This chapter discusses the physical relevance of potential fluid flow to flows in microfluidic devices and describes analytical tools for creating potential flow solutions. This chapter also focuses on the use of complex mathematics for 2D potential problems with plane symmetry. These plane-symmetric flows are relevant for microsystems, because microchannels are often shallower than they are wide and thus depth-averaged properties are often well approximated by 2D analysis.

In particular, we want to retain perspective on the engineering importance of these flows as well as on the relative importance of analysis versus numerics. The Laplace equation is rather straightforward to solve numerically, and therefore numerical simulation is a suitable approach for most Laplace equation systems. For example, simulation of the electroosmotic flow within a microdevice with a complicated geometry would be simulated, because analytical solution would be impossible. Despite the importance of numerics, the analytical solutions are important because they lend physical insight and because simple analytical solutions for important cases (for example, the potential flow around a sphere) facilitate expedient solutions of more complicated problems. For example, the study of electrophoresis of a suspension of charged spheres is typically analyzed with techniques informed by the analytical solution for potential flow around a sphere and not with detailed and extensive numerical solutions of the Laplace equation.