In

fluid dynamics In physics, physical chemistry and engineering, fluid dynamics is a subdiscipline of fluid mechanics that describes the flow of fluids – liquids and gases. It has several subdisciplines, including (the study of air and other gases in motion ...

, the Morton number (Mo) is a

dimensionless number Dimensionless quantities, or quantities of dimension one, are quantities implicitly defined in a manner that prevents their aggregation into unit of measurement, units of measurement. ISBN 978-92-822-2272-0. Typically expressed as ratios that a ...

used together with the

Eötvös number In fluid dynamics the Eötvös number (Eo), also called the Bond number (Bo), is a dimensionless number measuring the importance of gravitational forces compared to surface tension forces for the movement of liquid front. Alongside the capillary ...

or Bond number to characterize the shape of bubbles or drops moving in a surrounding fluid or continuous phase, ''c''. It is named after Rose Morton, who described it with W. L. Haberman in 1953.

Definition

The Morton number is defined as :

\mathrm = \frac,

where ''g'' is the acceleration of gravity,

\mu_c

is the

viscosity Viscosity is a measure of a fluid's rate-dependent drag (physics), resistance to a change in shape or to movement of its neighboring portions relative to one another. For liquids, it corresponds to the informal concept of ''thickness''; for e ...

of the surrounding fluid,

\rho_c

the

density Density (volumetric mass density or specific mass) is the ratio of a substance's mass to its volume. The symbol most often used for density is ''ρ'' (the lower case Greek letter rho), although the Latin letter ''D'' (or ''d'') can also be u ...

of the surrounding fluid,

\Delta \rho

the difference in density of the phases, and

\sigma

is the

surface tension Surface tension is the tendency of liquid surfaces at rest to shrink into the minimum surface area possible. Surface tension (physics), tension is what allows objects with a higher density than water such as razor blades and insects (e.g. Ge ...

coefficient. For the case of a bubble with a negligible inner density the Morton number can be simplified to :

\mathrm = \frac.

Relation to other parameters

The Morton number can also be expressed by using a combination of the

Weber number The Weber number (We) is a dimensionless number in fluid mechanics that is often useful in analysing fluid flows where there is an interface between two different fluids, especially for multiphase flows with strongly curved surfaces. It is named ...

Froude number In continuum mechanics, the Froude number (, after William Froude, ) is a dimensionless number defined as the ratio of the flow inertia to the external force field (the latter in many applications simply due to gravity). The Froude number is ba ...

and

Reynolds number In fluid dynamics, the Reynolds number () is a dimensionless quantity that helps predict fluid flow patterns in different situations by measuring the ratio between Inertia, inertial and viscous forces. At low Reynolds numbers, flows tend to ...

, :

\mathrm = \frac.

The Froude number in the above expression is defined as :

\mathrm = \frac

where ''V'' is a reference velocity and ''d'' is the

equivalent diameter In applied sciences, the equivalent radius (or mean radius) is the radius of a circle or sphere with the same perimeter, area, or volume of a non-circular or non-spherical object. The equivalent diameter (or mean diameter) (D) is twice the equiva ...

of the drop or bubble.

References

{{NonDimFluMech Bubbles (physics) Dimensionless numbers of fluid mechanics Fluid dynamics