Effect of a Time Varying Electric Field on the Charge Transport Equation

The charge transport equation is affected by thermal and concentration gradients as well as any applied electric field. In the charge transport equation the electrical conductivity, the electrical diffusivity and the electrical thermophoresis coefficient are all dependent on the electrical mobility which in turn is dependent on the collision time. When a time varying electric field is applied to a material it is known that the electrical mobility and the electrical conductivity become complex with a real and imaginary part. Does this mean the diffusion coefficient and the thermophoresis coefficient will also become complex? In this paper a time varying electric field is applied to a material (solid, liquid or gas), and the charge transport equation is developed using the contiguous collision averaging method. It is found that although the electrical mobility and the electrical conductivity do become complex the diffusion coefficient and the thermophoresis coefficient remain dependent on just the zero frequency mobility.