What is the Diffusion Coefficient?

The diffusion coefficient (also known as diffusivity) is a proportionality constant between the molar flux due to molecular diffusion and the gradient in the concentration of the species. In simpler terms, it measures how fast a substance spreads through a medium like a liquid or gas. It is a critical parameter in chemical engineering, molecular biology, and material science.

This calculator specifically uses the Stokes-Einstein equation, which is the most reliable model for calculating the diffusion of spherical particles undergoing Brownian motion in a viscous fluid.

How to Use This Calculator

Follow these simple steps to calculate the diffusivity of your particle:

• Temperature: Enter the temperature in degrees Celsius. The calculator will automatically convert this to Kelvin (K) for the thermodynamic calculation.
• Dynamic Viscosity: Enter the viscosity of the fluid in Pascal-seconds (Pa·s). For example, water at 25°C is approximately 0.00089 Pa·s.
• Particle Radius: Provide the radius of the diffusing particle in nanometers (nm).
• Calculate: Click the button to view the coefficient in m²/s along with the step-by-step breakdown.

Frequently Asked Questions (FAQs)

Why does temperature affect diffusion?

According to the kinetic theory, increasing the temperature increases the kinetic energy of molecules. This leads to more frequent and energetic collisions, causing the particles to spread (diffuse) faster. This is why temperature (T) is in the numerator of the Stokes-Einstein equation.

What are the typical units for diffusion?

The standard SI unit for the diffusion coefficient is meters squared per second (m²/s). In laboratory settings, you might also see centimeters squared per second (cm²/s).

What is k_B?

k_B is the Boltzmann constant, a fundamental physical constant that relates the average relative kinetic energy of particles in a gas with the thermodynamic temperature of the gas. Its value is approximately 1.380649 × 10⁻²³ J/K.