The work is devoted to the study of the gravitational motion of a liquid film under evaporation conditions into a flow of neutral gas as applied to film machines with a plane-parallel nozzle. The aim of the work is to develop a mathematical model of such a process and establish its laws. The model is based on the physical concepts of a liquid film flowing down a flat surface heated from outside under the assumption that the film flows in isothermal conditions under steady-state laminar mode without wave formation and in the absence of friction between the gas and the film. The mathematical description of the film flow down process in these conditions includes the equation of motion and the continuity equation for the liquid film, which are supplemented by the equations of mass transfer, the material balance of the gas phase in the evaporated liquid, the relative content of the vaporized substance in the gas phase and the equation expressing the Dalton's law. As a result of solving this system of equations, dependencies are obtained that make it possible, at known values of the mass transfer coefficient in the gas phase, to carry out calculations and simulate the hydrodynamics of the liquid film flow under conditions of evaporation into a flow of neutral gas. For the water-to-air system, regularities were established in which the film thickness and speed of movement along the surface height were varied for different types of film interaction with the air flow: forward flow, backflow, and cross-flow, as well as with different hydrodynamic and temperature conditions of its flow down under cross interactions conditions of the flows. It has been shown that in all cases a decrease in the thickness and speed of movement of the film is observed, with the largest decrease occurring during cross-interaction, which is associated with an intense removal of the resulting vapor from the film surface. The developed mathematical model can be used to evaluate the operating modes of film machines with a plane-parallel nozzle.

The work is devoted to the study of heat and mass transfer in a liquid film flowing down on a heated surface under conditions of evaporation into a crossflow of a gas neutral with respect to the liquid. The work aimed to experimentally determine the average heat transfer coefficients from a heated surface to the film, heat transfer and mass transfer from the film to the gas flow and to establish their dependence on the input parameters of the heat and mass transfer process. To achieve this goal, an experimental setup was created, and a research technique was developed based on the proposed mathematical model of the heat and mass transfer process. The results of the study showed that the dependences of the average heat and mass transfer coefficients on the initial liquid flow rate are extreme with the minimum values of these coefficients at the liquid flow rate, which corresponds to the critical value of the Reynolds criterion Re l cr ≈ 500, which indicates a transition from the laminar falling films to turbulent mode under the considered conditions. The dependences of the heat and mass transfer coefficients on other process parameters for both modes of film falling are established. A generalization of the experimental data made it possible to obtain empirical equations for calculating these coefficients. Keywords: heat and mass transfer, cross flow, film apparatus, heat and mass return coefficient, neutral gas.

The article presents the results of the investigation of the process of concentrating solutions of low-volatile liquids in a flowing film under the conditions of evaporation in the cross-flow of neutral gas. The purpose of the study was to establish the features of solution composition change along the film length. The study was carried out using the developed mathematical model with experimental determination of model parameters: heat and mass transfer coefficients. It was found that at the beginning of the film, the change in the concentration of the solution has a character close to linear, and then the concentration sharply increases until the solvent evaporates completely. It was shown that this pattern of change in the composition of the solution is related to the distribution of the temperature of the solution along the length of the film. The intensity of the concentration process increases with decreasing initial flow rate of the solution and its initial concentration as well as with increasing initial temperature of the solution, initial temperature of the gas and temperature of the surface of the wall along which the film flows. The concentration intensity decreases with an increase in the velocity of the gas entering the space above the film. Comparison of the calculation results concerning aqueous glycerol solution with the experimental data showed their good agreement. The data obtained in the article allow calculating the height of the film concentrator nozzle at which a given concentration of the solution is provided.