Interfacial turbulence in falling liquid films

A falling film is a convectively unstable open-flow hydrodynamic system with a rich variety of spatial/temporal structures and a sequence of wave instabilities and transitions which are generic to a large class of hydrodynamic and other nonlinear systems: white noise at the inlet, filtering mechanism of linear instability, secondary modulation that transforms the primary wave field into two-dimensional (2D -- 1+1 dimensions) solitary pulses and eventually transition of the 2D pulses into a fully developed three-dimensional (3D -- 2+1 dimensions) wave regime. This stage of the evolution is frequently referred to as `interfacial turbulence'. This is low-dimensional spatio-temporal chaos or alternatively `weak/dissipative turbulence': indeed, despite the apparent complexity of the system one can still identify 3D solitary pulses in what appears to be a randomly disturbed surface. 3D pulses then become elementary processes so that the dynamics of the film can be described as a superposition of these pulses. Hence, a falling liquid film can serve as a canonical reference system for the study of weak/dissipative turbulence.In addition to the purely theoretical interest, falling liquid films play a central role in the development of efficient means of heat and mass transfer in a wide variety of engineering and technological applications, such as evaporators, heat exchangers, absorbers, scrubbers, rectification columns, crystallizers and falling film reactors. This is mainly due to the small heat and mass transfer resistance of a falling film at relatively small flow rates. This resistance is further decreased by the presence of 2D/3D solitary pulses at the free surface of the film mentioned earlier which typically lead to a significant enhancement of heat and mass transfer.Not surprisingly, therefore, falling liquid films have been a topic of fundamental and applied research for several decades. However,despite the several developments and considerable attention that wave evolution on a falling film has received, a large number of issues and problems have not been resolved, and in particular, the interaction of 3D solitary pulses and eventual transition to interfacial turbulence, still elude us. In an attempt to answer these questions, the field of research to be pursued during the tenure of this project concerns the theoretical development of a coherent structures theory of 3D solitary pulses on a falling film with the principal aim to advance our understanding of interfacial turbulence.