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
Ca
Bo
Describing the ratio of gravitational to capillary forces, the Eötvös or Bond number is given by the equation:
\Delta\rho
\gamma
The Bond number can also be written aswhere 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. 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. This is defined as: