Free-surface and multiphase flows are relevant to a variety of industrial and natural processes. At relatively small spatial scales, droplet impacts with solid surfaces are important for spray cooling, ink-jet printers, film coating, spray painting, erosion in steam turbines, and soil erosion due to rainfall. In fuel sprays the disintegration of liquid jets is attained via primary breakup of the fluid column and secondary breakup of the generated droplets. To optimize the injection systems and the subsequent combustion, it is crucial to determine the drop size distribution function. The interaction of a large number of droplets is relevant to boiling water–steam flows in pipes and to rain formation. At greater scales the wind is responsible for the wave formation and breaking on the ocean surface.

Finding the flow around an advancing ship is a difficult free-surface problem whose solution would bring large rewards in design and optimization. All these processes are quite complex in themselves, but it is also necessary to couple the fluid dynamics description to other effects such as the chemistry of combustion or solid mechanics, for example, to determine the stress tensor in the hull of a fast ship moving in rough seas. Experimental techniques have shown the intrinsic beauty of drop impact, formation, and coalescence to such an extent that these processes are widely used in commercial advertisements.