Abstract
The present study is devoted to the classical problem on stability of a magnetic fluid layer under the influence of gravity and a uniform magnetic field. A periodical peak‐shaped stable structure is formed on the fluid surface when the applied magnetic field exceeds a critical value. The mathematical model describes a single peak in the pattern assuming axial symmetry of the peak shape. The field configuration in the whole space, the magnetic particle concentration inside the fluid and the free surface structure are unknown quantities in this model. The unknown free surface is treated explicitly, using a parametric representation with respect to the arc length. The nonlinear problem is discretized by means of a finite element method for the Maxwell's equations and a finite‐difference method for the free surface equations. Numerical modelling allows to get over‐critical equilibrium free surface shapes in a wide range of applied field intensities. Our numerical results show a significant influence of the particle diffusion on the overcritical shapes.
Highlights
Magnetic fluids are stable colloidal suspensions of ferromagnetic nano-particles in a carrier liquid
The present study is devoted to the classical problem of ferrohydrostatics on stability of a horizontal semi-infinite layer of a magnetic fluid under the influence of gravity and a uniform magnetic field normal to the plane free surface of the layer [13]
The main goal of the present study is to investigate the influence of the particle diffusion on a free magnetic-fluid surface shape in the case of uniform external magnetic fields
Summary
Magnetic fluids are stable colloidal suspensions of ferromagnetic nano-particles (of size 3-15 nm) in a carrier liquid (water, oil, bio-compatible liquid and others). The present study is devoted to the classical problem of ferrohydrostatics on stability (known as the normal field instability or the Rosensweig instability) of a horizontal semi-infinite layer of a magnetic fluid under the influence of gravity and a uniform magnetic field normal to the plane free surface of the layer [13]. A periodical peak-shaped structure is formed on the fluid surface when the applied magnetic field exceeds a critical value. A modified free surface of the layer presents a new static state. This phenomenon was observed first experimentally [5]. Up to now all analytical and numerical investigations of the Rosensweig instability assumed a uniform ferromagnetic particle distribution in the bulk of the magnetic fluid for any applied field intensity
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