The capillary number represents the relative effect of viscous forces and surface tension acting across an interface between a liquid and a gas, or between two immiscible liquids. It is defined as
where μ is the viscosity of the liquid, v is a characteristic velocity, and σ is the surface or interfacial tension between the two fluid phases.
Such a number is typically defined as a product or ratio of quantities which do have units, in such a way that all units cancel.
Dimensionless numbers are widely used in the fields of mathematics, physics, and engineering but also in everyday life.
The power consumption of a stirrer with a particular geometry is a function of the density and the viscosity of the fluid to be stirred, the size of the stirrer given by its diameter, and the speed of the stirrer.
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