Electrophoretic Component of the Drift Velocity

The electrophoretic component Vg of the drift velocity of an ion is equal to the electrophoretic velocity of its ionic cloud because the central ion shares in the motion of its cloud. If one ignores the asymmetry of the ionic cloud, a simple calculation of the electrophoretic velocity Vg can be made. 

The ionic atmosphere is accelerated by the externally applied electric force Z6qX but is retarded by a Stokes viscous force. When the cloud attains a steady-state electrophoretic velocity v, then the viscous force is exactly equal and opposite to the electric force driving the cloud 

The general formula for Stokes viscous force is 6nnjv, where r and v are the radius and velocity of the moving sphere. In computing the viscous force on the cloud. 

This is the expression for the eiectrophoretic contribution to the drift veiocity of an ion. 

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