Morton number
Encyclopedia
In fluid dynamics
, the Morton number (
) 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
where g is the acceleration of gravity,
is the viscosity
of the surrounding fluid,
the density
of the surrounding fluid,
the difference in density of the phases, and 
is the surface tension
coefficient.
For the case of a bubble with a negligible inner density the Morton number can be simplified to
The Morton number can also be expressed by using a combination of the Weber number
, Froude number
and Reynolds number,
The Froude number in the above expression is defined as
where V is a reference velocity and d is the equivalent diameter
of the drop or bubble.
Fluid dynamics
In physics, fluid dynamics is a sub-discipline of fluid mechanics that deals with fluid flow—the natural science of fluids in motion. It has several subdisciplines itself, including aerodynamics and hydrodynamics...
, the Morton number (
) is a dimensionless number used together with the Eötvös numberEötvös number
In fluid dynamics the Eötvös number is a dimensionless number named after Hungarian physicist Loránd Eötvös . It is also known as the Bond number...
to characterize the shape of bubbles or drops moving in a surrounding fluid or continuous phase, c.
The Morton number is defined as
where g is the acceleration of gravity,
is the viscosityViscosity
Viscosity is a measure of the resistance of a fluid which is being deformed by either shear or tensile stress. In everyday terms , viscosity is "thickness" or "internal friction". Thus, water is "thin", having a lower viscosity, while honey is "thick", having a higher viscosity...
of the surrounding fluid,
the densityDensity
The mass density or density of a material is defined as its mass per unit volume. The symbol most often used for density is ρ . In some cases , density is also defined as its weight per unit volume; although, this quantity is more properly called specific weight...
of the surrounding fluid,
the difference in density of the phases, and is the surface tensionSurface tension
Surface tension is a property of the surface of a liquid that allows it to resist an external force. It is revealed, for example, in floating of some objects on the surface of water, even though they are denser than water, and in the ability of some insects to run on the water surface...
coefficient.
For the case of a bubble with a negligible inner density the Morton number can be simplified to
The Morton number can also be expressed by using a combination of the Weber number
Weber number
The Weber number 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 can be thought of as a measure of the relative importance of the...
, Froude number
Froude number
The Froude number is a dimensionless number defined as the ratio of a characteristic velocity to a gravitational wave velocity. It may equivalently be defined as the ratio of a body's inertia to gravitational forces. In fluid mechanics, the Froude number is used to determine the resistance of an...
and Reynolds number,
The Froude number in the above expression is defined as
where V is a reference velocity and d is the equivalent diameter
Equivalent spherical diameter
In science, the equivalent spherical diameter of an irregularly-shaped object is the diameter of a sphere of equivalent volume.According to the IUPAC definition, the equivalent diameter of a non-spherical particle is equal to a diameter of a spherical particle that exhibits identical property to...
of the drop or bubble.