Melt-Blowing of Viscoelastic Jets in Turbulent Airflows: Stochastic Modeling and Simulation

In melt-blowing processes mico- and nanofibers are produced by the extrusion of polymeric jets into a directed, turbulent high-speed airflow. Up to now the physical mechanism for the drastic jet thinning is not fully understood, since in the existing literature the numerically computed/predicted fiber thickness differs several orders of magnitude from those experimentally measured. Recent works suggest that this discrepancy might arise from the neglect of the turbulent aerodynamic fluctuations in the simulations. In this paper we confirm this suggestion numerically. Due to the complexity of the process direct numerical simulations of the multiscale-multiphase problem are not possible. Hence, we develop a numerical framework for a growing fiber in turbulent air that makes the simulation of industrial setups feasible. For this purpose we employ an asymptotic viscoelastic model for the fiber. The turbulent effects are taken into account by a stochastic aerodynamic force model where the underlying velocity fluctuations are reconstructed from a $k$-$\epsilon$ turbulence description of the airflow. Our numerical results show the significance of the turbulence on the jet thinning and give fiber diameters of realistic order of magnitude

Whipping of electrified visco-capillary jets in airflows

An electriFied visco-capillary jet shows different dynamic behavior, such as cone forming, breakage into droplets, and whipping and coiling, depending on the considered parameter regime. The whipping instability, which is of fundamental importance for electrospinning, has been approached by means of stability analysis in previous papers. In this work, we propose an alternative model framework in which the instability can be computed straightforwardly as the stable stationary solution of an asymptotic Cosserat rod description. For this purpose, we adopt a procedure from Ribe [Proc. R. Soc. Lond. Ser. A Math. Phys. Eng. Sci. 2051 (2004), pp. 3223-3239] by describing the jet dynamics with respect to a frame rotating with the a priori unknown whipping frequency, which itself becomes part of the solution. The rod model allows for stretching, bending, and torsion and takes inertia, viscosity, surface tension, electric Field, and air drag into account. For the resulting parametric boundary value problem of ordinary differential equations we present a continuationcollocation method. On top of an implicit sixth order Runge-Kutta scheme, which leads to a Fifth order collocation scheme, our continuation procedure makes the eficient and robust simulation and navigation through a high-dimensional parameter space possible. Despite the simplicity of the employed electric force model, the numerical results are very convincing, and the whipping effect is qualitatively well characterized.SCOPUS: ar.jinfo:eu-repo/semantics/publishe