Stokes Law and the Microscopic Interpretation of

One of the early results of continuum fluid mechanics was the determination of the frictional force exerted on a spherical particle as it moved through a viscous fluid. Stokes law relates the force on the particle f, to the particle radius r, its drift velocity v, and the viscosity of the medium r.  

In an electric field E = —Vy), the force on a representative ion of charge z is zeE if the ion is not being accelerated this force is balanced by friction in the same direction so that 

The ion mobility u, defined as velocity per unit electric field strength, is therefore 

To relate u to A consider an ionic species with mean velocity v the ion 

It is a question of some interest whether the solvent can be presumed to stick to the solvated ion as it diffuses through the solution. If instead it is assumed that the solvent slips by the solute the factor 6jt in (3.20) is reduced to 4n. This has no great qualitative effect on the picture to be developed. For a derivation of Stokes law see R. M. Fuoss and F. Accascina, Electrolyte Conductance (New York Interscience, 1959), pp. 53-59. Theoretical studies on hard-sphere liquids indicate that Stokes law applies if it is assumed that solvent slips by the molecules [B. J. Alder, D. M. Gass, and T. E. Wain-wright, /. Chem. Phys. 53, 3813 (1970)]. 

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