A computational model is developed to investigate fundamental flow physics and transport phenomena of evaporating wavy-laminar falling liquid films of water and black liquor. The computational model is formulated from first principles based on the conservation laws for mass, momentum, energy and species in addition to a phase transport equation for capturing interface deformation and evolution. Free surface waves are generated by monochromatic perturbation of velocity. Continuum models for interfacial evaporation define source terms for liquid vaporization and species enrichment in the conservation laws. A phenomenological crystallization model is derived to account for species depletion due to salt precipitation during black liquor falling film evaporation. Using highly resolved numerical grids on parallel computers, the computational model is implemented to analyze the dynamics of capillary separation eddies in low Reynolds number falling films, investigate the dominant mechanisms of heat transfer enhancement in falling films at moderately high Reynolds numbers and study the fundamental wave structures and wave induced transport in black liquor falling films on flat and cylindrical walls. From simulation results, a theory based on the dynamics of wavefront streamwise pressure gradient is proposed to explain interfacial waves interaction that give rise to multiple backflow regions in films dominated by solitary-capillary waves. The study shows that the mechanism of heat transfer enhancement in moderately high Reynolds number films follows from relatively lower conduction thermal resistance and higher crosswise convective transport at newly formed intermediate wavefronts. Interfacial phenomena such as wave-breaking and vapor entrainment observed in black liquor falling films is explained in terms of a mechanistic theory based on evolution of secondary instabilities and large amplitude wave force imbalances.