The Net Drift Velocity of an Ion Interacting with Its Atmosphere

The minus sign is used because both the electrophoretic and relaxation forces act in a direction opposite to that of the externally applied field. 

Since an ion is subject to a resuitant or net force, its drift velocity also must be a net drift veiocity resolvable into components. Furthermore, since each component force shouid produce a component of the overaii drift velocity, there must be three components of the net drift veiocity. The first component, which will be designated v°, is the direct result of the externally applied field only and excludes the influence of interactions between the ion and the ionic cloud the second is the electrophoretic component Vg and arises from the participation of the ion in the electrophoretic motion of its cioud finaiiy, the third component is the reiaxation field component originating from the reiaxation force that retards the drift of the ion. Since the electrophoretic and reiaxation forces act in a sense opposite to the externally applied eiectric field, it follows that the electtophoretic and relaxation components must diminish the overall drift velocity (Fig. 4.91), i.e., 

The next step is to evaluate the electrophoretic and relaxation components of the net drift velocity of an ion. 

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