The effects of entrainment accompanying mass, momentum, and energy transport from the keyhole wall on keyhole collapse during high-power-density laser or electron beam drilling are theoretically and systematically investigated in this study. High intensity beam drilling is widely used in components, packaging and manufacturing technologies, micro-electromechanical-systems (MEMS), rapid prototyping manufacturing, and keyhole welding. This study proposes a quasi-steady, one-dimensional transport model to predict supersonic and subsonic flow behavior of the two-phase, vapor–liquid dispersion in a keyhole and applies the Young–Laplace equation to calculate the keyhole shape. The results show that the keyhole collapse, representing decreased or vanished radius, is susceptible to mass ejection at the base and entrainment from the side wall. Deposition of a mixture of gas and droplets in the keyhole stabilizes deformation of the keyhole. Enhanced energy and decreased axial component of momentum associated with entrainment are also apt to keyhole collapse. The predicted results agree with axial variations of transport variables of a compressible flow through a divergent and convergent nozzle, and their exact analytical solutions in the absence of friction, energy absorption, and entrainment. An understanding of the effects of ejected and entrained mass in the keyhole on drilling efficiency is therefore provided.

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