Boundary Effects on Ideal Fluid Forces and Kelvin's Minimum Energy Theorem

The electrostatic force on a charge above a neutral conductor is generally attractive. Surprisingly, that force becomes repulsive in certain geometries (Levin & Johnson 2011), a result that follows from an energy theorem in electrostatics. Based on the analogous minimum energy theorem of Kelvin (1849), valid in the theory of ideal fluids, we show corresponding effects on steady and unsteady fluid forces in the presence of boundaries. We present a model of a body approaching a boundary, where the unsteady force is typically repulsive (Lamb 1975, §137). We also present a model of a Bernoulli suction gripper, for which the steady force is typically attractive. Both the unsteady and steady forces are shown to reverse sign when boundaries approximate flow streamlines, at energy minima predicted by Kelvin's theorem.