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 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 Interpretation
- Low Bond Number (Bo < 1) - Surface tension forces dominate over gravitational forces. This is common in small-scale systems (tiny droplets or capillary tubes), where the shape of the fluid interface is primarily determined by surface tension, often resulting in spherical or nearly spherical shapes.
- High Bond Number (Bo > 1) - Gravitational forces dominate over surface tension. This occurs in larger systems, where the fluid interface flattens or deforms significantly under the influence of gravity (a large puddle of water on a surface).
- Bond Number (Bo ≈ 1) - The forces of gravity and surface tension are comparable, and the behavior of the system is influenced by both in roughly equal measure.
Bond Number formula |
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\( Bo \;=\; \dfrac{ \rho \cdot a \cdot l^2 }{ \sigma }\) (Bond Number) \( \rho \;=\; \dfrac{ Bo \cdot \sigma }{ a \cdot l^2 }\) \( a \;=\; \dfrac{ Bo \cdot \sigma }{ \rho \cdot l^2 }\) \( l \;=\; \sqrt{ \dfrac{ Bo \cdot \sigma }{ \rho \cdot a } }\) \( \sigma \;=\; \dfrac{ \rho \cdot a \cdot l^2 }{ Bo }\) |
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| 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 | \(lbf-ft\) | \(N-m\) |
