2013 1(12)

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Aktershev S.P., Alekseenko S.V.

Institute of Thermophysics SB RAS, Novosibirsk, Russia


Aktershev, S.P. and Alekseenko, S.V., (2013) Three-dimensional waves in the liquid film, Modern Science: Researches, Ideas, Results, Technologies, Iss. #1(12), PP. 83 - 89.


liquid film; three-dimensional waves; stability; numerical simulation of non-linear waves


Interest to the flows of a liquid film is caused both scientific significance and various applications of this type of flows. The important characteristic of such flows is their wave structure influencing both on transport processes, and on features of a flow. Problems of an intensification of heat transfer and mass transfer processes demand the further development and generalization the available models of wavy film flows. The general reason restraining development of theoretical models is not only the complexity of a problem, but also an insufficient study of three-dimensional waves in liquid films. At present time there are relatively a few experimental and theoretical works devoted to three-dimensional waves in thin liquid films. The goal of the presented paper is to develop the model describing three-dimensional waves in a film which takes into consideration the complex conditions on an interface without assuming self-similarity of velocity. The proposed model is based on an integral approach and an expansion of velocity into system of linearly independent basis functions (harmonics). This model, to a certain extent, is a generalization of the Shkadov’s IBL model, however, possesses a greater «degree of freedom» for the velocity profile shape. The proposed model allows describing in more details the dynamics of waves and the features of transport processes in wavy films of liquid. A linear analysis of flow stability concerning two-dimensional and three-dimensional perturbations is performed for the falling film and also a numerical simulation of non-linear waves is carried out. Results of calculations for two-dimensional waves agree well with available experimental data. As an example of three-dimensional waves the simulation of evolution of the localized perturbation of soliton type in vertical liquid film is carried out.


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