Deformation of a magnetic liquid drop and unsteady flow inside and outside it in a non-stationary magnetic field

TL;DR

This paper theoretically investigates the deformation and unsteady flow of a magnetic liquid drop in a non-stationary magnetic field, considering low Reynolds numbers and quasi-stationary magnetic variations.

Contribution

It introduces a theoretical model for small oscillations of a magnetic liquid drop under slow, non-stationary magnetic fields, accounting for unsteady flow and magnetic effects.

Findings

Flow inside and outside the drop is characterized under non-stationary magnetic influence.

The model accounts for unsteady inertia effects at low Reynolds numbers.

Magnetic field variations are slow enough to justify quasi-stationary approximation.

Abstract

Small steady-state deformational oscillations of a drop of a viscous magnetic liquid in a non-stationary uniform magnetic field are theoretically investigated for low Reynolds numbers. The drop is suspended in another viscous magnetic liquid immiscible with the former. The non-stationary magnetic field causes flow inside and outside the drop. The inertia is taken into account by regarding the flow as essentially unsteady. The variation of the magnetic field is so slow that the approximation of quasi-stationary magnetic field may be used.