ЧИСЕЛЬНЕ МОДЕЛЮВАННЯ ТЕЧІЇ В'ЯЗКОПРУЖНОЇ РІДИНИ З ІНТЕГРАЛЬНИМ РЕОЛОГІЧНИМ ЗАКОНОМ У ПЛОСКОМУ АБО ЦИЛІНДРИЧНОМУ КАНАЛАХ

Abstract

The viscoelastic liquid may be a melt of a polymeric material from a rheological point of view. Therefore, emphasis will place on the practical application of the results of the solution of the mathematical model of the flow of viscoelastic fluid in the study of the process of filling the cavity of the mold with polymeric material. High shear stresses can occur in flat or cylindrical channels. During the flow of viscoelastic fluid, in which the carbon bonds of macromolecules are broken, which leads to a decrease in the average molecular weight, and this leads to a change in molecular weight distribution, which significantly reduces the performance product. Therefore, it is important, in our opinion, to create a method for determining the stress field that arises in the process of forming products. The article is devoted to the development of a mathematical model of the flow of viscoelastic fluid in flat or cylindrical channels and its implementation by numerical methods. The calculation of this model will allow to determine the stress field in the middle of the viscoelastic fluid during its movement in flat or cylindrical channels under certain initial and boundary conditions. The paper proposes to introduce the concept of "memory" into the model and to assume that the stress determined by the complete history of polymer deformation. This assumption allowed us to express the stress tensor as an isotropic functional of the deformation history. To solve the developed numerical model of viscoelastic fluid flow with integrated rheological law, a procedure for calculating its finite difference method proposed. Numerical mathematical model of viscoelastic fluid in its implementation by the finite difference method (MAC method) allows determine the stress field in the middle of the entire flow region. The results of this modeling can used in the development of injection molding equipment and improvement of equipment for injection molding of polymer products.