Numerical simulations of breakage, coalescence and droplet size distribution

The dynamics of surfactant-laden droplets are investigated in this thesis using Direct Numerical Simulations (DNS) of turbulence coupled with a two-order-parameter Phase Field (PF) method to describe interface and surfactant dynamics. This problem is characterized by the presence of a deformable interface transported by the (eventually turbulent) flow and of a soluble surfactant. The complex interplay among flow, interface and surfactant, whose effects are deeply intertwined, is presented in detail in the following chapters and is also briefly summarized here with the help of the graphical abstract. The flow deforms the interface and advects surfactant via the shear stresses at the interface. In turn, the interface feeds back onto the flow field via capillary stresses (normal to the interface). The interface also, while deforming, breaking and merging, modifies the local surfactant concentration over the interface. Surfactant locally reduces surface tension of the interface, changing the local deformability of the interface. In addition, eventual surface tension gradients, generated by an uneven surfactant distribution, introduce stresses tangential to the interface (Marangoni stresses). Surfactant, indeed, feeds back onto the flow field via Marangoni stresses and onto the interface by locally reducing surface tension. In the thesis, the outcome of this complex interplay is characterized, starting from simpler laminar cases (as for instance the deformation and interaction of droplets in laminar flow) and concluding with the more complex case of a swarm of surfactant-laden droplets in turbulence.