BOND

Overview

The BOND function calculates the Bond number (Bo), a dimensionless number that characterizes the relative importance of gravitational forces compared to surface tension forces acting on a fluid interface. The Bond number is commonly used in fluid mechanics to analyze bubble and droplet formation, capillarity, and multiphase flows. The Bond number is defined as:

where:

• $g$ is the acceleration due to gravity (m/s², fixed at 9.80665)
• $\rho_l$ is the density of the liquid (kg/m³)
• $\rho_g$ is the density of the gas (kg/m³)
• $L$ is the characteristic length (m)
• $\sigma$ 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:

=BOND(rhol, rhog, sigma, L)

• rhol (float, required): Density of the liquid (kg/m³).
• rhog (float, required): Density of the gas (kg/m³).
• sigma (float, required): Surface tension (N/m).
• L (float, required): Characteristic length (m).

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

Examples

Example 1: Water-Air Interface

In Excel:

=BOND(1000, 1.2, 0.0589, 2)

Expected output:

Example 2: Oil-Gas Interface

In Excel:

=BOND(850, 1.2, 0.032, 1.5)

Expected output:

Example 3: Mercury-Air Interface

In Excel:

=BOND(13546, 1.2, 0.485, 0.5)

Expected output:

Example 4: Small Droplet

In Excel:

=BOND(1000, 1.2, 0.072, 0.01)

Expected output:

Python Code

import micropip
await micropip.install('fluids')
from fluids.core import Bond as fluids_bond
 
def bond(rhol, rhog, sigma, L):
    """
    Calculate the Bond number (Bo), a dimensionless number comparing gravitational and surface tension forces.
 
    Args:
        rhol: Density of the liquid (kg/m³).
        rhog: Density of the gas (kg/m³).
        sigma: Surface tension (N/m).
        L: Characteristic length (m).
 
    Returns:
        The Bond number (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:
        rhol_ = float(rhol)
        rhog_ = float(rhog)
        sigma_ = float(sigma)
        L_ = float(L)
    except Exception:
        return "Invalid input: could not convert arguments to float."
    if sigma_ <= 0 or L_ <= 0 or rhol_ < 0 or rhog_ < 0:
        return "Invalid input: arguments must be positive."
    try:
        result = fluids_bond(rhol_, rhog_, sigma_, L_)
    except Exception as e:
        return f"Error: {str(e)}"
    return round(result, 3)

Live Notebook

Edit this function in a live notebook .

Live Demo