(435f) Discretized Modeling of a Simple Motionless 3D Printer Based on Retarded Bending Motion and Electrically Controlled Patterning of Fiber Deposition

The electrospinning process is widely used to produce fibers with diameters in the sub-micron range. In the electrospinning process, a polymer solution is slowly extruded out of a needle and fibers are formed as the solution is accelerated by an electric field. The electrically driven fibers have been of interest in the area of 2D and 3D printing to fabricate ordered fiber mats. These fiber mats have applications in filtration, catalysis, tissue engineering, drug delivery, and energy storage systems. In printing, the nozzle system or the substrate moves to form patterns on the substrate. For this, there needs to be a proper alignment of the nozzle and the substrate to avoid any errors while printing. Therefore, we developed a motionless 3D printer in which the print pattern was formed by electrically controlling the fiber deposition. In our approach, the nozzle system is stationary and the fiber is electrically guided for printing on the substrate. As there are no degrees of freedom in this system, this approach prevents the alignment issues and the print resolution is limited only by the material delivery system.

The 3D printer in this study is developed using the immersed electrospinning process, in which the fiber is electrospun in a liquid medium rather than in air or vacuum. The wet spinning medium improves the collection thickness of the nonwoven fiber and controls its porosity. In general, several instabilities are observed on the polymer fiber in the electrospinning process. In particular, the bending instability results in a non-axisymmetric behavior of the polymer fiber, causing the fiber to undergo a helical motion instead of travelling in a straight line. This bending motion makes it difficult to control the deposition of the fiber. As the immersed spinning setup uses liquid spinning medium, the drag force by this surrounding liquid inhibits the bending motion of the fiber, which makes it easy to electrically control the fiber trajectory. In this paper, we first studied the bending instability of fiber in the system followed by a subsequent study examining the pattern formation for 3D printing with the use of an immersed spinning process.

First, the bending instability of the fiber was studied from simulations and experiments to understand the feasibility of the immersed electrospinning process for 3D printing. In the immersed electrospinning setup, the spinning dope was comprised of polyacrylonitrile (PAN) in the dimethylformamide (DMF) solvent. The PAN/DMF solution was spun in a coagulation bath containing a mixture of chloroform and mineral oil as the spinning medium. With this liquid spinning medium, it was much easier to visualize the bending motion because of the reduced chaotic motion of the fiber. This fiber trajectory obtained from the experiments was used to test the validity of the simulations. For the simulation, we used the discretized model, in which, the fiber is assumed to be a series of beads connected with springs. In this model, the beads are introduced at regular intervals in the nozzle, and the trajectory of the fiber is obtained by applying Newton’s Second Law of Motion to each bead. The drag force by the liquid spinning medium was incorporated into the discretized model. To obtain the bending motion of the fiber, normal mode perturbations at different frequencies and amplitudes were applied to the beads when they are introduced in the system. The rate of increase in the helical radius of the fiber trajectory is the instability growth rate. This growth rate was calculated at different frequencies and the frequency with the maximum growth rate is responsible for the onset of the instability. In addition, from the simulations and experiments, the growth rate of the bending instability increases with voltage due to larger Coulombic repulsions between the surface charges of the fiber. Therefore, the bending instability is shown to be in the conducting mode. The radius of the fiber from the simulation is similar to the experimental observation. Overall, the discretized model provided a good prediction of the fiber’s bending motion. Thus, this model was also used to predict the electrically controlled pattern formation of the fiber on the collector. The process conditions for lower bending instability growth rate were used for our next study with simulations and experiments on the electrically controlled pattern formation.

In the second study, the collector in the immersed electrospinning setup was modified to form a square pattern. The collector was designed by attaching four copper plates in a square shape to a non-conducting material. These plates are the lattice sites on the collector, and the voltage is conducted only at these sites. The fiber is guided to that lattice point that has the voltage switched ON. As the fiber reaches one lattice point, its voltage is switched OFF, and based on the desired pattern the voltage at the next lattice point is switched ON. This process was repeated until the end of the printing time. The size and the structural arrangement of the lattice points determine the accuracy of the pattern. The formation of a square pattern was also studied with the discretized model by using a temporal boundary condition for the voltage on the collector. The pattern formed from the discretized model was compared with the experiments. This approach can be developed further by increasing the lattice sites to improve the print resolution. For this, the electrode arrays can be used as a collector, and this will increase the accuracy of the pattern. In addition, the switching of the voltage at the lattice points can be controlled with MOSFETs, which can reduce the delay between the switching of the voltage among the lattice sites. Furthermore, the predictions from the discretized model can be used to decide the process conditions for the 3D printing of various other patterns.