Variables
Description
What is this formula?
The Stokes-Einstein equation calculates the diffusion coefficient of spherical particles suspended in a fluid based on temperature, viscosity, and particle size.
When to use it
Use this formula in chemical physics, colloid science, nanotechnology, and biophysics when estimating molecular or particle diffusion in liquids.
Example
A nanoparticle with radius 5×10^-9 m diffuses in water at 298 K. The dynamic viscosity of water is 0.001 Pa·s.
Data:
kB = 1.380649×10^-23 J/K
T = 298 K
eta = 0.001 Pa·s
r = 5×10^-9 m
Formula:
D = kB*T/(6*pi*eta*r)
Substitution:
D = (1.380649×10^-23 × 298)/(6 × pi × 0.001 × 5×10^-9)
Result:
D ≈ 4.37×10^-11 m²/s
The particle diffusion coefficient is approximately 4.37×10^-11 m²/s.
Applications
- Nanoparticle transport
- Colloidal suspensions
- Molecular diffusion studies
- Biophysics and cell transport
- Polymer and fluid science