Thermocapillary instabilities in additive manufacturing environments*

In additive manufacturing, or three-dimensional printing, material is deposited under rapidly moving heat sources and subsequently solidifies under the ambient thermal field. The substrate on which the melt is deposited ranges from solid to liquid. A model is proposed in which the deposited melt feels effective slip and heat transfer at its base. We determine the effect of various substrates on the hydrothermal instabilities of the liquid melt pool. In particular, we investigate the onset of three-dimensional thermocapillary instabilities in a low-capillary-number liquid layer of arbitrary depth and find that the preferred mode of instability consists of a selection of two- and three-dimensional hydrothermal waves, longitudinal rolls and longitudinal travelling waves. Which of these appear depends intricately on the properties of the substrate involved. As the slip increases, two-dimensional hydrothermal waves and longitudinal travelling waves exchange stability with longitudinal rolls and oblique hydrothermal waves. The details of the instability affect the microstructure of the solidified material, which is crucial as it determines the properties of the resulting product.