CAPILLARY

Overview

The CAPILLARY function calculates the Capillary number (Ca), a dimensionless number that characterizes the relative effect of viscous forces versus surface tension forces acting across an interface between a liquid and a gas, or between two immiscible liquids. It is widely used in fluid mechanics, microfluidics, and enhanced oil recovery to describe the behavior of multiphase flows. The Capillary number is defined as:

where:

• $V$ is the characteristic velocity (m/s)
• $\mu$ is the dynamic viscosity (Pa·s)
• $\sigma$ is the surface tension (N/m)

For more information, see the fluids.core documentation  and the fluids GitHub repository .

This example function is provided as-is without any representation of accuracy.

Usage

To use the function in Excel:

=CAPILLARY(V, mu, sigma)

• V (float, required): Characteristic velocity in meters per second (m/s).
• mu (float, required): Dynamic viscosity in Pascal-seconds (Pa·s).
• sigma (float, required): Surface tension in Newtons per meter (N/m).

The function returns a single value (float): the Capillary number (dimensionless), or an error message (string) if the input is invalid or out-of-range.

Examples

Example 1: Water in a microchannel

In Excel:

=CAPILLARY(1.2, 0.01, 0.1)

Expected output:

Example 2: Oil droplet in water

In Excel:

=CAPILLARY(0.5, 0.05, 0.2)

Expected output:

Example 3: Low viscosity, high surface tension

In Excel:

=CAPILLARY(2.0, 0.001, 0.5)

Expected output:

Example 4: High viscosity, low velocity

In Excel:

=CAPILLARY(0.1, 0.2, 0.05)

Expected output:

Python Code

import micropip
await micropip.install('fluids')
from fluids.core import Capillary as _capillary
 
def capillary(V, mu, sigma):
    """
    Calculate the Capillary number (Ca) for a fluid system.
 
    Args:
        V: Characteristic velocity in meters per second (m/s).
        mu: Dynamic viscosity in Pascal-seconds (Pa·s).
        sigma: Surface tension in Newtons per meter (N/m).
 
    Returns:
        The Capillary number (dimensionless, float), or an error message (str) if the input is invalid or out-of-range.
 
    This example function is provided as-is without any representation of accuracy.
    """
    try:
        V_ = float(V)
        mu_ = float(mu)
        sigma_ = float(sigma)
    except Exception:
        return "Invalid input: could not convert arguments to float."
    if sigma_ == 0:
        return "Invalid input: sigma (surface tension) must not be zero."
    try:
        result = _capillary(V_, mu_, sigma_)
    except Exception as e:
        return f"Error: {str(e)}"
    return round(result, 6)

Live Notebook

Edit this function in a live notebook .

Live Demo