Features of using a lowviscosity Newtonian medium in an extrusion apparatus for three-dimensional printing

Abstract

This research aims to investigate the motion of a high-viscosity liquid in a narrow heated channel simulating the process of extrusion of polymers for the three-dimensional printing. The selection of polymer mass movement and heat exchange parameters is an important element for this type of tasks. Its purpose is to obtain a stable product molding. Here, it consists in feeding the slightly overheated mass to the appropriate place, where it will quickly solidify; therefore the printed product shape is stably retained. Corresponding polymers with the required properties are used as a working medium. A Newtonian liquid is used to reveal the physical features of the process. Its properties are close to those of polyethylene terephthalate, which is also used in the three-dimensional printing technology. The problem of motion and heat exchange is formulated within the framework of the narrow channel model theory with regard for the mechanical energy dissipation. It is necessary to consider the dissipative terms, since large velocity gradients can lead to a large value of the dissipation and, accordingly, to a large increase in the temperatures. The feature turns out to be extremely important for this particular task type. In addition to a liquid close to PETF, the motion and heating of a liquid, the viscosity of which is 10 times less than the viscosity of the polymer, is considered for a clearer presentation of the resilts. The solution was carried out using the method of stripes, in which the temperature and, accordingly, the viscosity, depending on it, are taken independent of the cross-coordinate. This makes it possible to use an analytical dependence for the velocities in each stripe, which makes the method semianalytical and facilitates the solution. The results ob tained numerically indicate that, within the working interval of the molding (about 0.1 m/s and 0.5 m/s), the dissipation has a really significant effect on the process. So, the overheating of a conventionally low-viscosity liquid at the end of the apparatus turns out to be significant, but it can be removed by the additional blowing. This is practically impossible to do for a highly viscous fluid, i.e. such a liquid cannot be used in an apparatus with the considered geometrical dimensions. Thus, the mathematical modeling of the process under study makes it possible to calculate the flow parameters and to determine the necessary conditions and, accordingly, the properties of the liquid for a stable three-dimensional printing.