Ohnesorge number
{{Short description|Number that relates the viscous forces to inertial and surface tension forces}}
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.{{cite journal | first1 = Gareth H. | last1 = McKinley | last2 = Renardy | first2 = Michael | year = 2011 | title = Wolfgang von Ohnesorge | journal = Physics of Fluids | volume = 23 | issue = 12 | pages = 127101–127101–6 | doi = 10.1063/1.3663616 |bibcode = 2011PhFl...23l7101M | hdl = 10919/24403 | s2cid = 50633355 | hdl-access = free }}{{cite journal | first1 = Marc-Antoine | last1 = Fardin | last2 = Hautefeuille | first2 = Mathieu | last3 = Sharma | first3 = Vivek | year = 2022 | title = Spreading, pinching, and coalescence: the Ohnesorge units | journal = Soft Matter | volume = 18 | issue = 17 | pages = 3291–3303 | doi= 10.1039/d2sm00069e | pmid = 35416235 | arxiv = 2112.06713 | bibcode = 2022SMat...18.3291F | s2cid = 245123849 | url = https://hal.archives-ouvertes.fr/hal-03795917/document }}
It is defined as:
:
Where
- 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
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.{{Cite book | author = Lefebvre, Arthur Henry | title = Atomization and Sprays | publisher = Hemisphere Publishing Corp. | location = New York and Washington, D.C. | year = 1989 | isbn = 978-0-89116-603-0 | oclc = 18560155 }}{{cite journal | last = Ohnesorge | first = W | title = Die Bildung von Tropfen an Düsen und die Auflösung flüssiger Strahlen | journal = Zeitschrift für Angewandte Mathematik und Mechanik | volume = 16 | issue = 6 | pages = 355–358 | date = 1936 | doi = 10.1002/zamm.19360160611 | bibcode = 1936ZaMM...16..355O }} English translation: {{cite journal | last = Ohnesorge | first = Wolfgang von | title = The formation of drops by nozzles and the breakup of liquid jets | date = 2019 | doi = 10.26153/tsw/3391 | journal = Texas Scholar Works | s2cid = 214403876 }}
In inkjet printing, liquids whose Ohnesorge number are in the range 0.1 < Oh < 1.0 are jettable (1
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.