Introduction

Electrostatics and electrodynamics are essential features of micro- and nanofluidics. At the macroscale pumps, compressors and other fluid-handling devices move fluid using a pressure difference, as was noted in Chapter 4. However, as was demonstrated in Chapter 1, this is often not feasible at the micro- and nanoscale because very large pressure drops on the order of atmospheres are required for flows through channels under about 0.1 µm, channels that are often used in applications.

The objective of this chapter is to introduce, in a general way, the concept of an electric field at the advanced undergraduate level, typically associated with the material presented in an introductory physics class for physics majors; for those students already familiar with the principles of electrostatics, this chapter may be scanned or skipped.

In this chapter, the basics of electrostatics are presented, paying particular attention to the electric field associated with one or more charged spheres, planes, or cylindrical surfaces. In the course of discussion, the concept of a surface charge density is defined, which is a concept central to electrochemistry and micro- and nanofluidics. This is followed by a discussion of the fundamental law of Gauss relating the electric field to the charge density of a given medium. The concept of electrical potential is then introduced, and the similarities between the velocity potential of fluid mechanics are noted.

Next, the concept of an electric dipole is introduced, followed by the derivation of the Poisson equation of electrostatics, which is solved for several different situations.