Solid and liquid sodium combustion with liquid water occurs through a thin gas layer where exothermic reactions happen with sodium and water vapors. It thus involves multiple interfaces separating liquid and gas in the presence of surface tension, phase transition and surface reactions. The gas phase reaction involves compressible effects resulting in possible shock wave appearance in both gas and liquid phases. To understand and predict the complexity of sodium combustion with water a diffuse interface flow model is built. This formulation enables flow resolution in multidimension in the presence of complex motion, such as for example Leidenfrost-type thermo-chemical flow. More precisely sodium drop autonomous motion on the liquid surface is computed. Various modelling and numerical issues are present and addressed in the present contribution. In the author's knowledge, the first computed results of such type of combustion phenomenon in multidimensions are presented in this paper thanks to the diffuse interface approach. Explosion phenomenon is addressed as well and is reproduced at least qualitatively thanks to extra ingredients such as turbulent mixing of sodium and water vapors in the gas film and delayed ignition. Shock wave emission from the thermo-chemical Leidenfrost-type flow is observed as reported in related experiments. emails : damien.furfaro@rs2n.eu richard.saurel@univ-amu.fr lucas.david@cea.fr francois.beauchamp@cea.fr 2 1. Introduction Fast-neutron reactors (FNR) as well as other engineering systems use sodium (a N) as coolant fluid. Sodium presents excellent physical properties regarding heat transfer efficiency as well as its ability to maintain kinetic energy of fast neutrons. However, it has major drawbacks regarding safety issues as it reacts exothermically with both air and water. In the limit, explosion may occur resulting in shock wave propagation in the liquid and surrounding media. When a liquid or solid sodium drop is set on a liquid water surface surprising phenomenon occurs. A reaction appears rapidly resulting in autonomous drop motion on the liquid surface. It seems that the drop is separated from liquid water by a small gas layer where combustion occurs both in the gas phase and at sodium surface. The phenomenon is reminiscent of the Leidenfrost effect except that the heat needed to vaporize sodium and water comes from the combustion of themselves or their vapors. This combustion induces liquid water evaporation and heating of the sodium drop. After some delay, typically a few seconds, explosion occurs. These complex events are qualitatively reported on many videos available on the web, such as [www.youtube.com/watch?v=ODf_sPexS2Q] for example. They clearly illustrate complexity of the physics and chemistry in presence. Quantitative analytic experiments have been carried out at CEA Cadarache, France, in the facilities SOCRATE, DINAMO, VIPERE and LAVINO (Carnevali 2012, Carnevali et al. 2013, Daudin 2015, Daudin et al. 2018, David et al. 2019). These experiments confirm an important fact: liquid sodium and liquid water are always separated by a gas layer or bubbly zone, resulting in significant lowering of the energy release efficiency compared to the theoretical one. To be more precise, typical reactions of sodium with water assume (ideal) molecular mixing, resulting in energy release of the order of 100 kJ/mol, which is considerable. However, in the experiments and engineering situations of interest, sodium is never mixed with water at molecular scale. Materials are separated by interfaces and the gas layer repels the reactive material (Na) from the oxidizer (water). It results in low energy release rate, with mechanical consequences and blast effects much lower than if the reaction was occurring with molecularly mixed materials. In the limit, reactive materials never mix because of projections, resulting in incomplete reaction, with moderate energy release. The present work attempts to model these effects to understand and predict the physics occurring in this complex two-phase combustion system. To determine the effective energy release and its kinetics in situations relevant to FNR safety, the mixing process between combustible sodium and oxidizer (water) must be modelled. Mixing of reactants controls the energy release rate. This mixing seems to occur through the gas layer separating the two liquids, resulting in temperature and pressure rise through exothermic reactions occurring in the gas phase and at the sodium surface, resulting in turn to autonomous drop motion and possibly explosion. In the author's knowledge, the present paper is the first attempt to model sodium combustion with liquid water in multidimensional configuration. Former contributions considered multidimensional water vapor flow interacting with a liquid sodium surface at rest through a diffusion flame (Deguchi et al., 2015). Marfaing (2014) and Marfaing et al. (2014) considered both liquid and vapor water in the presence of a diffusion flame in 1D spherical configuration. The assumption of 1D flow seemed restrictive, as in reality gas escapes from the film to the atmosphere, as illustrated in the Figure 1.