TheOhnesorge number (Oh) is adimensionless number that relates theviscous forces toinertial andsurface tension forces. The number was defined by Wolfgang von Ohnesorge in his 1936 doctoral thesis.^[1][2]

It is defined as:

${\displaystyle \mathrm{O}\mathrm{h}=\frac{\mu }{\sqrt{\rho \sigma L}}=\frac{\sqrt{\mathrm{W}\mathrm{e}}}{\mathrm{R}\mathrm{e}}\sim \frac{\text{viscous forces}}{\sqrt{\text{inertia}\cdot \text{surface tension}}}}$

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 theReynolds number
• We is theWeber 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.^[3][4]

Ininkjet 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]

• Laplace number - There is an inverse relationship,${\displaystyle \mathrm{O}\mathrm{h}=1/\sqrt{\mathrm{L}\mathrm{a}}}$, between theLaplace number and the Ohnesorge number. It is more historically correct to use the Ohnesorge number, but often mathematically neater to use theLaplace number.

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