FEM Study of the Strain Kinematics in the 3D Nanofibrous Structure Prepared by the Electrospinning Process

Michal Petrů, Ondřej Novák, David Vejrych, Petr Lepšík

Department of Machine Elements and Mechanism, Technical University of Liberec, Liberec, Czech Republic.
Department of Nonwovens, Technical University of Liberec, Liberec, Czech Republic.
Institute for Nanomaterials, Advanced Technologies and Inovation, Technical University of Liberec, Liberec, Czech Republic.

DOI: 10.4236/am.2013.45A010                

Abstract

Finite element model (FEM) was used for the study and description of the arising 3D nanofiber structure strain caused by the pressure of the flowing gas. Computer simulation using an adaptive networking through implicit FEM algorithm can be utilized for a significant improvement of the study of anisotropic strain in the deformed 3D nanostructure. The created model is based on the empirical Laplace-Poisson differential equation for the flow, where gas particles are moving with certain kinetic energy. The kinetic energy depends on the speed, time and temperature and affects the resulting strain of 3D nanofiber structure. The simulation results were compared to the results obtained from the image analysis of real samples and showed that this FEM model can determine individual phases of structure strain. The comparison shows that the developed FEM model can be an important tool in the study of the strain in the arising 3D nano- fiber structure and it can provide valuable information for optimization of 3D nanofiber structure production by the electrospinning process.

Keywords

FEM; Strain; 3D Nanofibrous Structure; Electrospinning; Gas Flow

1. Introduction

The production of nanofibers became the center of interest of the many research departments in the last decade. Even though this principle is known for a long time, the first patent of A. Formhals was published in 1934 [1]; this process has not been mastered in terms of productivity for a long time. The turning point was brought by the new method of electrospinning—Nanospider^TM principle, which significantly increased the process productivity. Simultaneously with the development of the nanofiber preparation technology the applications of nanofiber layers were also developed. The nanofiber layers are characterized by the almost isotropic arrangement, the contact points are linked with straightened fibers. The distance among the fiber contacts in the surface of fabric is relatively large, but the distance of each layer, which can be viewed and distinguished in the cross section of nanofiber material is relatively low. Consequently, the fiber layer is relatively compact and has a large specific density. There are procedures that can change the arrangement of nanofibers in the layer. In [2] authors describe the finite element method (FEM) model of four different collectors for the preparation of the desired structures, including required alignment of the fibers. The simulation was performed and analyzed in the Ansys Maxwell 3d. Also the analysis of two fibers was accomplished. The results can be used for optimization of the fiber structure by the help of different arrangement of collectors. In [3] the simulation of electrostatic field of coil, which is used for needless electrospinning from the liquid surface is described. The dependencies of distance between the coil winding and electrical intensity are calculated. The simulation is used for optimization of the coil design. The Comsol 3.5 software was used for simulation in this study. Authors in the article [4] focused on preparation of nanofibers from polypropylene. They irradiated the material with laser beam when passing through jet with supersonic flow of the air. The work includes FEM simulation of the jet formed from three different orifices in ANSYS CFZ 11.0. The simulation shows the distribution of air velocities, which is very important for the creation of nanofibers. In the [5] authors describe the simulation of electrical field distribution in process of bubble electrospinning. In this method Taylor cones can be created more easily by the help of pressured gas which flows through the electrospun liquid. Taylor cones are created directly on the bubbles. For better understanding an electrical field distribution around the bubble was computed. The simulation was performed in the of ANSYS 11.0. Above mentioned simulations are dealing with the flow of the gas or by the shape of electrical field. In this article an increase of thickness was simulated as combination of gas flow from jet through the porous layer of nanofiber structure together with the influence of electrostatic forces. These processes were causing the change in the fiber orientation in the planar layer. The orientation of fibers perpendicular to the plane determined the bulkiness, porosity and mechanical properties such as stiffness, flexibility, compressibility, and especially permeability. This paper describes a modified electrospinning technology, which allows controlling the change of the layer bulkiness. The process modification consists in the utilization of the additional gas flowing perpendicularly to the surface of fabric and expanding the formed layer. Understanding this process is very important for the control of the obtained layer properties. The process of nanofibrous layer creation was described by FEM model. The input parameters of the process were represented by the real mechanical properties of formed layers and properties of the applied flow. The influence of the surrounding environment is also taken into account. FEM simulation is very practical tool during the study of complex phenomena, especially in the optimization, because it can also help to build the corresponding analytical models [6-9]. During the preparation of the FEM model, the suitable assembly was also solved. The part representing the geometry of the electrode and the nozzle can be considered as a macrostructure, whereas the fiber part composed of nanofibers can be considered as a micro, respectively nano-structure. This should correspond to the dimensions of the finite mesh. In the case of nanofiber mesh the elements should not be larger than 20 nm. For given dimension of model geometry represents millions of elements. For connection of fine mesh with macrostructure, this macrostructure has to have similarly sized elements. Fine mesh of macrostructure would lead to ten millions elements and a failure of the calculation. In the case of the coarse mesh of macrostructure singularity occurs in connections. Therefore, the continuum model instead of the structural model was chosen for the description of the flow in nanostructure. Similar models of flow were described and applied, but not for the flow in the 3D nanostructure.

