Capillary number

In fluid dynamics, the capillary number (Ca) represents the relative effect of viscous forces versus surface tension acting across an interface between a liquid and a gas, or between two immiscible liquids. For example an air bubble in a liquid flow tends to be deformed by the friction of the liquid flow due to viscosity effects, but the surface tension forces tend to minimize the surface. The capillary number is defined as:

$\mathrm{Ca} = \frac{\mu V}{\gamma}$

where µ is the dynamic viscosity of the liquid, V is a characteristic velocity and $\gamma$ is the surface or interfacial tension between the two fluid phases.

The capillary number is a dimensionless quantity, hence its value does not depend on the system of units.

For low capillary numbers (a rule of thumb says less than 10⁻⁵), flow in porous media is dominated by capillary forces whereas for high capillary number the capillary forces are negligible compared to the viscous forces.

See also

• Bond number
• Reynolds number
• Capillary pressure
• Froude number