# Bond Number

on . Posted in Dimensionless Numbers

Bond number, abbreviated as Bo, a dimensionless number, used in fluid dynamics to describe the relationship of gravitational force to surface tension force in a fluid system.

The interpretations of the Bond number depend on its magnitude:

• Bo << 1:  When the Bond number is much smaller than 1, surface tension forces dominate over gravitational forces.  In such cases, surface tension is the primary factor determining the fluid behavior, such as the formation of droplets or capillary effects.

• Bo >> 1:  When the Bond number is much larger than 1, gravitational forces dominate over surface tension forces.  The effects of gravity become more pronounced, and fluid behavior is primarily influenced by gravity, such as in free surface flows or large-scale fluid motion.

• Bo ≈ 1:  When the Bond number is close to 1, gravitational and surface tension forces are of comparable magnitude.  In this regime, both forces contribute significantly to the fluid behavior, and their interplay determines the specific characteristics of the system.

The Bond number is particularly relevant in the study of fluid mechanics involving small scale or microscale flows, such as droplet formation, liquid bridges, or fluid interactions with solid surfaces.  It provides insights into the balance of forces and aids in understanding the behavior of fluids in various applications.

## Bond Number formula

$$\large{ Bo = \frac{ \rho \; a \; l^2}{\sigma} }$$
Symbol English Metric
$$\large{ Bo }$$ = Bond number $$\large{dimensionless}$$
$$\large{ \rho }$$  (Greek symbol rho) = density $$\large{\frac{lbf}{in^2}}$$ $$\large{Pa}$$
$$\large{ a }$$ = acceleration $$\large{\frac{ft}{sec^2}}$$ $$\large{\frac{m}{s^2}}$$
$$\large{ l }$$ = length $$\large{in}$$  $$\large{mm}$$
$$\large{ \sigma }$$ = surface tension  $$\large{\frac{lbf}{ft}}$$  $$\large{\frac{N}{m}}$$ 