Platinum Group Metal (PGM) nanoparticles, more specifically platinum, rhodium, and palladium, are essential components in auto-catalysts in the outlets of cars, since they work as active sites for catalytic reactions. Due to increasingly stringent environmental regulations, the demand for these metals increases yearly. Since PGMs are very scarce, efficient recycling of these metals has become an important issue. Currently, the smelting process is the most commonly employed pyrometallurgical approach for concentrating PGMs. The behavior of the PGM particles during the process cannot be observed directly in experiments, due to the scale of the industrial furnaces and the small size of the PGM nanoparticles. Computational modeling of this process can thus provide a very useful addition to fill this gap. This PhD aims to develop a modeling framework combining a multi-phase-field model with DFT calculations to study the local dissolution behavior of PGM nanoparticles from spent auto-catalysts in a metallurgical slag containing collector metal droplets. This framework will be used to uncover the dominant dissolution mechanism, leading to new insights into the effects of pyrometallurgical process parameters on the dissolution of these PGM particles, useful for interpreting observations from and optimizing industrial recovery operations. Once the framework is established, it could be applied to different recovery processes as well, increasing its relevance towards the industry.