Thermocapillary instability in deep weld keyholes

A theory is derived for the onset of a thermocapillary instability at the wall of the vapor-gas cavity formed during deep-penetration welding of metals by intense laser radiation. The basic physical factors causing the instability are identified. The quantitative conditions for its occurrence are derived. The curve of neutral (monotonic) stability is derived analytically. This curve relates the critical Marangoni number (or the intensity of the laser radiation) to the parameters of the wave perturbations and properties of the medium. When the thermocapillary effect and capillary perturbations of the free surface are taken into account simultaneously, the threshold for stability of the melt with respect to monotonic perturbations is lowered, particularly at small wave numbers. Estimates of the critical intensities of the laser radiation found here lie in the range (3–6) · 10⁹ W/m². This range corresponds roughly to the conditions prevailing during the laser processing of metals under deep penetration conditions.