Eötvös 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

Describing the ratio of gravitational to capillary forces, the Eötvös or Bond number is given by the equation:[6]

.
  • : difference in density of the two phases, (SI units: kg/m3)
  • g: gravitational acceleration, (SI units : m/s2)
  • L: characteristic length, (SI units : m) (for example the radii of curvature for a drop)
  • : surface tension, (SI units : N/m)

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 [6]. 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.

gollark: This might be useful to you if you... need to implement... osmarks internet radio™...?
gollark: Too bad, I read 100000 words or more today for no apparent reason and so you should obviously read my dubiously useful OIR™ information.
gollark: It really shouldn't be, but the entire subsystem crashes mysteriously sometimes for no reason.
gollark: Unfortunately, as I said, this is horribly broken for no debuggable reason. Fun!
gollark: This meant it could now do websockets, which would in theory allow greater interactivity and such, but which are currently just used to ship song data more efficiently.

References
  1. 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.
  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. 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. 1937. Bibcode:1937Natur.140Q.716.. doi:10.1038/140716a0.
  6. 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.
This article is issued from Wikipedia. The text is licensed under Creative Commons - Attribution - Sharealike. Additional terms may apply for the media files.