Linear stability of a ferrofluid centred around a current-carrying wire

Investigated first is the linear stability of a Newtonian ferrofluid centred on rigid wire, surrounded by another with different magnetic susceptibility. An electric current runs through generating an azimuthal field that produces stress at interface fluids. Three-dimensional disturbances to system are considered, and linearised Navier–Stokes equations solved analytically in terms implicit expression for growth rate disturbance. The found numerically arbitrary Reynolds number, given explicitly inviscid Stokes regimes. next whose susceptibility varies radially, subject non-uniform field. It proven if gradient positive anywhere fluid, then linearly unstable. Moreover, it applying axial can stabilise both continuous discontinuous susceptibilities.