DEVELOPMENT OF A MATHEMATICAL MODEL OF THE CAVITATION IMPREGNATION PROCESS OF TEXTILE MATERIALS

Abstract

The paper presents the mathematical modeling of the cavitation impregnation process for textile materials under continuous production conditions. The relevance of the research is associated with the need to improve the efficiency of textile impregnation with functional reagents, ensure their uniform distribution throughout the material structure, and establish a theoretical foundation for the design of modern automated processing equipment. To develop the mathematical model, a continuous-type ultrasonic cavitation impregnation unit was designed, and its operating principle was used as the physical basis for investigating mass transfer phenomena occurring during cavitation treatment. A comprehensive system of interconnected mathematical models describing both the operation of the impregnation unit and the impregnation process itself was developed. In particular, mathematical models were formulated for the transportation of the textile web through the ultrasonic treatment zone, web tension stabilization, roll winding dynamics, the energy characteristics of the installation, and the distribution of ultrasonic field intensity within the working medium. Based on the analysis of the physical mechanisms governing the process, a differential equation describing the accumulation of the impregnating agent within the porous structure of the textile material was derived and subsequently integrated, resulting in an integral mathematical model of the cavitation impregnation process. The proposed model accounts for the intensity of ultrasonic exposure, the residence time of the material within the treatment zone, the distance between the textile material and the ultrasonic transducers, the transportation speed of the textile web, the stability of its movement, and the physical properties of the textile material. Analysis of the obtained mathematical relationships demonstrated that the efficiency of cavitation impregnation is determined by the combined influence of the installation's design parameters and operating conditions. The developed mathematical model can be applied to predict the performance of the cavitation impregnation process, optimize the design parameters of the equipment, and determine rational operating modes for ultrasonic cavitation impregnation systems.