Laws of migration

If the ion is in a fluid medium, then the electrostatic force seeking to accelerate the ion is opposed by a viscous force trying to slow the ion down. Though it strictly applies only to spheres of macroscopic dimensions, Stoke s law can provide an approximate expression 

If M/NA is the mass of the ion, then from Newton s second law of motion 

For common inorganic ions in aqueous solution, one can take the typical values M — 0.1 kg mol-1, r — 1.0 x 10-3 kgm 1s 1, z = (1 or 2), r— 0.3 nm and calculate a time constant of the order of 3xl0 14 s. Evidently, the limiting velocity is acquired virtually instantaneously, so that the adjective limiting may be dropped and v(t) contracted to v. 

Using the same typical values gives the (velocity/field) ratio as 

This quantity is known as the mobility of the ion and is given the symbol u. Some experimental values are given in Table 2 for ions in dilute aqueous solution. 

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Ravenstein, E. (1889) The Laws of Migration. Joiirnol of the Royal Statistical Society 52(2) 241-305. 

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