Ohnesorge number

The Ohnesorge number is a dimensionless number that relates the viscous forces to inertial and surface tension forces. The number was defined by Wolfgang von Ohnesorge in his 1936 doctoral thesis.
It is defined as:
Whereμ is the dynamic viscosity of the liquidρ is the density of the liquidσ is the surface tensionL is the characteristic length scale

Re is the Reynolds number
We is the Weber number

Applications

The Ohnesorge number for a 3 mm diameter rain drop is typically ~0.002. Larger Ohnesorge numbers indicate a greater influence of the viscosity.
This is often used to relate to free surface fluid dynamics such as dispersion of liquids in gases and in spray technology.
In inkjet printing, liquids whose Ohnesorge number are in the range 0.1 < Oh < 1.0 are jettable.