2. Background: Study of 3D Nanostructure Strain

2.1. Experimental Analysis

Strain study of the 3D nanofiber layer creation have been carried out on the basis of real experiment [10] in the experimental electrospinning device NanoLab^TM (Figure 1). The polymer solution of polyamide 6 (PA6) with a concentration of a 12% of acetic acid was used for the electrospinning. The process was carried out at a temperature, humidity 30% and potential gradient of electrostatic field 75 kV and 0,084 mA. Strain in the formed 3D nanofibrous structures is caused by the pressure of applied gas flow that passes through nozzles in the negative electrode (collector), acting in the opposite direction to the nanofibre collection.

The principle is schematically shown in Figure 2. Reorganization of nanofiber layers is caused by the movement of the gas flow. The flow can be characterized by pressure and velocity. In the presented experiment three different gases were used. The flow rate of the individual gases was changed, because of the different specific densities, but output pressure was kept constant. Constant output pressure results in the equivalent deformation of the structure.

The parameters of the flowing media are shown in Table 1. The character of the resulting strain is shown in

Figure 1. Experiment: Measurements are carried out on the NanoLab^TM device.

Figure 2. Principle of the electrostatic spinning.

Table 1. Paremeters of the gass flow.

Figure 3. It is shown that acting flow of gas results in regularly wrinkled structure. The gas penetrates and extends layers not only in places of nozzles, but also outside of them because the gas flows also in pores of arising nanofiber layer.

Conflicts of Interest

The authors declare no conflicts of interest.

