Hydrodynamic and hydromagnetic stability

On the application of high electric fields to a dielectric fluid, a convective motion of the fluid is induced. By controlling the fluid motion in nonuniform dc fields, a new type of fluid motor is developed. An angular velocity of more than 15 s−1 (150 rpm) can be achieved at a dc voltage of 5 kV for a motor with a rotor radius of 10 mm. The efficiency of energy transformation from electric to kinetic energy is about 4%. Since magnetic fields and switching circuits are not required, the advantage of the fluid motor will be enhanced by size reduction. The dielectric fluid motor is attractive as a source of mechanical energy in a micromachine.

Dielectric fluid motors

In this paper we use a combination of analytical and numerical techniques to analyse the effect of a uniform vertical magnetic field on the onset of steady Benard-Marangoni convection in a horizontal layer of quiescent, electrically conducting fluid subject to a uniform vertical temperature gradient. The critical values of the Rayleigh and Marangoni numbers for the onset of steady convection are calculated and the latter is found to be critically dependent on the non-dimensional Crispation and Bond numbers. The stability of the layer to long wavelength disturbances is analysed and the two different asymptotic limits of strong surface tension (small Crispation number) and strong magnetic field (large Chandrasekhar number) are investigated. In the latter case analytical results for the critical Rayleigh and Marangoni numbers are obtained and are found to be in excellent agreement with the results of numerical calculations. We conclude that the presence of the magnetic field always has a stabilising effect on the layer. Treating the Marangoni number as the critical parameter we show that if the free surface is non-deformable then any particular disturbance can be stabilised with a sufficiently strong magnetic field, but if the free surface is deformable and gravity waves are excluded then the layer is always unstable to infinitely long wavelength disturbances with or without a magnetic field. Including gravity has a stabilising effect on the long wavelength modes, but not all disturbances can be stabilised no matter now strong the magnetic field is.

The effect of a uniform magnetic field on the onset of steady Bénard-Marangoni convection in a layer of conducting fluid

Onset of natural convection under an electric fieldt

In this paper a combination of analytical and numerical techniques are used to analyze the effect of a uniform vertical magnetic field on the onset of steady Marangoni convection in a horizontal layer of quiescent, electrically conducting fluid with a uniform vertical temperature gradient subject to a prescribed heat flux at its rigid lower boundary. Critical Marangoni numbers for the onset of instability are calculated which are significantly different from those calculated previously in the case of an isothermal lower boundary. Analytical results for the behavior of the critical Marangoni number in the asymptotic limit of large magnetic field strength are also obtained. It is concluded that the magnetic field always has a stabilizing effect on the onset of steady Marangoni convection, but that when the free surface is deformable situations with a sufficiently large Marangoni number will always have unstable modes no matter how strong the applied magnetic field is.

The effect of a uniform magnetic field on the onset of steady Marangoni convection in a layer of conducting fluid with a prescribed heat flux at its lower boundary

Tanasawa Ichiro

Papers

Onset of natural convection under an electric fieldt

Effect of magnetic field on onset of Marangoni convection

Effect of magnetic field and buoyancy on onset of Marangoni convection