Capillary number and inertia

[joshmccraney]

Hi PF!

The capillary number is defined as $Ca = \mu V/\sigma$. Does more inertia in a fluid increase the capillary number?

As inertia increases, it's my intuition that so does velocity. Then it seems (all else constant) that $Ca$ increases too. Is this correct?

 

[Chestermiller]

The capillary number represents the ratio of viscous to surface tension effects. The ratio of inertial to viscous effects is determined by the Reynolds number. So, the product of the two is the ratio of inertial to capillary effects. What does this give you? What are you defining as inertia?

 

[joshmccraney]

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What does this give you? What are you defining as inertia?

This gives us $\rho V^2 L / \sigma$, which is the velocity dependence I would expect. I know inertia characteristically scales proportional to $V^2$. Holding everything constant but letting velocity change implies more inertial yields higher capillary number. Thanks for the help!