References

[1]	A. Formhals, “Process and Apparatus for Preparing Artificial Threads,” US patent No. 1.975.504, 1934.
[2]	Y. Wang, et al., “Modeling and Fabrication of Electros pun Polymer Nanofibers with Tailored Architectures for Tissue Engineering Scaffold Applications,” IEEE International Conference on Computational Intelligence for Measurement Systems and Applications, CIMSA ‘09, 11-13 May 2009, pp. 226-229, doi:10.1109/CIMSA.2009.5069954
[3]	X. Wang, H. Niu, X. Wang and T. Lin, “Needleless Elec trospinning of Uniform Nanofibers Using Spiral Coil Spinnerets,” Journal of Nanomaterials, Vol. 2012, 2012, Article ID: 785920. doi:10.1155/2012/785920
[4]	A. Suzuki and K. Arino, “Polypropylene Nanofiber Sheets Prepared by CO2 Laser Supersonic Multi-Drawing,” European Polymer Journal, Vol. 48, No.7, 2012, pp. 1169-1176. doi:10.1016/j.eurpolymj.2012.04.003
[5]	L. Dong, Y. Liu, R. Wang, W. M. Kang and B. W. Cheng, “Mathematical Model of Electric Field Distribution at a Critical State in Bubble Electrospinning, ” Journal of Fiber Bioengineering and Informatics, Vol. 3, No. 2, 2010, pp. 117-120. doi:10.3993/jfbi09201010
[6]	M. Petru, O. Novak and P. Lepsik, “Increase of the Efficiency of the Production Lines for the Spinning of Inor ganic Nanofibers by the Electrostatic Field Intensity Op timization,” MM Science Journal, 2012, pp. 382-385. http://www.mmscience.eu/archives/MM_Science_201217.pdf
[7]	D. Herak, A. Kabutey, M. Divisova and S. Simanjuntak, “Mathematical Model of the Mechanical Behavior of Jatropha curcas L. Seed under Compression Loading,” Bio systems Engineering, Vol. 114, No. 3, 2013, pp. 279-288. doi:10.1016/j.biosystemseng.2012.12.007
[8]	M. Petru, O. Novak, D. Herak and S. Simanjuntak, “Finite Element Method Model of the Mechanical Behavior of Jatropha curcas L. Seed under Compression Loading,” Biosystems Engineering, Vol. 111, No. 4, 2012, pp. 412-421. doi:10.1016/j.biosystemseng.2012.01.008
[9]	M. Petru, O. Novak and P. Lufinka, “Study and Analysis of Transmissibility of Car Seat with Non Polyurethane Material,” Proceedings of 50th Annual Conference on Experimental Stress Analysis, Tabor, 4-7 June 2012, pp. 321-326.
[10]	D. Vejrych and L. Sevcik, “Assesing the Distribution of Deformation in Layers in 3D Nanostructures Spinning into Another Space,” Proceedings of the 5th International Mechanical Engineering Forum, Prague, 20-22 June 2012, pp. 962-970.
[11]	M. Dekys and O. Broncek, “Measuring Strain of the Lattice Towers,” Communications: Scientific Letters of the University of Zilina, Vol. 14, No. 3, 2012, pp. 39-42. http://www.uniza.sk/komunikacie/archiv/2012/3/3_2012en.pdf
[12]	Z .Bittnar and J. Sejnoha, “Numerical Methods in Structural Mechanics,” Pitman Monographs and Surveys in Pure and Applied Mathematics, Thomas Telford Publications, London, 1996.
[13]	K. Levenberg, “A Method for the Solution of Certain Non-Linear Problems in Least Squares,” Quarterly of Applied Mathematics, Vol. 2, 1944, pp. 164-168.
[14]	D. Marquardt, “An Algorithm for Least-Squares Estimation of Non-Linear Parameters,” SIAM Journal of Applied Mathematics, Vol. 11, No. 2, 1963, pp. 431-441. doi:10.1137/0111030
[15]	J. Jedrysiak, “Free Vibrations of Thin Periodic Plates Interacting with an Elastic Periodic Foundation,” International Journal of Mechanical Sciences, Vol. 45, No. 8, 2003, pp. 1411-1428. doi:10.1016/j.ijmecsci.2003.09.011
[16]	I. E. Avramidis and K. Morfidis “Bending of Beams on the Three-Parameter Elastic Foundation,” International Journal of Solids and Structures, Vol. 43, No. 2, 2006, pp. 357-375. doi:10.1016/j.ijsolstr.2005.03.033
[17]	S. K. Papachristou and D. S. Sophianopoulos, “Buckling of Beams on Elastic Foundation Considering Discontinous (Unbonded) Contact,” International Journal of Mechanics and Applications, Vol. 3, No. 1, 2013, pp. 4-12.
[18]	K. Rektorys, “Varitional Methods in Mathematics, Science and Engineering,” 2th Edition, D. Reidel Publishing Company, Boston, 1980.
[19]	M. Krizek and P. Neittanmaki, “Finite Element Approximation of Variational Problems and Applications,” Pit man Monographs and Surveys in Pure and Applied Mathematics, 50. Longman Scientific and Technical Publications, Copublished by John Wiley and Sons, Inc., New York, 1990.
[20]	M. Komarek and L. Martinova, “Design and Evaluation of Melt-Electrospinning Electrodes,” Proceedings of 2nd NANOCON International Conference, Olomouc, 12-14 October 2010, pp. 72-77.
[21]	B. Neckar and D. Das, “Modelling of Fibre Orientation in Fibrous Materials,” Journal of the Textile Institute, Vol. 103, No. 3, 2012, pp. 330-340. doi:10.1080/00405000.2011.578357
[22]	C. C. Tsai, et al., “Nanoporous Artificial Proboscis for Probing Minute amount of Liquids,” Nanoscale, Vol. 3, No. 11, 2011, pp. 4685-4695. doi:10.1039/c1nr10773a
[23]	D. H. Reneker, A. L. Yarin, E. Zussman and H. Xu, “Electrospinning of Nanofibers from Polymer Solutions and Melts,” Advances in Applied Mechanics, Vol. 41, 2007, pp. 43-195. doi:10.1016/S0065-2156(07)41002-X
[24]	J. H. Yu, S. V. Fridrikh and G. C. Rutledge, “Production of Submicrometer Diameter Fibers by Two-Fluid Electrospinning,” Advanced Materials, Vol. 16, No. 17, 2004, pp. 1562-1566. doi:10.1002/adma.200306644
[25]	R. Wienands and W. Joppich, “Practical Fourier Analysis for Multigrid Methods,” Chapman & Hall/CRC, 2005, p. 217.