Laplace number#
Also known as: Suratman number.
Named after: Pierre-Simon Laplace (1749-1827).
$$\text{La} \stackrel{\text{def}}{=} \frac{\rho \sigma L}{\mu^{2}} \sim \frac{\text{inertia and surface tension}}{\text{viscous damping}}$$
Description#
Measures inertial and capillary effects relative to viscous damping. It is the inverse-square counterpart of the Ohnesorge number for free-surface motion.
Quantities#
| Name | Symbol | SI units | Dimension |
|---|---|---|---|
| mass density | \(\rho\) | \(\mathrm{kg}\,\mathrm{m}^{-3}\) | \(\text L^{-3}\,\text M\) |
| surface tension | \(\sigma\) | \(\mathrm{N}\,\mathrm{m}^{-1}\) | \(\text M\,\text T^{-2}\) |
| characteristic length | \(L\) | \(\mathrm{m}\) | \(\text L\) |
| dynamic viscosity | \(\mu\) | \(\mathrm{Pa}\,\mathrm{s}\) | \(\text L^{-1}\,\text M\,\text T^{-1}\) |
Regimes#
Free surface flow
| Range | Regime | Description |
|---|---|---|
| 0 – 1 | viscous dominated | Viscous stresses damp interfacial motion rapidly. Surface waves and breakup are sluggish. |
| 1 – 1000 | transitional | Viscous damping competes with inertia and surface tension. Interface motion depends strongly on geometry and forcing. |
| 1000 – ∞ | inertia and capillarity dominated | Inertia and surface tension dominate over viscous damping. Capillary waves and rapid pinch off are prominent. |