# Capillary Number

on . Posted in Dimensionless Numbers

Capillary number, abbreviated as Ca, a dimensionless number, representing the relative effect of viscous forces against the surface tension between a liquid/gas or liquid/liquid interface.  It is the ratio of viscous forces to surface tension forces.  It's particularly relevant when dealing with fluid flows in small-scale or capillary systems, where surface tension effects become more pronounced.  The capillary number helps determine whether the fluid behavior will be dominated by viscous effects or by surface tension effects.

### capillary number Interpretation

• When Ca ≪ 1  -  Viscous forces dominate, and the fluid behaves like a viscous fluid, with little influence from surface tension.
• When Ca ≫ 1  -  Surface tension forces dominate, and the fluid's behavior is strongly influenced by the presence of surface tension, leading to phenomena such as capillary action, meniscus formation, and droplet formation.

The capillary number is particularly important in microfluidics, where fluid behavior at small scales is significantly influenced by surface tension due to the relatively large surface area-to-volume ratios.  It's also relevant in understanding the behavior of fluids in porous media, capillary tubes, and other systems where both viscous and surface tension effects play a role.

## Capillary number formula

$$\large{ Ca = \frac{ \mu \; v }{ \sigma } }$$
Symbol English Metric
$$\large{ Ca }$$ = Capillary number $$\large{dimensionless}$$
$$\large{ \mu }$$  (Greek symbol mu) = dynamic viscosity $$\large{\frac{lbf-sec}{ft^2}}$$ $$\large{ Pa-s }$$
$$\large{ v }$$ = velocity of fluid $$\large{\frac{ft}{sec}}$$ $$\large{\frac{m}{s}}$$
$$\large{ \sigma }$$  (Greek symbol sigma) = surface tension $$\large{\frac{lbf}{ft}}$$ $$\large{\frac{N}{m}}$$ Tags: Fluid