This PhD project is part of research on fluid–structure interactions (FSI) in complex media, particularly fluid mixtures involving multiple phases (liquid/liquid or liquid/gas) and/or suspended particles. The objective is to develop a thorough, multi-scale understanding of the coupled mechanisms between deformable structures (such as droplets, interfaces, or flexible walls) and the flows of complex mixtures, by combining theoretical modelling, advanced numerical simulations, and comparison with experimental data.