BOND

Overview

The BOND function calculates the Bond number (Bo), also known as the Eötvös number (Eo), a dimensionless quantity that measures the relative importance of gravitational forces compared to surface tension forces acting on a fluid interface. This function uses the fluids library’s Bond implementation from the fluids.core module.

The Bond number is fundamental in analyzing the behavior of liquid drops, bubbles, and menisci. When Bo >> 1, gravitational forces dominate and the interface tends to flatten; when Bo << 1, surface tension forces dominate and the interface maintains a more spherical shape. This makes the Bond number essential for applications such as two-phase flow analysis, bubble dynamics, droplet behavior in microfluidics, and capillary phenomena.

The Bond number is calculated using the following formula:

Bo = \frac{g(\rho_l - \rho_g)L^2}{\sigma}

where g is the acceleration due to gravity (9.80665 m/s²), \rho_l is the liquid density (kg/m³), \rho_g is the gas density (kg/m³), L is the characteristic length such as droplet diameter (m), and \sigma is the surface tension (N/m).

The function accepts four required parameters: rhol for liquid density, rhog for gas density, sigma for surface tension, and L for the characteristic length. For more details on the Bond number and related dimensionless numbers, see the fluids.core documentation and Perry’s Chemical Engineers’ Handbook (8th Edition, McGraw-Hill Professional, 2007).

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

Excel Usage

=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)

Returns (float): Bond number (float), or error message string.

Examples

Example 1: Water-air interface at typical scale

Inputs:

rhol	rhog	sigma	L
1000	1.2	0.0589	2

Excel formula:

=BOND(1000, 1.2, 0.0589, 2)

Expected output:

665187.23

Example 2: Oil-gas interface at medium scale

Inputs:

rhol	rhog	sigma	L
850	1.2	0.032	1.5

Excel formula:

=BOND(850, 1.2, 0.032, 1.5)

Expected output:

585273.13

Example 3: Mercury-air interface at small scale

Inputs:

rhol	rhog	sigma	L
13546	1.2	0.485	0.5

Excel formula:

=BOND(13546, 1.2, 0.485, 0.5)

Expected output:

68468.61

Example 4: Small water droplet in air

Inputs:

rhol	rhog	sigma	L
1000	1.2	0.072	0.01

Excel formula:

=BOND(1000, 1.2, 0.072, 0.01)

Expected output:

13.6

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 using fluids.core.Bond.

    See: https://fluids.readthedocs.io/fluids.core.html

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

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

    Returns:
        float: Bond number (float), or error message string.
    """
    try:
        rhol_ = float(rhol)
        rhog_ = float(rhog)
        sigma_ = float(sigma)
        L_ = float(L)
    except Exception:
        return "Error: All parameters must be numeric values."
    if sigma_ <= 0 or L_ <= 0:
        return "Error: sigma and L must be positive."
    if rhol_ < 0 or rhog_ < 0:
        return "Error: rhol and rhog must be non-negative."
    try:
        result = fluids_bond(rhol_, rhog_, sigma_, L_)
    except Exception as e:
        return f"Error: {str(e)}"
    return result

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