Eötvös number

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In fluid dynamics the Eötvös number (Eo), also called the Bond number (Bo), is a dimensionless number measuring the importance of surface tension forces compared to body 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[edit]

The Eötvös or Bond number is given by

\mathrm{Eo}=\mathrm{Bo}=\frac{\Delta\rho \,g \,L^2}{\sigma}

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:

\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[edit]

  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.