5.6 Summary [electrodynamics top]

This chapter presents basic relations for electrostatic and electrodynamics in electrolyte solutions. The most important electrostatic relation is Gauss’s law for electricity:

which relates the divergence of the electric displacement to the charge density when charge is motionless. Gauss’s law is the source of the Poisson equation as well as the electrostatic boundary conditions. The key electrodynamic relation is the charge conservation equation:

which describes the motion of charge and its relation to the net charge density. These two equations prescribe the solution of the electrical component of microfluidic problems. We can solve for the electric field distribution caused by charges, either net areal charge densities on surfaces (which are observed on most microfluidic substrates and at all electrode surfaces) or net volumetric charge densities in the fluid (which are observed near the substrate surface and throughout nanofluidic systems) with the relations in this chapter. In many microfluidic systems, electric fields play a central role through the effect of Coulomb forces on net charge density in the fluid.

We also present electrical circuit analysis, which simplifies our analytical task when the electrical components can be discretized. The key governing equations for electrical circuits are Ohm’s law:

combined with Kirchoff’s law

These relations combined with the voltage-current relationships for specific circuit elements cast the physical system of an electrical circuit in terms of a set of algebraic equations. We introduce analytic representations of the voltage and current, because the complex mathematics simplifies analysis for sinusoidal signals.

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