Abstract: Droplets carried in turbulent fluids rely, for their existence, on tiny interfaces. Interfaces are not property of the drop or of the the carrier fluid and are inherently a non-place. However, in environmental and industrial processes, their role is enormously important since it is across the interfaces that momentum, heat and mass transfer fluxes coupling the drop to the carrier fluid occur: the accurate determination of their position, shape and interaction with the fluid turbulence is crucial to predict physical phenomena, and industrial and environmental processes. To this aim, Direct Numerical Simulation (DNS) of turbulence and accurate tracking of the interface are required, but the range of scales involved for most ofpractical environmental and industrial applications is so wide that performing this task is a formidable challenge for present day computers: The grid resolution for DNS of turbulence is of the order of the Kolmogorov scale, but of course physical interfaces have a much smaller scale (order of few molecules) making the direct resolution unfeasible. In this talk, we will briefly review the current computational methodologies used to interfaces and the we will focus on the phase-field approach in turbulent flows: In this Eulerian approch, the phase distribution is described by the order parameter φ. We will examine several flow instances and phenomena ranging from turbulent stratified flows to turbulent dispersion of drops and bubbles so to reveal potentials and limitations of the phase-field method. Interface interactions with turbulence, coalescence and
breakup phenomena for different values of fluids density and viscosity will be discussed in connection with the characteristics of turbulence. Finally, the physics modelling and the method required to include the effect of surfactants will also be examined.