Predictions of metal droplet formation in gas metal arc welding. II. Journal of Applied Physics 84, 3530 (1998) Abstract. The mathematical model was developed for the initial stage of formation of an electrode metal droplet in the process of arc welding. Its essence lies in the fact that the presence of a temperature gradient in the boundary layer of the molten metal causes thermo-capillary instability, which leads to the formation of electrode metal droplets. А system of equations including Navier-Stokes equations, heat conduction and Maxwell's equations was solved as well as the boundary conditions for the system electrodes-plasma. Dispersion equation for thermo-capillary waves in the linear approximation for the plane layer was received and analyzed. The values of critical wavelengths, at which thermocapillary instability appears in the nanometer wavelength range, were found. The parameters at which the mode of a finedroplet transfer of the material takes place were theoretically defined.