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:


  • μ is the dynamic viscosity of the liquid
  • ρ is the density of the liquid
  • σ is the surface tension
  • L is the characteristic length scale (typically drop diameter)
  • Re is the Reynolds number
  • We is the Weber number


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 Ohnesorge 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.


  1. ^ a b McKinley, Gareth H.; Renardy, Michael (2011). "Wolfgang von Ohnesorge". Physics of Fluids. 23 (12): 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). "Die Bildung von Tropfen an Düsen und die Auflösung flüssiger Strahlen". Zeitschrift für Angewandte Mathematik und Mechanik. 16 (6): 355–358. Bibcode:1936ZaMM...16..355O. doi:10.1002/zamm.19360160611. English translation: Ohnesorge, Wolfgang von (2019). "The formation of drops by nozzles and the breakup of liquid jets". doi:10.26153/tsw/3391. Cite journal requires |journal= (help)
  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. Bibcode:2010AnRMS..40..395D. doi:10.1146/annurev-matsci-070909-104502. ISSN 1531-7331.