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][2]

It is defined as:



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.[3][4]

In inkjet printing, liquids whose Ohnesorge number are in the range 0.1 < Oh < 1.0 are jettable (1<Z<10 where Z is the reciprocal of the Ohnesorge number).[1][5]

See also


  1. ^ a b McKinley, Gareth H.; Renardy, Michael (2011). "Wolfgang von Ohnesorge". Physics of Fluids. 23 (12): 127101–127101–6. Bibcode:2011PhFl...23l7101M. doi:10.1063/1.3663616. hdl:10919/24403. S2CID 50633355.
  2. ^ Fardin, Marc-Antoine; Hautefeuille, Mathieu; Sharma, Vivek (2022). "Spreading, pinching, and coalescence: the Ohnesorge units". Soft Matter. 18 (17): 3291–3303. arXiv:2112.06713. Bibcode:2022SMat...18.3291F. doi:10.1039/d2sm00069e. PMID 35416235. S2CID 245123849.
  3. ^ Lefebvre, Arthur Henry (1989). Atomization and Sprays. New York and Washington, D.C.: Hemisphere Publishing Corp. ISBN 978-0-89116-603-0. OCLC 18560155.
  4. ^ 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. S2CID 214403876. ((cite journal)): Cite journal requires |journal= (help)
  5. ^ Derby, Brian (2010). "Inkjet Printing of Functional and Structural Materials: Fluid Property Requirements, Feature Stability, and Resolution" (PDF). Annual Review of Materials Research. 40 (1): 395–414. Bibcode:2010AnRMS..40..395D. doi:10.1146/annurev-matsci-070909-104502. ISSN 1531-7331. S2CID 138001742.