Diffusion Coefficient Calculator
Relate particle size, fluid viscosity, and temperature to Brownian diffusion rates for spherical particles.
Diffusion coefficient
2.1827e-10 m2/s
How to Use This Calculator
Measure particle size
Provide the hydrodynamic radius of the diffusing particle in meters.
Determine fluid viscosity
Enter dynamic viscosity in Pascal seconds (Pa*s). Water at room temperature is about 0.001 Pa*s.
Enter absolute temperature
Use Kelvin for consistency with the Boltzmann constant.
Review diffusion rate
The result gives m2 per second, useful for estimating mixing or residence times.
Formula
D = kB T / (6 pi mu r)
kB is the Boltzmann constant, T temperature in Kelvin, mu dynamic viscosity, r particle radius.
Example
At 298 K, mu = 0.001 Pa*s, r = 1e-9 m: D = 1.38e-23 * 298 / (6 pi * 0.001 * 1e-9) about 4.36e-10 m2/s.
Full Description
The Stokes-Einstein relation links random Brownian motion to fluid friction, assuming spherical particles in a continuum fluid.
It provides a quick way to estimate diffusion for nanoparticles, proteins, or droplets and can help interpret dynamic light scattering measurements.
Frequently Asked Questions
Can I use diameter instead of radius?
Convert diameter to radius by dividing by two before entering the value.
Does the equation work for gases?
It is less accurate for gases where free molecular effects dominate. Use Chapman-Enskog correlations instead.
What if the particle is not spherical?
Use an effective hydrodynamic radius that matches experimental diffusion measurements or apply correction factors.
Can viscosity be temperature dependent?
Yes. Supply the viscosity at the same temperature as the diffusion calculation for best results.
How does solvent choice affect D?
Higher viscosity solvents decrease diffusion proportionally, while higher temperatures increase it linearly.