Eötvös number


In fluid dynamics the Eötvös number, also called the Bond number, is a dimensionless number
measuring the importance of gravitational forces compared to surface tension forces and is used to characterize the shape of bubbles or drops moving in a surrounding fluid. The two names commemorate the Hungarian physicist Loránd Eötvös and the English physicist Wilfrid Noel Bond, 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:
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 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:
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.