Ohnesorge number

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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:

 \mathrm{Oh} = \frac{ \mu}{ \sqrt{\rho \sigma L }} = \frac{\sqrt{\mathrm{We}}}{\mathrm{Re}} \sim \frac{\mbox{viscous forces}}{\sqrt{{\mbox{inertia}} \cdot {\mbox{surface tension}}}}

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[edit]

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]

See also[edit]

  • Laplace number - There is an inverse relationship,  \mathrm{Oh} = 1/\sqrt{\mathrm{La}}, 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[edit]

  1. ^ 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.