:
In
fluid dynamics, the Morton number (Mo) is a
dimensionless number
A dimensionless quantity (also known as a bare quantity, pure quantity, or scalar quantity as well as quantity of dimension one) is a quantity to which no physical dimension is assigned, with a corresponding SI unit of measurement of one (or 1) ...
used together with the
Eötvös number 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
:
where ''g'' is the acceleration of gravity,
is the
viscosity
The viscosity of a fluid is a measure of its resistance to deformation at a given rate. For liquids, it corresponds to the informal concept of "thickness": for example, syrup has a higher viscosity than water.
Viscosity quantifies the inte ...
of the surrounding fluid,
the
density
Density (volumetric mass density or specific mass) is the substance's mass per unit of volume. The symbol most often used for density is ''ρ'' (the lower case Greek letter rho), although the Latin letter ''D'' can also be used. Mathematical ...
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
:
Relation to other parameters
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.
References
{{NonDimFluMech
Dimensionless numbers
Bubbles (physics)
Dimensionless numbers of fluid mechanics
Fluid dynamics