Stokes–Einstein relation
E31544
The Stokes–Einstein relation is a fundamental equation in statistical physics that links the diffusion coefficient of a particle in a fluid to its size, the fluid’s viscosity, and temperature.
Statements (49)
| Predicate | Object |
|---|---|
| instanceOf |
equation in statistical physics
→
physical law → |
| appliesTo |
Brownian particles
→
Newtonian fluids → dilute suspensions → spherical particles → |
| assumes |
continuum hydrodynamics
→
isotropic medium → low Reynolds number → no-slip boundary condition → overdamped motion → thermal equilibrium → |
| category |
diffusion
→
transport phenomena → |
| derivedFrom |
Einstein theory of Brownian motion
→
Stokes law for viscous drag → |
| describes |
translational diffusion of spherical particles
→
|
| expresses |
diffusion coefficient is directly proportional to temperature
→
diffusion coefficient is inversely proportional to fluid viscosity → diffusion coefficient is inversely proportional to particle radius → |
| field |
colloid science
→
physical chemistry → soft condensed matter physics → statistical physics → |
| hasComponentConcept |
Brownian motion
→
viscous drag → |
| hasForm |
D = k_B T / (6 π η R)
→
|
| knownLimitation |
breaks down for supercooled liquids
→
may fail for highly crowded environments → may fail for strongly interacting colloids → |
| namedAfter |
Albert Einstein
→
George Gabriel Stokes → |
| relatesQuantity |
Boltzmann constant
→
absolute temperature → diffusion coefficient → fluid viscosity → particle radius → |
| usedFor |
characterizing colloidal dispersions
→
estimating particle size from diffusion measurements → interpreting dynamic light scattering experiments → microrheology → nanoparticle size determination → |
| validWhen |
hydrodynamic interactions are well described by continuum theory
→
particle size is much larger than solvent molecules → |
| variable |
D
→
R → T → k_B → η → |
Referenced by (1)
| Subject (surface form when different) | Predicate |
|---|---|
|
Einstein–Smoluchowski relation
→
|
relatedConcept |