In direct numerical simulation (DNS) of two-phase flows, all the interfaces of the two-phase system are tracked individually. If this technique is computationally expensive, it is also very powerful, especially to study basic phenomena. In particular, it helped to better understand fundamental issues such as the forces acting on a single bubble (e.g. [1]) or the interaction of a couple of bubbles in a bubbly flow (e.g. [2,3]) and it now begins to be used to assess average models in detail ([4]). Currently, most of the basic phenomena studied involve non-miscible fluids, where no mass transfer between the phases occurs (air and water for instance). However, in many applications of industrial interest, phase-change phenomena are very important because high heat flux can be achieved with moderate temperature gradients (since the energy exchange through latent heat occurs at a constant temperature). It is thus widely used in the energy industry (nuclear energy in particular) and it is used to design compact heat exchangers (e.g. heat pipes for space or electronic devices). Moreover, basic phenomena related to phase-change are, to a large extent, still misunderstood, which make phase-change phenomena of fundamental interest as well. For instance, despite several decades of valuable scientific studies, the boiling crisis, which is an instability of the nucleate boiling regime, is still misunderstood from a fundamental point of view. It is one of the very few fundamental issues that are still open in fluid mechanics. Since DNS has already been successful to study fundamental issues in two-phase flows of non-miscible fluids, it should be successful to study these issues as well. However, the DNS of two-phase flows with phase-change is more difficult than that of two-phase flows involving non-miscible phases. These issues are both numerical and physical and some of them are discussed in this paper.

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