Electrostatic Gradients Cause Ion Flows

Concentration gradients can cause particles to flow, whether the particles are neutral or charged. In addition, charged particles flow if they are subject to gradients of electrostatic potential. According to Equation (20.12), the force on a charged particle equals (charge ze) x (electrostatic field E), 

Equation (22.40) is an expression of Ohm s law, which says that electrical current flow is linearly proportional to the difference in applied electrostatic potential, orvoltage. When a voltage V = (//(0)-(/y( ) is applied, charge carriers (ions or electrons) will flow, giving an electrical current I, 

If an ion is driven by both a gradient of its concentration and a gradient of electrostatic potential, then its flux Jp will be the sum of the component fluxes. 

Equation (22.42) is the Nemst-Planck equation. The subscript p on the flux Jp indicates that this is the flux of particles. Because each particle carries a charge ze, the flux of charge Jc can be expressed as 

Substituting Equation (22.43) and the Einstein relation D = ukT into Equation (22.42) gives 

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