# Eötvös number

(Redirected from Bond number)

In fluid dynamics the Eötvös number (Eo) is a dimensionless number used (together with Morton number) to characterize the shape of bubbles or drops moving in a surrounding fluid. Eötvös number may be regarded as proportional to buoyancy force divided by surface tension force. It was named after Hungarian physicist Loránd Eötvös (1848–1919).[1][2]

## Definition

The Eötvös number is given by

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

## Bond number

The Eötvös number is also known in a slightly different form as the Bond number (Bo),[2][3][4] named after the English physicist Wilfrid Noel Bond (1897–1937).[3][5] The term Eötvös number is more frequently used in Europe, while Bond number is commonly used in other parts of the world.[citation needed]

The Bond number is given by

$\mathrm{Bo} = \frac{\rho a L^2}{\gamma}$

where

• Bo is the Bond Number
• $\rho$ is the density, or the density difference between fluids.
• a the acceleration associated with the body force, almost always gravity.
• L the 'characteristic length scale', e.g. radius of a drop or the radius of a capillary tube.
• $\gamma$ is the surface tension of the interface.

The Bond number is a measure of the importance of surface tension forces compared to body forces. A high Bond number indicates that the system is relatively unaffected by surface tension effects; a low number (typically less than one is the requirement) indicates that surface tension dominates. Intermediate numbers indicate a non-trivial balance between the two effects.

The Bond number is the most common comparison of gravity and surface tension effects and 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 dimensionless numbers are related to the Bond number:

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

Where Eo, Go, and De are respectively the Eötvös, Goucher, and Deryagin numbers. The "difference" between the Goucher and Deryagin numbers is that the Goucher number (which arises in wire coating problems) uses the letter R to represent length scales while the Deryagin number (which arises in plate film thickness problems) uses L.

## 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. ^ a b 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.