# 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.  It is commonly used to analyze the behavior of fluids or fluid interfaces, especially in situations where surface tension plays a significant role.

The Bond number compares the weight or inertial forces acting on a fluid column or interface to the cohesive forces caused by surface tension.  A low Bond number indicates that surface tension forces dominate, leading to a more pronounced liquid behavior, such as capillary action or droplet formation.  On the other hand, a high Bond number suggests that gravitational or inertial forces are dominant, resulting in less noticeable surface tension effects.

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

$$Bo \;=\; \rho \; a \; l^2 \;/\; \sigma$$     (Bond Number)

$$\rho \;=\; Bo \; \sigma \;/\; a \; l^2$$

$$a \;=\; Bo \; \sigma \;/\; \rho \; l^2$$

$$l \;=\; \sqrt{ Bo \; \sigma \;/\; \rho \; a }$$

$$\sigma \;=\; \rho \; a \; l^2 \;/\; Bo$$

Symbol English Metric
$$Bo$$ = Bond Number $$dimensionless$$ $$dimensionless$$
$$\rho$$  (Greek symbol rho) = Fluid Density $$lbf\;/\;in^2$$ $$Pa$$
$$a$$ = Fluid Acceleration $$ft\;/\;sec^2$$ $$m\;/\;s^2$$
$$l$$ = Length $$in$$  $$mm$$
$$\sigma$$ = Fluid Surface Tension  $$lbf-ft$$  $$N-m$$

Tags: Flow Fluid