Control equations for the propagation of nonlinear waves in viscous film flows with a mass source

The paper devotes to theoretical description and mathematical modelling the nonlinear modes of liquid film flows in the presence of possible mass sources, in the case of film condensation as a sample. The main new scientific result of the study is a theoretical description of the influence of the mass source on the characteristics of nonlinear waves arising during the flow of a viscous condensate film over a non-isothermal surface. The study was carried out within the framework of the long-wave approximation. The conditions for the existence of solutions describing the propagation of single nonlinear waves in condensate films are determined, and equations are derived for calculating the evolution of their wave characteristics. Relationships are obtained for estimating the scale of the propagation length of nonlinear waves in liquid films with variable flow rate. The conclusions of the work can be useful in design work and in developing process and apparatus control systems in the chemical and pharmaceutical industries.

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