Weakly Nonlinear Marangoni Convection under an External Magnetic Field

Abstract

Nonlinear Marangoni instability in a thin layer of conducting fluid in the presence of a magnetic field is studied. The layer is bounded from below by a rigid, thermally and electrically perfect conductor and from above by the planar free surface. The ambient gas phase is assumed to be either insulating or conducting. The analysis is carried out by a successive approximation method, which allows for finite amplitude disturbances. Two amplitude equations are derived with coefficients depending on the Chandrasekhar and magnetic Prandtl numbers representing the magnetic field strength and the electromagnetic properties of the fluid. It is shown that the magnetic field does not change the flow pattern established in the case of thermocapillary convection without a magnetic field. But, the relevant parameters determining the conditions for emerging convective cells are influenced by its strength. A domain of subcritical instability is also displayed.