Mathematical modeling of electrokinetic effects in micro and nano fluidics

Abstract

In engineering applications familiar from everyday experience fluid flow is almost always pressure driven. The scaling law for the pressure head needed to drive a fixed flux through a circular capillary, is according to the celebrated Poiseuille formula, inversely proportional to the fourth power of capillary diameter. Thus, when it comes to small scales: microns and below; the electrokinetic method of transporting fluids appear increasingly attractive. Here the Voltage drop needed to maintain a flux increases inversely as only the second power of the capillary diameter. In this brief introduction to the subject of electrokinetic flows, the foundations are developed assuming that the reader has only minimal prior knowledge in the area. First, the laws of incompressible hydrodynamics are summarized followed by a review of electrostatics. These two streams are then interwoven with the laws of ionic transport to explore electroosmotic flow and its effect on transport of solutes. The focus of this exposition is on practical applications in microfluidic systems such as capillary electrophoresis. © 2010 Springer-Verlag US.