Diffusion Coefficient Calculator
Calculate the diffusion coefficient (D) for particles in a medium using the Einstein-Smoluchowski equation. Determine how fast molecules or particles diffuse based on size, temperature, and medium viscosity.
Temperature in Celsius (will be converted to Kelvin)
Viscosity of medium in Pa·s (water = 0.001 at 20°C)
Radius of particle in meters (e.g., 1 μm = 1×10⁻⁶ m)
Select common medium or enter custom viscosity
What is diffusion coefficient?
Diffusion coefficient (D) measures how fast particles diffuse through a medium. It appears in Fick's law and the Einstein-Smoluchowski equation. Higher D means faster diffusion. Typical values: small molecules in water: 10⁻⁹ to 10⁻¹⁰ m²/s; proteins in water: 10⁻¹¹ m²/s; large particles: even smaller.
How do you calculate diffusion coefficient?
Use the Stokes-Einstein equation: D = kT / (6πηr), where k = 1.380649×10⁻²³ J/K (Boltzmann constant), T = temperature in Kelvin, η = dynamic viscosity in Pa·s, r = particle radius in meters. For a 1 μm particle in water at 298K: D = (1.38×10⁻²³ × 298) / (6π × 0.001 × 10⁻⁶) ≈ 2.2×10⁻¹³ m²/s.
What affects diffusion coefficient?
Three main factors: (1) Temperature: higher T → higher D (diffusion faster); (2) Particle size: larger r → lower D (harder to move); (3) Medium viscosity: higher η → lower D (more resistance). Also matters particle shape and medium structure.
What is the Einstein-Smoluchowski equation?
The Einstein-Smoluchowski equation relates D to thermal energy: D = kT / f, where f is the friction coefficient. For spheres, f = 6πηr (Stokes drag), giving D = kT / 6πηr. This comes from equating Brownian motion displacement to viscous drag, connecting diffusion to temperature and medium properties.
Why is diffusion coefficient important?
Diffusion coefficient determines reaction rates, particle transport, and mixing in biological and chemical systems. In cells, it limits how fast molecules reach enzymes. In drug delivery, it affects absorption. In environmental science, it predicts contaminant spread. In chromatography, it determines column efficiency.