Effects of uniform and constant electromagnetic fields on the stability of thin layer of liquid metal flow

The use of thin liquid metal layers as shield against erosion and thermal loads of the inner reactor walls continues to be of interest. The degree and reliability of the protection depend on the stability of the liquid metal layer under the influence of the surrounding magnetic field. In this paper we treat analytically the problem dealing in particular with the stability of the liquid metal layer under the influence of a uniform surface normal magnetic field and its control by means of a transversal electrical field. The Karman-Polhausen integral method is used to reduce the system into two equations that describe the spatio-temporal variations of the flow rate and the film thickness. The proposed model improves the formulation of Korsunsky (1999) for high Reynolds numbers by including the second order terms. It is shown that Korsunsky's formulation overestimates the cut-off frequency and it does not foresee periodic stationary waves to develop on the free liquid surface. The electrical and magnetic fields' abilities to stabilize or destabilize the flow, as a function of the critical Reynolds number, are examined. The influence of the electromagnetic fields on the cut-off wave-number and growth rate of the perturbations in terms of the Reynolds number and wave-number is also presented.