Self-healing liquid Metal Divertors (LMDs) are currently being considered among the alternative strategies to address the power exhaust problem in future fusion reactors such as the EU DEMO tokamak. To characterize the power exhaust scenario for a tokamak equipped with an LMD, a self-consistent approach is required, accounting for the mutual interactions between the Scrape-Off Layer (SOL) plasma, the divertor targets and the evaporated metal. To this aim, the SOLPS-ITER code, a 2D multi-fluid solver for the plasma and neutral species, was coupled to a purposely developed LM target erosion/evaporation model and then applied to simulate the EU DEMO plasma in the presence of a liquid Sn divertor. Calculations considering only D and Sn as plasma (and neutral) species indicates that vapor shielding arising from the interactions of the eroded/evaporated metal with the near-surface plasma effectively mitigates the target heat flux, reducing the computed peak value from similar to 60 MW/m(2) (computed for a pure D case, mimicking a solid divertor) to similar to 44 MW/m(2). However, this value is still larger than the power handling limit of similar to 40 MW/m(2) for the considered LMD design. Moreover, the computed Sn concentration in the core plasma was close to the estimated compatibility limit of similar to 0.05%. These results motivated further simulations considering the injection of Ar in the SOL plasma to radiate part of the plasma power before it reaches the target, also leading to a reduced erosion/evaporation rate. The results indicated a significant widening of the operational window for the EU DEMO equipped with an LMD using Sn, both in terms of tolerable target heat fluxes and in terms of core plasma contamination.