Capillary number

The capillary number ( symbol :) is a dimensionless number , it shows the ratio of viscosity forces to surface tensions at the phase boundaries ( interfaces ) of liquids and gas or immiscible liquids. ${\displaystyle {\mathit {Ca}}}$

The capillary number is defined as:

${\displaystyle {\mathit {Ca}}={\frac {\eta \,V}{\sigma }}={\frac {\nu \,\rho \,V}{\sigma }}}$

in which:

• ${\displaystyle \eta }$: Dynamic viscosity of the liquid (in SI units: Pa · s )
• ${\displaystyle \nu }$: kinematic viscosity of the liquid (in SI units: m ² s ⁻¹ )
• ${\displaystyle V}$: characteristic speed (in SI units: m / s)
• ${\displaystyle \sigma }$: Surface tension (in SI units: N / m)

Alternatively, the capillary number can be calculated as the ratio of Weber number ( ) to Reynolds number ( ): ${\displaystyle {\mathit {We}}}$ ${\displaystyle {\mathit {Re}}}$

${\displaystyle {\mathit {Ca}}={\frac {\mathit {We}}{\mathit {Re}}}}$

The capillary number can also be understood as the ratio of the speed to the characteristic relaxation speed of a liquid . ${\displaystyle v_{\text{char}}={\frac {\sigma }{\eta }}}$

${\displaystyle {\mathit {Ca}}={\frac {V}{v_{\text{char}}}}}$

The relaxation is the effort induced by the surface tension to assume the smallest possible surface. This endeavor is inhibited by the viscosity. If the number of capillaries is much smaller than one, the relaxation rate is higher than that external to z. B. a drop applied speed and this takes on a statically ideal shape of the smallest surface at every moment. If the capillary speed is much greater than one, the relaxation of the drop can no longer follow the external speed and the drop remains deformed without being able to take on a form of the smallest surface.

See also

• Morton number
• Elasto capillary number