Fluid Dynamics | 2021
Deformation of an Inviscid Magnetizable Liquid Drop in a Non-Stationary Magnetic Field
Abstract
Abstract— Variation in the shape of a magnetizable liquid drop suspended in another immiscible magnetizable liquid in the presence of a non-stationary uniform magnetic field is theoretically investigated in the case of high Reynolds numbers. The system of equations consists of the continuity equation for incompressible liquid, the equation of motion for an ideal incompressible liquid, and Maxwell’s equations in the quasi-stationary and ferrohydrodynamic approximations. To solve the problem, the representation of the magnetic field strength and the liquid velocity in form of a multipole expansion expressed in terms of irreducible tensors is used. In such an approach the magnetic field strength and the velocity can be sought for in the form of series with vector and tensor coefficients for which some relations are obtained that make it possible to determine the coefficients. Using these relations, the coefficients are sought in the form of asymptotic expansions in a parameter whose smallness ensures small deformations of the drop. The flow velocity, the magnetic field strength, and the shape of drop are found correct to terms of the first order with respect to the small parameter. The problems of forced and natural drop oscillations generated by switching on instantaneously-applied harmonically oscillating and rotating magnetic fields are solved.