Interfacial collocation equations of thin liquid film in the presence of interfacial shear: Stability analysis

Stability analysis on counter- and cocurrent sheared falling is considered. The governing equations for the mass continuity and liquid motion of thin-film flow in the presence of interfacial shear are presented in terms of the parameters at the free interface, the so-called collocation line. As the instability phenomenon is associated essentially with characteristics of the near-interface region, a stability analysis is carried out on the interfacial collocation equations and results in simple algebraic "stability equations", which relate the wave characteristics at inception to the interfacial shear, external pressure drop and the Weber and Reynolds numbers of the flow. It is also shown that simple analytical asymptotic solutions can easily be derived from the algebraic equation,.