Nonlinear dynamics of heated falling films under the influence of long-range Van Der Walls intermolecular force interactions

Thin liquid film flowing on an inclined plane and subjected to various physico-chemical effects such as thermocapillarity, solutal-Marangoni and evaporative instabilities at the film surface and subjected to van der Waals intermolecular interaction forces, has been numerically simulated using explicit and implicit finite difference methods. There are several works published on flow of thin liquid films employing various flow configurations of thin film such as thin film on plane, inclined, and wavy surfaces over the past years. Thin film flow on inclined surface compared to on a horizontal surface, also experiences the gravity force which may play substantial role in the nonlinear dynamics of the film coupled with other forces. In this research, we attempt to update our previous study of the stability and dynamics of thin liquid films subjected to thermocapillary and evaporative instabilities at the free surface by including additional instabilities owing to long range van der Waals force in the film model. Similar to the previous studies cited in the literature (Joo et al., 1991; Hamza, 2017), for a Newtonian liquid, flow in thin liquid film on an inclined support and bounded by a passive gas, is represented by Navier-Stokes equation, equation of continuity and appropriate boundary conditions. The external effects are incorporated in the body force term of the Navier-Stokes equation. Following the procedure as outlined in the literature these governing equations are simplified followinga long-wave asymptotic analysis to derive a nonlinear fourth order partial differential equation, henceforth referred to as equation of evolution (EOE), which describes the temporal and spatial evolution of the interfacial instability in the film caused by complex nonlinear interactions of internal and/or external forces. We carried out extensive numerical simulations for various combinations of thin film flow parameters representative of different physical flow situations encountered in practice. Especially the effect of van der Waals forces on the film morphology and breakup is investigated at depth. This clearly shows that van der Walls forces though insignificant in thick films (proportional to h-6, where h is the film thickness) assumes significant role at short distances imparting catastrophic effect on the film instability as thin film approached breakup point. Here we present the results of our numerical simulation as an attempt to decipher the complex nonlinear dynamics of thin film flows especially delineating the role of van der Waals interaction forces in combination with other antagonistic physico-chemical effects