At low Reynolds number, which equation relates the diffusion coefficient of spherical particles to temperature, viscosity, and particle radius?

At low Reynolds number, which equation relates the diffusion coefficient of spherical particles to temperature, viscosity, and particle radius?

• A. Fick's law
• B. Stokes-Einstein equation
• C. Boyle's law
• D. Raoult's law

Answer: (B)

At low Reynolds numbers, diffusion of a spherical particle in a viscous fluid is governed by the Stokes-Einstein relation, which links the diffusion coefficient to temperature, viscosity, and particle radius: D = k_B T / (6 π η R). This shows diffusion increases with temperature (more thermal energy to drive motion) and decreases with the fluid’s viscosity and the particle’s size (greater resistance and larger drag). The diffusion coefficient’s dependence on T, η, and R is not captured by Fick’s law, which just describes how flux relates to a concentration gradient, nor by Boyle’s or Raoult’s laws, which pertain to gas behavior and vapor-liquid equilibrium.

At low Reynolds numbers, diffusion of a spherical particle in a viscous fluid is governed by the Stokes-Einstein relation, which links the diffusion coefficient to temperature, viscosity, and particle radius: D = k_B T / (6 π η R). This shows diffusion increases with temperature (more thermal energy to drive motion) and decreases with the fluid’s viscosity and the particle’s size (greater resistance and larger drag). The diffusion coefficient’s dependence on T, η, and R is not captured by Fick’s law, which just describes how flux relates to a concentration gradient, nor by Boyle’s or Raoult’s laws, which pertain to gas behavior and vapor-liquid equilibrium.