Capillary number
In fluid dynamics, the capillary number (Ca) is a dimensionless quantity representing the relative effect of viscous drag forces versus surface tension forces acting across an interface between a liquid and a gas, or between two immiscible liquids. Alongside the Bond number, commonly denoted , this term is useful to describe the forces acting on a fluid front in porous or granular media, such as soil. The capillary number is defined as: where is the dynamic viscosity of the liquid, is a characteristic velocity and is the surface tension or interfacial tension between the two fluid phases. Being a dimensionless quantity, the capillary number's value does not depend on the system of units. In the petroleum industry, capillary number is denoted instead of . 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 numbers the capillary forces are negligible compared to the viscous forces. Flow through the pores in an oil reservoir has capillary number values in the order of 10−6, whereas flow of oil through an oil well drill pipe has a capillary number in the order of unity. The capillary number plays