We study the electrohydrodynamic capillary instability of the interface between two uniform superposed viscous and electrically conducting fluids in the presence of a free surface charge, when there is heat and mass transfer across the interface. The fluids are subjected to the uniform electric field in the axial direction and the viscous potential flow theory is used for the investigation. A quadratic dispersion relation that accounts for the growth of disturbance waves is derived for the linear stability analysis and the stability of the system is analyzed theoretically and numerically. The stability criterion is given in terms of the critical value of applied electric field as well as critical wave number. Various graphs with respect to physical parameters such as electric field, heat transfer coefficients, conductivity and permittivity ratio are drawn and effect of various parameters is described. It is observed that free surface charge and electric field both have stabilizing effect on the stability of the system.
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