# Eötvös number

(Redirected from Bond number)

In fluid dynamics the Eötvös number (Eo), also called the Bond number (Bo), is a dimensionless number measuring the importance of gravitational forces compared to surface tension forces and is used (together with Morton number) to characterize the shape of bubbles or drops moving in a surrounding fluid. The two names commemorate the Hungarian physicist Loránd Eötvös (1848–1919) [1] [2] [3] [4] and the English physicist Wilfrid Noel Bond (1897–1937),[3][5] respectively. The term Eötvös number is more frequently used in Europe, while Bond number is commonly used in other parts of the world.

## Definition

The Eötvös or Bond number is given by

${\displaystyle \mathrm {Eo} =\mathrm {Bo} ={\frac {\Delta \rho \,g\,L^{2}}{\sigma }}}$
• ${\displaystyle \Delta \rho }$: difference in density of the two phases, (SI units: kg/m3)
• g: gravitational acceleration, (SI units : m/s2)
• L: characteristic length, (SI units : m)
• ${\displaystyle \sigma }$: surface tension, (SI units : N/m)

A high value of the Eötvös or Bond number indicates that the system is relatively unaffected by surface tension effects; a low value (typically less than one) indicates that surface tension dominates. Intermediate numbers indicate a non-trivial balance between the two effects. It may be derived in a number of ways, such as scaling the pressure of a drop of liquid on a solid surface. It is usually important, however, to find the right length scale specific to a problem by doing a ground-up scale analysis. Other similar dimensionless numbers are:

${\displaystyle \mathrm {Bo} =\mathrm {Eo} =2\,\mathrm {Go} ^{2}=2\,\mathrm {De} ^{2}\,}$

where Go and De are the Goucher and Deryagin numbers, which are identical: the Goucher number arises in wire coating problems and hence uses a radius as a typical length scale while the Deryagin number arises in plate film thickness problems and hence uses a Cartesian length.

## References

1. ^ Clift, R.; Grace, J. R.; Weber, M. E. (1978). Bubbles Drops and Particles. New York: Academic Press. p. 26. ISBN 0-12-176950-X.
2. ^ Tryggvason, Grétar; Scardovelli, Ruben; Zaleski, Stéphane (2011). Direct Numerical Simulations of Gas–Liquid Multiphase Flows. Cambridge, UK: Cambridge University Press. p. 43. ISBN 9781139153195.
3. ^ a b Hager, Willi H. (2012). "Wilfrid Noel Bond and the Bond number". Journal of Hydraulic Research. 50 (1): 3–9. doi:10.1080/00221686.2011.649839.
4. ^ de Gennes, Pierre-Gilles; Brochard-Wyart, Françoise; Quéré, David (2004). Capillarity and Wetting Phenomena: Drops, Bubbles, Pearls, Waves. New York: Springer. p. 119. ISBN 978-0-387-00592-8.
5. ^ "Dr. W. N. Bond". Nature. 140 (3547): 716–716. 1937. Bibcode:1937Natur.140Q.716.. doi:10.1038/140716a0.