Modeling the Dynamics of the Aerodynamic Forming of Fibers

Abstract

The dynamics of the aerodynamic forming of fibers is studied. The forces are calculated as functions of the fiber-forming path for different final fiber velocities. It is shown that there is a substantial difference between classic and aerodynamic forming in regard to the behavior of the rheological and aerodynamic forces along the path. The extrema of the functions of these forces are determined as a function of the difference between the velocity of the fiber and the velocity of the air leaving the ejector. It is found that the final velocity of the fiber depends linearly on average air velocity in the ejector. This dependence makes it possible to control the radius of the fiber as it is being formed. The essence of the process of aerodynamically forming chemical fibers from melts (AFFM) is the fact that the pulling force is the aerodynamic frictional force F aero (x) which is created between the fiber and air by the use of an ejector. The ejector forms an air flow along the fiber that is being created [1, 2]. In the production of nonwovens from polymer melts, the use of this method makes it possible to obtain the fiber and the finished product in a single processing stage. The mathematical description of this process differs from the formation of chemical fibers with a receiving element (FFM) because the final speed of the fibers is unknown and because the spinneret is followed by a shaft heater. The aerodynamic force determines the final fiber speed, while the presence of the heater significantly increases the temperature of the fibers. The pulling force - which is the main factor that governs the motion of the molten stream - is the force created by the interaction of the stream with the accompanying air flow and is referred to as the aerodynamic friction force (or simply the aerodynamic force) F aero . This force depends on many factors, including the velocity of the moving stream v(x). The velocity of the stream is an unknown in the equation of motion. This situation gives rise to a problem in which the boundary condition depends on the solution of the equation of motion [3]. A new approach has been proposed for determining the boundary conditions in modeling AFFM. The essence of this approach is that if we have a set of functions which describe the total force along the path of fiber formation F reo (x) for different initial values for the velocity gradient v’(0), we can select a function which corresponds to movement of the stream exclusively as a result of the aerodynamic force. The other functions F reo (x) correspond to cases in which the stream is acted upon by an additional external tensile force [3, 4]. The relation used to calculate the aerodynamic force [4] has the form