Kinetic and Related Models (KRM)

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

Pages: 97 - 112, Volume 5, Issue 1, March 2012      doi:10.3934/krm.2012.5.97

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Axel Klar - Fachbereich Mathematik, Technische Universit├Ąt Kaiserslautern, Germany (email)
Johannes Maringer - Fachbereich Mathematik, Technische Universit├Ąt Kaiserslautern, Germany (email)
Raimund Wegener - Fraunhofer ITWM, Kaiserslautern, Germany (email)

Abstract: 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.

Keywords:  Fiber dynamics, stochastic processes, Fokker-Planck equations, diffusion approximation.
Mathematics Subject Classification:  37H10, 35Q84, 41A60.

Received: March 2011;      Revised: August 2011;      Available Online: January 2012.