Effect of magnetic field on the entrainment of magnetic fluid by a moving boundary of a plane slot

The effect of constant magnetic field on the outgoing flow of a magnetic fluid (MF) from a fluid “plug” (bridge) that it forms in a thin horizontal slot is studied. The flow is driven by the motion of the lower slot boundary (substrate) with constant velocity. The system is treated in the general framework of the Landau–Levich approximation. Namely, the solutions are, first, obtained for two distinct zones: the steady meniscus near the slot edge and the film flow along the moving substrate. The dynamics problem in the outgoing film, being singular on both its boundaries, is highly nontrivial and needs sophisticated handling. The overall flow regime is derived by splicing the “near” and “far” zone solutions. Involvement of magnetic field changes the situation drastically in comparison with the classical case as the field creates a body force inside the MF and an additional pressure jump at its surface. The resulting solution evidences that in the presence of magnetic field, the MF drain saturates and allows for large slot thicknesses, the regime that is totally impossible for any ordinary fluid. The built-up description may serve as a model prototype for an MF acoustic contact, an inherent element in any ultrasonic nondestructive testing technique. Such a contact can reduce the drain and stabilize the fluid bridge, for example, at rough scanned surfaces. The developed theory may also be applied to the coating problems, making ferromagnetic doping of the deposited compound a technologically advantageous feature.