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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 gravitational forces compared to surface tension forces for the movement of liquid front. Alongside the Capillary number, commonly denoted , which represents the contribution of viscous drag, is useful for studying the movement of fluid in porous or granular media, such as soil.[1] The Bond number (or Eötvös number) is also used (together with Morton number) to characterize the shape of bubbles or drops moving in a surrounding fluid. The two names used for this dimensionless term commemorate the Hungarian physicist Loránd Eötvös (1848–1919)[2][3][4][5] and the English physicist Wilfrid Noel Bond (1897–1937),[4][6] respectively. The term Eötvös number is more frequently used in Europe, while Bond number is commonly used in other parts of the world.

Definition

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Describing the ratio of gravitational to capillary forces, the Eötvös or Bond number is given by the equation:[7]

The Bond number can also be written as where is the capillary length.

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.[7] 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: 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.

In order to consider all three of the forces that act on a moving fluid front in the presence of a gas (or other fluid) phase, namely viscous, capillary and gravitational forces, the generalized Bond number, which is denoted commonly as Bo*, can be used.[1] This is defined as:

References

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  1. ^ a b Dynamics of viscous entrapped saturated zones in partially wetted porous media. Transport in Porous Media (2018), 125(2), 193-210
  2. ^ Clift, R.; Grace, J. R.; Weber, M. E. (1978). Bubbles Drops and Particles. New York: Academic Press. p. 26. ISBN 978-0-12-176950-5.
  3. ^ Tryggvason, Grétar; Scardovelli, Ruben; Zaleski, Stéphane (2011). Direct Numerical Simulations of Gas–Liquid Multiphase Flows. Cambridge, UK: Cambridge University Press. p. 43. ISBN 9781139153195.
  4. ^ a b Hager, Willi H. (2012). "Wilfrid Noel Bond and the Bond number". Journal of Hydraulic Research. 50 (1): 3–9. Bibcode:2012JHydR..50....3H. doi:10.1080/00221686.2011.649839. S2CID 122193400.
  5. ^ 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.
  6. ^ "Dr. W. N. Bond". Nature. 140 (3547): 716. 1937. Bibcode:1937Natur.140Q.716.. doi:10.1038/140716a0.
  7. ^ a b Li, S (2018). "Dynamics of Viscous Entrapped Saturated Zones in Partially Wetted Porous Media". Transport in Porous Media. 125 (2): 193–210. arXiv:1802.07387. doi:10.1007/s11242-018-1113-3. S2CID 53323967.