Capillary Number Calculator

Capillary Number Inputs

Formula Used

The capillary number compares viscous stresses to surface tension forces in a moving interface. It is defined as:

Ca = μ V / σ

• μ = dynamic viscosity (Pa·s)
• V = characteristic velocity (m/s)
• σ = surface tension (N/m)

This calculator also supports μ = νρ and V = Q/A when those measurements are available.

How to Use This Calculator

1. Choose a viscosity method: enter μ directly, or compute μ from ν and ρ.
2. Choose a velocity method: enter V directly, or compute V from Q and area or diameter.
3. Enter surface tension σ and select the correct unit.
4. Click Calculate to display Ca above the form.
5. Use the export buttons to download CSV or PDF records.

Example Data Table

Example Ca values are computed using Ca = (μ·V)/σ with μ in Pa·s and σ in N/m.

Capillary Number Guide

1) What the capillary number represents

The capillary number, Ca, is a dimensionless ratio of viscous stresses to surface tension forces. It helps predict whether an interface resists deformation or stretches with flow. Low values favor rounded droplets and stable menisci, while higher values promote elongation, film formation, and wetting transitions.

2) Typical parameter ranges in practice

Many aqueous systems have surface tension around 20–80 mN/m, while oils can be lower, especially with surfactants. Dynamic viscosity spans roughly 1 mPa·s (water-like) to 1000+ mPa·s (polymeric or heavy oils). Characteristic velocities can range from millimeters per second in porous media to meters per second in coating jets.

3) Interpreting Ca regimes with useful thresholds

A common engineering split is Ca < 0.01 where surface tension dominates, 0.01 ≤ Ca < 1 where both effects matter, and Ca ≥ 1 where viscous forces dominate. These bands are practical guides for estimating droplet breakup likelihood, contact line mobility, and the tendency to leave liquid films on walls.

4) Microfluidics and droplet formation insights

In microchannels, a modest velocity increase can shift Ca by orders of magnitude because channel sizes encourage precise, high-speed flows. For example, μ = 2 mPa·s, V = 0.05 m/s, σ = 30 mN/m gives Ca ≈ 0.0033, typically yielding stable, surface-tension-controlled droplets. Raising V to 0.5 m/s lifts Ca to ~0.033, often changing breakup frequency and droplet length.

5) Coating, printing, and film thickness behavior

Coating flows frequently target intermediate capillary numbers where films form smoothly without excessive ribbing. When Ca rises, viscous drag pulls thicker films, but surface tension still acts to level the interface. In many coating studies, values from ~0.01 to 0.3 are common, depending on viscosity and substrate speed, with σ reductions (via additives) increasing Ca for the same operating speed.

6) Porous media and enhanced oil recovery context

In porous media displacement, increasing Ca can help overcome capillary trapping. Typical velocities are low, but μ can be high for injected polymers, and σ may be reduced with surfactants. Even a tenfold reduction in σ can produce a tenfold increase in Ca, which can alter residual saturation and improve mobilization. Use consistent velocity definitions (e.g., Darcy vs. pore velocity) for meaningful comparisons.

7) Measurement tips and data quality checks

Surface tension is sensitive to temperature, contamination, and surfactant concentration; record measurement conditions alongside σ. For viscosity, verify whether your value is dynamic μ or kinematic ν, and convert with density using μ = νρ when needed. For velocity, choose a characteristic value tied to the interface motion, not an unrelated bulk average.

8) Using this calculator for reporting and audits

This tool standardizes unit conversions and keeps a clear audit trail by exporting results to CSV or PDF. When comparing experiments, report μ, V, and σ in SI alongside Ca, and state the chosen velocity definition. If results change unexpectedly, re-check σ units (mN/m vs N/m) and verify that area or diameter-based velocity inputs match the actual flow geometry.

FAQs

1) Is capillary number the same as Weber number?

No. Ca compares viscous forces to surface tension, while Weber number compares inertial forces to surface tension. Use Ca for viscosity-driven interface behavior and We for high-speed, inertia-dominated breakup.

2) What units should I use for surface tension?

Use N/m in SI. This calculator accepts N/m, mN/m, and dyn/cm. Remember: 1 mN/m equals 1 dyn/cm equals 0.001 N/m.

3) How do I convert kinematic viscosity to dynamic viscosity?

Multiply kinematic viscosity by density: μ = νρ. Ensure ν is in m²/s and ρ is in kg/m³ to obtain μ in Pa·s.

4) Which velocity should I choose for Ca?

Use a characteristic velocity tied to the interface motion, such as mean channel velocity in microfluidics, substrate speed in coating, or pore velocity in porous media studies.

5) Why is my Ca extremely large?

Check units first. A common error is entering σ in mN/m while selecting N/m. Also confirm viscosity units and whether velocity was computed using the correct area or diameter.

6) What Ca range indicates surface-tension control?

Many flows behave surface-tension controlled when Ca is below about 0.01. Interfaces tend to remain rounded, and capillary pressure strongly influences meniscus and droplet shapes.

7) Can Ca predict droplet breakup by itself?

It helps, but breakup also depends on geometry, viscosity ratio, confinement, and sometimes inertia. Combine Ca with device dimensions and, when needed, other groups like Reynolds or Weber numbers.