Interfacial instability of ferrofluid flow under the influence of a vacuum magnetic field

doi:10.1007/s10483-021-2758-7

Abstract

Abstract: This study is to numerically test the interfacial instability of ferrofluid flow under the presence of a vacuum magnetic field. The ferrofluid parabolized stability equations (PSEs) are derived from the ferrofluid stability equations and the Rosensweig equations, and the characteristic values of the ferrofluid PSEs are given to describe the ellipticity of ferrofluid flow. Three numerical models representing specific cases considering with/without a vacuum magnetic field or viscosity are created to mathematically examine the interfacial instability by the computation of characteristic values. Numerical investigation shows strong dependence of the basic characteristic of ferrofluid Rayleigh-Taylor instability (RTI) on viscosity of ferrofluid and independence of the vacuum magnetic field. For the shock wave striking helium bubble, the magnetic field is not able to trigger the symmetry breaking of bubble but change the speed of the bubble movement. In the process of droplet formation from a submerged orifice, the collision between the droplet and the liquid surface causes symmetry breaking. Both the viscosity and the magnetic field exacerbate symmetry breaking. The computational results agree with the published experimental results.

Key words: interfacial instability, ferrofluid, vacuum magnetic field, parabolized stability equation (PSE)

2010 MSC Number:

35K55
76T10

Mingjun LI, Li ZHU. Interfacial instability of ferrofluid flow under the influence of a vacuum magnetic field. Applied Mathematics and Mechanics (English Edition), 2021, 42(8): 1171-1182.

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