Capillary number, abbreviated as Ca, a dimensionless number, representing the relative effect of viscous forces against the surface tension between a liquid/gas or liquid/liquid interface. It is the ratio of viscous forces to surface tension forces. It's particularly relevant when dealing with fluid flows in small-scale or capillary systems, where surface tension effects become more pronounced. The capillary number helps determine whether the fluid behavior will be dominated by viscous effects or by surface tension effects.
Capillary number formula |
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\( Ca \;=\; \dfrac{ \mu \cdot v }{ \sigma }\) (Capillary Number) \( \mu \;=\; \dfrac{ Ca \cdot \sigma }{ v }\) \( v \;=\; \dfrac{ Ca \cdot \sigma }{ \mu }\) \( \sigma \;=\; \dfrac{ \mu \cdot v }{ Ca }\) |
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| Symbol | English | Metric |
| \( Ca \) = Capillary Number | \(dimensionless\) | \(dimensionless\) |
| \( \mu \) (Greek symbol mu) = Fluid Dynamic Viscosity | \(lbf-sec \;/\; ft^2\) | \( Pa-s \) |
| \( v \) = Fluid Velocity | \(ft \;/\; sec\) | \(m \;/\; s\) |
| \( \sigma \) (Greek symbol sigma) = Surface Tension | \(lbf \;/\; ft\) | \(N \;/\; m\) |
Capillary Number Interpretation
- Low Capillary Number (Ca << 1) - Surface tension dominates over viscous forces. This means the shape and behavior of interfaces (like droplets or bubbles) are primarily controlled by surface tension. For example, in a capillary tube, a liquid might form a spherical meniscus or resist moving because surface tension is holding it back.
- High Capillary Number (Ca >> 1) - Viscous forces dominate over surface tension. Here, the flow is strong enough to overcome surface effects, and interfaces might stretch, deform, or break apart more easily. Think of a fast-moving liquid dragging droplets along or shearing them.
- Intermediate Ca (Ca ≈ 1) - This is a transitional regime where viscous and surface tension forces are comparable, leading to complex behaviors depending on the specific system (droplet breakup or coalescence).
