The purpose of this chapter is to highlight the influences of gravity and inertia on the critical draw ratio. Each effect is treated separately in order to isolate the associated dynamics. Besides the correlations between the critical draw ratio and the particular control parameters, the focus lies here on the physical mechanism underlying the change in stability behavior. Moreover, the alternative stability criteria of Kim and Jung, ( 3.33 ) and ( 3.36 ), respectively, will be tested for applicability. Simplified versions of the film model derived in Sect.  2.2 will be used to study the influence of inertia and gravity. Note that the results will be equivalent for the fiber model with neglecting surface tension by simply replacing the thickness h with the cross-section a and the constant Trouton ratio of 4 by 3. The latter can be achieved as well by multiplication of \(Re\) or, respectively, \(Re/F\!r\) with 3/4, which can be directly seen in the momentum equations.

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Influence of Gravity and Inertia

  • Mathias Bechert,
  • Benoit Scheid

摘要

The purpose of this chapter is to highlight the influences of gravity and inertia on the critical draw ratio. Each effect is treated separately in order to isolate the associated dynamics. Besides the correlations between the critical draw ratio and the particular control parameters, the focus lies here on the physical mechanism underlying the change in stability behavior. Moreover, the alternative stability criteria of Kim and Jung, ( 3.33 ) and ( 3.36 ), respectively, will be tested for applicability. Simplified versions of the film model derived in Sect.  2.2 will be used to study the influence of inertia and gravity. Note that the results will be equivalent for the fiber model with neglecting surface tension by simply replacing the thickness h with the cross-section a and the constant Trouton ratio of 4 by 3. The latter can be achieved as well by multiplication of \(Re\) or, respectively, \(Re/F\!r\) with 3/4, which can be directly seen in the momentum equations.