2026, Vol. 11, No. 2. - go to content...

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Doriomedov A.S. Mathematical modeling of the electrostatic state of a rounded fiber. Journal of Clothing Science. 2026; 11(2). Available at: https://kostumologiya.ru/PDF/30TLKL226.pdf (in Russian).

Mathematical modeling of the electrostatic state of a rounded fiber

Doriomedov Aleksandr Sergeevich
Russian State University named A.N. Kosygin (Technologies. Design. Art), Moscow, Russia
ORCID: https://orcid.org/0000-0001-5092-4648
RSCI: https://elibrary.ru/author_profile.asp?id=1227748

Abstract. To assess the electrical parameters of textile materials, it is necessary to know the electrical capacitance at the design stage of the material. The task of finding an analytical expression for the electrical capacitance based on its defining factor, the dielectric constant, is highly relevant. The analysis of the structural features of textile materials led to the consideration of a single fiber model with an adjacent air shell. The author has developed a mathematical model of the electrostatic state of rounded fibers, taking into account the air layer surrounding the fibers. Based on this mathematical model, a scheme for studying and predicting the electrostatic properties of fibers has been proposed. In the article, using mathematical methods, the functional dependence of the electrocapacity on the dielectric permeability of round-shaped fibers, taking into account the air, is investigated, and it is noted that the ratio of the semi-axes of the fibers (the stretching of the fibers vertically or horizontally) plays an important role in the value of the function under study. A graph of the dependence of the electrocapacity of a round-shaped fiber on the dielectric permeability is constructed. The article discusses methods for approximating the electrocapacity function to determine the value of the function with lower accuracy compared to the exact value obtained from the analytical functional dependence. An example of approximation is presented, obtained as a result of covering the functional dependence on the interval sections of the argument with linear functions, the inverse dependence, which makes it possible to determine the dielectric constant by the known value of the electrocapacity. Based on the data obtained, the author’s mathematical technique for developing a model of the electrostatic state of the fiber is proposed, which made it possible to develop a model of the electrostatic state of the fiber of a rounded shape, taking into account the air layer for the functional dependence between the electrocapacity of the fiber and the coefficient of the dielectric constant.

Keywords: fiber; electric capacity; layer; permeability; dependence; integration; model; materials

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