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# Bond number

In fluid mechanics, the Bond number, notated Bo, is a dimensionless number expressing the ratio of body forces (often gravitational) to surface tension forces:

${\rm Bo} = \frac{\rho a L^2}{\gamma}$

where

• ρ is the density, or the density difference between fluids.
• a the acceleration associated with the body force, almost always gravity.
• L the 'characteristic length scale', e.g. radius of a drop or the radius of a capillary tube.
• γ is the surface tension of the interface.

Sometimes the density scale used is the difference in density between the two phases, Δρ.

The Bond number is a measure of the importance of surface tension forces compared to body forces. A high Bond number indicates that the system is relatively unaffected by surface tension effects; a low number (typically less than one is the requirement) indicates that surface tension dominates. Intermediate numbers indicate a non-trivial balance between the two effects.

The Bond number is the most common comparison of gravity and surface tension effects and 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 dimensionless numbers are related to the Bond number:

$\rm Bo = Eo = 2 Go^2 = 2 De^2\,$

Where Eo,Go, and De are respectively the Eötvös, Goucher, and Deryagin numbers. The "difference" between the Goucher and Deryagin numbers is that the Goucher number (arises in wire coating problems) uses the letter R to represent length scales while the Deryagin number (arises in plate film thickness problems) uses L.