Diffusion Coefficient Calculator

Diffusion is the motion of particles in a medium according to the concentration gradient. It's a type of mass transport that relies on random molecular motions to distribute particles from high to low concentration areas.

The diffusion coefficient (D) quantifies how fast particles spread through a medium. It has units of area per time (m²/s) and depends on particle size, medium properties, and temperature.

The calculation method depends on your system. For spherical particles in liquids, use the Stokes-Einstein equation: D = kT/(6πηr). For binary gas systems, use the Wilke-Lee correlation. For other shapes, use the Einstein relation with friction coefficients.

For a 2 nm spherical particle in water at 25°C (298 K), using water's viscosity of ~0.001 Pa·s, the diffusion coefficient is approximately 1.1 × 10⁻¹⁰ m²/s using the Stokes-Einstein equation.

The friction coefficient represents resistance to particle motion through the medium. According to Einstein's relation, D = kT/ξ, where ξ is the friction coefficient. Higher friction means slower diffusion and lower diffusion coefficient.

Use the Wilke-Lee correlation for estimating diffusion coefficients in binary gas systems at low pressure. It's an empirical correlation that typically agrees with experimental values within 5-10% accuracy.

Key factors include temperature (higher T increases D), particle size (smaller particles diffuse faster), medium viscosity (higher viscosity decreases D), and particle shape (affects friction coefficient).

Common units are m²/s (SI units) and cm²/s. For reference: water molecules in water have D ≈ 2.3 × 10⁻⁹ m²/s, while large proteins have much smaller coefficients around 10⁻¹¹ m²/s.