Morton Number formula |
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\( Mo \;=\; \dfrac{ g \cdot \mu^4 \cdot \Delta \rho }{ \rho^2 \cdot \sigma^3 }\) \( \mu \;=\; \sqrt[4] { \dfrac{ Mo \cdot \rho^2 \cdot \sigma^3 }{ g \cdot \Delta \rho } }\) \( \Delta \rho \;=\; \dfrac{ Mo \cdot \rho^2 \cdot \sigma^3 }{ g \cdot \mu^4 }\) \( \rho \;=\; \sqrt{ \dfrac{ g \cdot \mu^4 \cdot \Delta \rho }{ Mo \cdot \sigma^3 } }\) \( \sigma \;=\; \sqrt[3] { \dfrac{ g \cdot \mu^4 \cdot \Delta \rho }{ Mo \cdot \rho^2 } }\) |
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| Symbol | English | Metric |
| \( Mo \) = Morton number | \(dimensionless\) | \(dimensionless\) |
| \( g \) = Gravitational Acceleration | \(ft\;/\;sec^2\) | \(m\;/\;s^2\) |
| \( \mu \) (Greek symbol mu) = Dynamic Viscosity of Surrounding Fluid | \(lbf-sec\;/\;ft^2\) | \( Pa-s \) |
| \( \Delta \rho \) = Density Differential in the Phases | \(lbm\;/\;ft^3\) | \(kg\;/\;m^3\) |
| \( \rho \) (Greek symbol rho) = Density of Surrounding Fluid | \(lbm\;/\;ft^3\) | \(kg\;/\;m^3\) |
| \( \sigma \) (Greek symbol sigma) = Surface Tension | \(lbf\;/\;ft\) | \(N\;/\;m\) |
Morton number, abbreviated as Mo, a dimensionless number, is used in fluid mechanics to characterize the behavior of bubbles or droplets in a surrounding fluid. It is particularly relevant in the study of multiphase flows, such as in bubbly liquids or emulsions. The Morton number helps describe the balance between viscous forces, gravitational forces, and surface tension forces acting on the bubble or droplet.
Morton Number Interpretation
- Low Morton Number (Mo << 1) - Surface tension dominates over viscous and gravitational forces. Bubbles or droplets tend to remain spherical because surface tension is strong enough to resist deformation. Common in systems with low viscosity, high surface tension, or small density differences.
- High Morton Number (Mo >> 1) - Viscous forces and gravity dominate over surface tension. Bubbles or droplets are more likely to deform into non-spherical shapes (ellipsoidal or irregular) because surface tension is insufficient to maintain a spherical form. Typical in highly viscous fluids or systems with low surface tension.
- Intermediate Morton Number - A transitional regime where all three forces (gravity, viscosity, and surface tension) are comparable. The shape and behavior depend on the specific values of other parameters like the Reynolds number or Eötvös number.
