Ohnesorge

The Ohnesorge number (Oh) is a dimensionless parameter in fluid dynamics that compares viscous forces to inertial and surface-tension forces in a liquid. It is defined as Oh = μ / sqrt(ρ σ L), where μ is dynamic viscosity, ρ is density, σ is surface tension, and L is a characteristic length scale (such as droplet diameter or jet radius). For Newtonian liquids, this expression provides a single measure of viscous effects in flows involving capillarity.

A small Oh indicates that inertial and capillary effects dominate over viscous forces, while a large Oh indicates that viscous effects are dominant, tending to damp capillary breakup and slow jetting. The value of Oh helps determine the balance of forces in droplet formation and jet breakup problems.

Applications of the Ohnesorge number include analysis of droplet formation and breakup in spray and inkjet processes, as well as microfluidic dispensing and capillary-driven flows. It is commonly considered alongside Reynolds, Capillary, and Weber numbers to describe regimes of dripping versus jetting and the stability of interfaces in small-scale liquid flows. The transitional regime near Oh ≈ 1 is of particular interest in precise droplet generation and atomization technologies.

History and naming: The number is named after a German engineer or physicist who studied capillary and viscous effects in liquids in the early 20th century. Its use spans research and industrial applications where viscous forces influence capillary-driven dynamics.

See also: Reynolds number, Capillary number, Weber number.