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]

• ${\displaystyle \Delta \rho }$: 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)
• ${\displaystyle \gamma }$: surface tension, (SI units : N/m)

The Bond number can also be written as

where ${\textstyle \lambda _{\rm {c}}={\sqrt {{\gamma }/{\rho g}}}}$ 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.

References[]