Ohnesorge number

The Ohnesorge number (Oh) 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.^[1]

It is defined as:

Where

• μ is the liquid viscosity
• ρ is the liquid density
• σ is the surface tension
• L is the characteristic length scale (typically drop diameter)
• 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.^[2][3]

In inkjet printing, liquids whose Ohnesorge number is less than 1 and greater than 0.1 are jettable (1<Z<10 where Z is the reciprocal of the Ohnersorge number).^[1][4]

See also

• Laplace number - There is an inverse relationship, , between the Laplace number and the Ohnesorge number. It is more historically correct to use the Ohnesorge number, but often mathematically neater to use the Laplace number.

References

1. 1 2 McKinley, Gareth H.; Renardy, Michael (2011). "Wolfgang von Ohnesorge". Physics of Fluids. 23: 127101. Bibcode:2011PhFl...23l7101M. doi:10.1063/1.3663616. 
2. ↑ Lefebvre, Arthur Henry (1989). Atomization and Sprays. New York and Washington, D.C.: Hemisphere Publishing Corp. ISBN 978-0-89116-603-0. OCLC 18560155. 
3. ↑ Ohnesorge, W (1936). "Formation of drops by nozzles and the breakup of liquid jets". Journal of Applied Mathematics and Mechanics. 16: 355–358. 
4. ↑ Derby, Brian (2010). "Inkjet Printing of Functional and Structural Materials: Fluid Property Requirements, Feature Stability, and Resolution". Annual Review of Materials Research. 40 (1): 395–414. doi:10.1146/annurev-matsci-070909-104502. ISSN 1531-7331.