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

Affiliation(s)

Institute for Nanomaterials, Advanced Technologies and Inovation, Technical University of Liberec, Liberec, Czech Republic.

Department of Nonwovens, Technical University of Liberec, Liberec, Czech Republic.

Department of Machine Elements and Mechanism, Technical University of Liberec, Liberec, Czech Republic.

Institute for Nanomaterials, Advanced Technologies and Inovation, Technical University of Liberec, Liberec, Czech Republic.

Department of Nonwovens, Technical University of Liberec, Liberec, Czech Republic.

Department of Machine Elements and Mechanism, Technical University of Liberec, Liberec, Czech Republic.

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.

Cite this paper

M. Petrů, O. Novák, D. Vejrych and P. Lepšík, "FEM Study of the Strain Kinematics in the 3D Nanofibrous Structure Prepared by the Electrospinning Process,"*Applied Mathematics*, Vol. 4 No. 5, 2013, pp. 80-90. doi: 10.4236/am.2013.45A010.

M. Petrů, O. Novák, D. Vejrych and P. Lepšík, "FEM Study of the Strain Kinematics in the 3D Nanofibrous Structure Prepared by the Electrospinning Process,"

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[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.