Stability Of Falling Liquid Films

Falling Liquid Films gives a detailed review of state-of-the-art theoretical, analytical and numerical methodologies, for the analysis of dissipative wave dynamics and pattern formation on the surface of a film falling down a planar inclined substrate. This prototype is an open-flow hydrodynamic instability, that represents an excellent paradigm for the study of complexity in active nonlinear media with energy supply, dissipation and dispersion. It will also be of use for a more general understanding of specific events characterizing the transition to spatio-temporal chaos and weak/dissipative turbulence. Particular emphasis is given to low-dimensional approximations for such flows through a hierarchy of modeling approaches, including equations of the boundary-layer type, averaged formulations based on weighted residuals approaches and long-wave expansions. Whenever possible the link between theory and experiment is illustrated, and, as a further bridge between the two, the development of order-of-magnitude estimates and scaling arguments is used to facilitate the understanding of basic, underlying physics. This monograph will appeal to advanced graduate students in applied mathematics, science or engineering undertaking research on interfacial fluid mechanics or studying fluid mechanics as part of their program. It will also be of use to researchers working on both applied, fundamental theoretical and experimental aspects of thin film flows, as well as engineers and technologists dealing with processes involving isothermal or heated films. This monograph is largely self-contained and no background on interfacial fluid mechanics is assumed.

The objective of this research project was to study, both theoretically and experimentally, the stabilizing effects of surface active agents on falling liquid films. Conclusion: The entrance region and the onset of waves are profoundly effected by the presence of surfactants while the wave structure of the unstable film is effected very little. (Author).

An analysis is presented for the linear stability of a liquid film adjacent to a compressible viscous gas stream. The analysis is valid for all wavelengths and liquid Reynolds numbers. The pressure and shear perturbations exerted by the gas on the liquid are calculated using a gas model which takes into account the gas viscosity, velocity profile, and heat transfer. The results show that an inviscid uniform stream model for the gas is inadequate unless the disturbed boundary layer is very thin. Although the present linear analysis is in fairly good agreement with the experimental observations for subsonic flow, it does not predict the observed wavelengths and wave speeds for supersonic flow. (Author).

Contributed papers presented at a seminar held during September 1-4, 2006.

The flows of thin film form the core of a large number of scientific, technological, and engineering applications. The occurrence of such flows can be observed in nature, for example on the windshield of vehicles in rainy weather. Thin film flows are also found in various engineering, geophysical, and biophysical ap- plications. Specific examples are nanofluidics, microfluidics, coating flows, intensive processing, tear-film rupture, lava flows, and dynamics of continental ice sheets. Important industrial applications of thin films include nuclear fusion research - for cooling the chamber walls surrounding the plasma, complex coating flows - where a thin film adheres to a moving substrate, distillation units, condensers, and heat exchangers, microfluidics, geophysical settings, such as gravity currents, mud, granular and debris flows, snow avalanches, ice sheet models, lava flows, biological and biophysical scenarios, such as flexible tubes, tear-film flows and many more. The dynamics of such films are quite complex and display rich behavior and this attracted many mathematicians, physicists, and engineers to the field. In the past three decades, the work in the area has progressed a lot with considerable stress on revealing the stability and dynamics of the film where the flow is driven by various forces such as gravity, capillarity, thermocapillarity, centrifugation, and inter- molecular. The flow may happen over structured or smooth and impermeable or slippery surfaces. The investigation approaches include modeling and analytical work, numerical simulations, and performing experiments to explain the instabilities that the film can exhibit. Direct analysis of the equations of the model of the interfacial flows is a very complicated mathematical exercise due to the existence of a free, evolving interface that bounds the liquid film. The mathematical complexity emerges from a number of things: (a) The Navier-Stokes (or Stokes or Euler) equations need to be solved in changing domains; (b) In certain applications one has to solve for the temperature or electrostatic or electromagnetic fields apart from the fluid equations; (c) Several nonlinear boundary conditions should be specified at the unknown interface(s) and (d) The solutions may not exist for all times. In fact in thin film problems, one may encounter finite-time singularities accompanied by topological transitions. The breakup of liquid jets is an example of that. However, in the subsequent chapters, we shall see that it is possible to use the different length scales appearing in thin film flows to our advantage. Thin films are characterized by much smaller length scales in the vertical direction as compared to those in the stream-wise direction. This gives rise to a small aspect ratio which makes the problem amenable for small amplitude perturbation expansions.