Extending the Hele-Shaw Analogy: Magnetic Fields Induce Circulation

Viscously-dominated flow between two closely-spaced plates is described by two-dimensional potential flow according to the standard Hele-Shaw approximation. When driven exclusively by pressure, the class of realizable potential flows is highly restricted: only flows with exactly zero circulation are possible. For example, the Hele-Shaw experiments presented in Van Dyke's famous Album of Fluid Motion clearly illustrate this zero-circulation restriction.  In the present work, we demonstrate how the Hele-Shaw cell can be used to capture flows with circulation -

by using a conducting fluid and applying a constant magnetic field normal to the plates. We describe the physical picture and experimentally re-create canonical Hele-Shaw flows from Album of Fluid Motion now with arbitrary amounts of circulation induced by electromagnetic effects. The experimental flows are well described by our accompanying theoretical model.