March  2012, 5(1): 97-112. doi: 10.3934/krm.2012.5.97

A smooth 3D model for fiber lay-down in nonwoven production processes

1. 

Fachbereich Mathematik, Technische Universität Kaiserslautern, Germany, Germany

2. 

Fraunhofer ITWM, Kaiserslautern, Germany

Received  March 2011 Revised  August 2011 Published  January 2012

In this paper we develop an improved three dimensional stochastic model for the lay-down of fibers on a moving conveyor belt in the production process of nonwoven materials. The model removes a drawback of a previous 3D model, that is the non-smoothness of the fiber paths. A similar result in the 2D case has been presented in [12]. The resulting equations are investigated for different limit situations and numerical simulations are presented.
Citation: Axel Klar, Johannes Maringer, Raimund Wegener. A smooth 3D model for fiber lay-down in nonwoven production processes. Kinetic & Related Models, 2012, 5 (1) : 97-112. doi: 10.3934/krm.2012.5.97
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L. Bonilla and T. Götz, A. Klar, N. Marheineke and R. Wegener, Hydrodynamic limit of a Fokker-Planck equation describing fiber lay-down processes,, SIAM J. Appl. Math., 68 (): 648.  doi: 10.1137/070692728.  Google Scholar

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ZAMM Z. Angew. Math. Mech., 89 (2009), 941-961. doi: 10.1002/zamm.200900282.  Google Scholar

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A. Klar, J. Maringer and R. Wegener, A 3D model for fiber lay-down processes in non-woven production processes,, to appear in MMMAS., ().   Google Scholar

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Springer, 2004. Google Scholar

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show all references

References:
[1]

Wiley, 2003. Google Scholar

[2]

Springer, 1978. Google Scholar

[3]

Studies in Mathematics and its Applications, 5, North-Holland Publishing Co., Amsterdam-New York, 1978.  Google Scholar

[4]

L. Bonilla and T. Götz, A. Klar, N. Marheineke and R. Wegener, Hydrodynamic limit of a Fokker-Planck equation describing fiber lay-down processes,, SIAM J. Appl. Math., 68 (): 648.  doi: 10.1137/070692728.  Google Scholar

[5]

J. Comp. Phys., 227 (2008), 7929-7951. doi: 10.1016/j.jcp.2008.05.002.  Google Scholar

[6]

J. Stat. Phys., 131 (2008), 989-1021. doi: 10.1007/s10955-008-9529-8.  Google Scholar

[7]

J. Dolbeault, A. Klar, C. Mouhot and C. Schmeiser, Hypocoercivity and a Fokker-Planck equation for fiber lay-down,, preprint., ().   Google Scholar

[8]

C. R. Acad. Sci. Paris, 347 (2009), 511-516.  Google Scholar

[9]

SIAM J. Appl. Math., 67 (2007), 1704-1717. doi: 10.1137/06067715X.  Google Scholar

[10]

Math. Models Methods Appl. Sci., 15 (2005), 737-752. doi: 10.1142/S021820250500056X.  Google Scholar

[11]

Journal of the Textile Institute, 67 (1976), 373-386. doi: 10.1080/00405007608630170.  Google Scholar

[12]

KRM, 2 (2009), 489-502. doi: 10.3934/krm.2009.2.489.  Google Scholar

[13]

ZAMM Z. Angew. Math. Mech., 89 (2009), 941-961. doi: 10.1002/zamm.200900282.  Google Scholar

[14]

A. Klar, J. Maringer and R. Wegener, A 3D model for fiber lay-down processes in non-woven production processes,, to appear in MMMAS., ().   Google Scholar

[15]

Springer, 2004. Google Scholar

[16]

Proc. R. Soc. Lond. Ser. A, 452 (1996), 1679-1694. doi: 10.1098/rspa.1996.0089.  Google Scholar

[17]

SIAM J. Appl. Math., 66 (2006), 1703-1726. doi: 10.1137/050637182.  Google Scholar

[18]

International Journal of Multiphase Flow, 37 (2011), 136-148. doi: 10.1016/j.ijmultiphaseflow.2010.10.001.  Google Scholar

[19]

Princeton University Press, Princeton, N.J., 1967.  Google Scholar

[20]

Kinetic and Related Models, 2 (2009), 363-378. doi: 10.3934/krm.2009.2.363.  Google Scholar

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