Capillary Number

The Capillary number (Ca) is a dimensionless parameter used in fluid mechanics to characterize the relative importance of viscous forces to surface tension forces in a fluid flow situation. 

Capillary number is proportional to { (viscous force) / (surface tension force) } and is used in momentum transfer in general and atomization and 2-phase flow in beds of solids calculations in particular. It is equivalent to (We/Re). It is normally defined in the following form




Dimensional constant






Surface tension




The Capillary number helps determine whether viscous forces or surface tension forces dominate the behavior of the fluid flow. Depending on the value of the Capillary number, different flow regimes can be identified:

  • If Ca ≪ 1, surface tension forces dominate over viscous forces, and the fluid tends to exhibit capillary effects, such as meniscus formation or capillary rise. This typically occurs in situations where surface tension is significant relative to viscosity, such as in small-scale flows or thin films.
  • If Ca ≫ 1, viscous forces dominate over surface tension forces, and the fluid behavior is primarily determined by viscosity. This typically occurs in situations where viscosity is significant relative to surface tension, such as in large-scale flows or high-speed flows.

The Capillary number is commonly used in the analysis of various fluid systems, including droplet formation, wetting phenomena, and microfluidic devices. It helps engineers and scientists understand and predict the behavior of fluids in different scenarios.

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