Stokes radius

The Stokes radius or Stokes-Einstein radius of a solute is the radius of a hard sphere that diffuses at the same rate as that solute. Named after George Gabriel Stokes, it is closely related to solute mobility, factoring in not only size but also solvent effects. A smaller ion with stronger hydration, for example, may have a greater Stokes radius than a larger ion with weaker hydration. This is because the smaller ion drags a greater number of water molecules with it as it moves through the solution.

Stokes radius is sometimes used synonymously with effective hydrated radius in solution.Hydrodynamic radius, R_H, can refer to the Stokes radius of a polymer or other macromolecule.

According to Stokes’ law, a perfect sphere traveling through a viscous liquid feels a drag force proportional to the frictional coefficient ${\displaystyle f}$:

${\displaystyle F_{drag}=fs=(6\pi \eta a)s}$

where ${\displaystyle \eta }$ is the liquid's viscosity, ${\displaystyle s}$ is the sphere's drift speed, and ${\displaystyle a}$ is its radius. Because ionic mobility ${\displaystyle \mu }$ is directly proportional to drift speed, it is inversely proportional to the frictional coefficient:

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