Bond number#

Also known as: Eötvös number.

Named after: Wilfrid Noel Bond (1897-1937), Loránd Eötvös (1848-1919).

$$\text{Bo} \stackrel{\text{def}}{=} \frac{\rho g L^{2}}{\sigma} \sim \frac{\text{gravity}}{\text{surface tension}}$$

Measures gravitational forcing relative to surface tension. It indicates whether interfaces are shaped more by weight or capillarity.

Name	Symbol	SI units	Dimension
mass density	$\rho$	$\mathrm{kg}\,\mathrm{m}^{-3}$	$\text L^{-3}\,\text M$
gravitational acceleration	$g$	$\mathrm{m}\,\mathrm{s}^{-2}$	$\text L\,\text T^{-2}$
characteristic length	$L$	$\mathrm{m}$	$\text L$
surface tension	$\sigma$	$\mathrm{N}\,\mathrm{m}^{-1}$	$\text M\,\text T^{-2}$

Capillary-gravity flow

Range	Regime	Description
0 – 1	capillary dominated	Surface tension controls interface shape. Droplets and menisci remain strongly curved by capillary forces.
1 – ∞	gravity dominated	Gravity controls interface deformation. Large droplets, bubbles, and free surfaces flatten or sag under their own weight.

Name	Symbol	SI units	Dimension
mass density	\(\rho\)	\(\mathrm{kg}\,\mathrm{m}^{-3}\)	\(\text L^{-3}\,\text M\)
gravitational acceleration	\(g\)	\(\mathrm{m}\,\mathrm{s}^{-2}\)	\(\text L\,\text T^{-2}\)
characteristic length	\(L\)	\(\mathrm{m}\)	\(\text L\)
surface tension	\(\sigma\)	\(\mathrm{N}\,\mathrm{m}^{-1}\)	\(\text M\,\text T^{-2}\)