Chapter 7
Potential fluid flow

This chapter discusses the physical relevance of potential fluid flowto flows in microfluidic devices and describes analytical tools for creating potential flow solutions. While Appendix F focuses on a mathematical approach—solving theLaplace Equation, this chapter focuses more on the physics of the potential flow problem and the solution approach of the potential flow technique. This chapter also focuses on the use of complex mathematics for two-dimensional potential problems with plane symmetry. These plane-symmetric flows are relevant for microsystems, since microchannels are often shallower than they are wide and thus depth-averaged properties are often well-approximated by two-dimensional analysis.

In particular, we want to retain perspective on the engineering importance of these flows as well as 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, since 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 solution to more complicated problems. For example, 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.

[Return to Table of Contents]