7.6 Supplementary reading [potential flow top]

Potential flow in fluids is a classical subject, and general fluid mechanics texts such as Panton [56], Batchelor [57], Kundu [58], and Currie [59] have succinct descriptions of analytical techniques for potential flow. Potential flow in fluids has been discussed in great detail in the aerodynamics literature, since aerodynamic lift on airfoils for attached flow is well predicted by two-dimensional potential flow descriptions combined with Bernoulli’s equation for the pressure. To this end, aerodynamics texts such as Kuethe and Chow [60] and Anderson [61] cover potential flow in detail, including detailed discussion of distributed multipolar solutions (though they use different terminology as compared to this text). A key difference between the aerodynamic treatment and the potential flow observed in electroosmotic flows is the presence of circulation in aerodynamic flows. While aerodynamic analysis often focuses on circulation owing to its relation to lift forces, electroosmotic flows have no circulation.

While most practicing engineers solve modest Laplace equation systems with commercial differential equation solvers, large simulations often require more specialized approaches. Numerical solution of the Laplace equation is covered in many texts, including Kundu and Cohen [58] and Chapra and Canale [62]. The transform techniques discussed in this chapter map established solutions, e.g., the flow over a circle, to solve other systems, e.g., flow over an ellipse. For those interested in more advanced transform techniques, including Schwarz-Christoffel transforms, see [58].

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