Entrainment of magnetic fluid by a moving boundary of a plane gap

A fluid mechanics problem is solved which technological prototype is a fluid acoustic contact that is an inherent element of ultrasonic non-destructive testing procedures. It is well known that the acoustic contact established with an ordinary fluid suffers from essential disadvantage that is the loss of stability due to the gravity-induced fluid leakage in the course of dynamic scanning. The use of magnetic fluid (MF) is one of the ways to resolve the issue. A compact portion of MF held in place by a permanent magnet enables one to maintain a stable acoustic contact (fluid bridge) under arbitrary orientation of the ultrasonic sensor and, simultaneously, to radically minimize the drain of the contact fluid. The model system under consideration comprises a MF bridge that fills a flat gap, one of whose boundaries moves with constant velocity. Due to its wetting by the fluid, the receding plane carries away a fluid film thus depleting the contact. Theoretical expressions are obtained which define the profile of the film in the dynamic regime and the dependencies of the magnetic fluid drain on the boundary velocity, gap height and configuration of the imposed magnetic field. On that basis the optimal parameters are evaluated which ensure effective retention of the fluid contact under minimal drain of the fluid from it.