Spinning Stress

Ziabicki [187] has given an extensive review of studies of the melt-spinning process. Some derivations from this review are discussed briefly. A simple analysis for predicting the effects of process parameters on fiber orientation are also discussed before polypropylene data are presented. To summarize, the properties of spun polypropylene fiber (and other fibers as well) are primarily determined by the stress existing in the spin line at the position of the final diameter, at least at moderate spinning speeds. The stress level is determined largely by  

Following Ziabicki [187], we may assume that the radial variation of velocity is negligible in a spin line. With this assumption, one may integrate the equations of motion to obtain a force balance for any axial position  

Term 1 is the total spin-line force at any spin-line position term 2 is the spin-line force at position of maximum die swell term 3 is the force due to acceleration of spin line term 4 is force due to surface tension term S is the force due to gravity and term 6 is force due to air drag. If cross-flow is present, there will be another term. This form of force balance presents a clear picture of the terms contributing to the stress at any position. For making calculations, the integration is carried out from the take-up position, where the force is measured, up to any arbitrary spin-line position. This will eliminate from the calculation the force term at the position of maximum diameter, which is not easily evaluated. 

If the absence of a radial temperature distribution is assumed, the following is obtained for the energy balance  

The temperature of the fiber at any axial position is of course determined by the extrusion temperature, convective heat transfer, radiative heat transfer, and heat liberation due to crystallization. Heat generated by viscous dissipation is negligible. 

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Another feature of high-speed spinning is that the fiber macro structure becomes non-uniform, with more orientation and crystallinity near the fiber surface than in the interior. This is a result of non-uniform solidification, where rapid cooling generates a lower temperature and higher viscosity at the surface. This leads to an oriented surface skin which supports the spinning stress, while higher temperatures within the interior allow more relaxation and disorientation. 

This transition is surprisingly sharp—occurs at a stress of about 0.1 g/d. Increasing the spinline stress increases the number of rows and decreases the diameter of the fibrillar structure. As the fibrils are stable only in the presence of the spinning stress, they may or may not be visible in the final fiber morphology. A useful way of conceptualizing the process is to divide the spinline into three regions, namely ... 

The features of the Nadella study are similar to those observed for polypropylene by other authors. The variations in the crystalline orientation functions are also similar to those reported for high-density polyethylene. Dees and Spruiell [196] interpreted these variations for polyethylene to indicate spherulitic structure at low spinning stresses but which undergo a... 

At low spinning speeds, usually 1000-2000 m/min, stress-induced crystallization is absent. Although an increasing level of spinning stress promotes polymer chain orientation, low spinning speeds do not have any significant effect on crystallization. 

Parameter Effect on Spinning Stress Effect on Filament Temperature Time Spent in Spinning Line Fiber Orientation Fiber Crystallinity Remarks... 

EOY speeds are the most recent development in PET spinning (78). Properties are similar to HOY and appear to be limited by the differential cooling rate from filament surface to filament core. This leads to radial distribution of viscosity, stress, and, consequentiy, molecular orientation (75). Eiber tensde strength is limited. Nevertheless, speeds up to 7000 m /min are commercial and forecasts are for speeds up to 9000 m /min by the year 2000 (79). Speeds to 9000 m/min have been studied (68,80,81). 

Elasticity is another manifestation of non-Newtonian behavior. Elastic Hquids resist stress and deform reversibly provided that the strain is not too large. The elastic modulus is the ratio of the stress to the strain. Elasticity can be characterized usiag transient measurements such as recoil when a spinning bob stops rotating, or by steady-state measurements such as normal stress ia rotating plates. 

Goldberg and Rubin [Ind. Eng. Chem. Proce.s.s Des. Dev., 6 195 (1967)] showed in tests with a disk spinning vertically to the foam layer that most mechanical procedures, whether centrifugation, mixing, or blowing through nozzles, consist basically of the application of shear stress. Subjecting foam to an air-jet impact can also provide a source... 

In the language of Section A.4, s and d are indifferent but s is not, involving extra terms in Q. In order to render the stress rate indifferent, the extra terms must be cancelled out. This may be done using the spin tensor w defined in (A.l Ij), following the steps leading to (A.68). The result is... 

In order to eliminate the last two terms on the right, it may be noted that the spin tensor in (A.612) gives rise to terms in Q. Postmultiplying (A.612) by the stress leads to... 

The melt-spinning process used to convert mesophase pitch into fiber form is similar to that employed for many thermoplastic polymers. Normally, an extruder melts the pitch and pumps it into the spin pack. Typically, the molten pitch is filtered before being extruded through a multi-holed spinnerette. The pitch is subjected to high extensional and shear stresses as it approaches and flows through the spinnerette capillaries. The associated torques tend to orient the liquid crystalline pitch in a regular transverse pattern. Upon emerging from the... 

There are basically two different computer simulation techniques known as molecular dynamics (MD) and Monte Carlo (MC) simulation. In MD molecular trajectories are computed by solving an equation of motion for equilibrium or nonequilibrium situations. Since the MD time scale is a physical one, this method permits investigations of time-dependent phenomena like, for example, transport processes [25,61-63]. In MC, on the other hand, trajectories are generated by a (biased) random walk in configuration space and, therefore, do not per se permit investigations of processes on a physical time scale (with the dynamics of spin lattices as an exception [64]). However, MC has the advantage that it can easily be applied to virtually all statistical-physical ensembles, which is of particular interest in the context of this chapter. On account of limitations of space and because excellent texts exist for the MD method [25,61-63,65], the present discussion will be restricted to the MC technique with particular emphasis on mixed stress-strain ensembles. 

It should be stressed that the amplitudes x introduced above are not the usual covariant amplitudes. Their relation to the more familiar covariant Klein-Gordon amplitude for a spin 0 particle and the covariant Dirac amplitude for a spin particle will be discussed at the appropriate place. In the next section we turn to a discussion of the covariant amplitudes describing spin 0 particles. 

When the length scale approaches molecular dimensions, the inner spinning" of molecules will contribute to the lubrication performance. It should be borne in mind that it is not considered in the conventional theory of lubrication. The continuum fluid theories with microstructure were studied in the early 1960s by Stokes [22]. Two concepts were introduced couple stress and microstructure. The notion of couple stress stems from the assumption that the mechanical interaction between two parts of one body is composed of a force distribution and a moment distribution. And the microstructure is a kinematic one. The velocity field is no longer sufficient to determine the kinematic parameters the spin tensor and vorticity will appear. One simplified model of polar fluids is the micropolar theory, which assumes that the fluid particles are rigid and randomly ordered in viscous media. Thus, the viscous action, the effect of couple stress, and... 

This apparent time dependent cell disruption is caused because of the statistically random distribution of the orientation of the cells within a flow field and the random changes in that distribution as a function of time, the latter is caused as the cells spin in the flow field in response to the forces that act on them. In the present discussion this is referred to as apparent time dependency in order to distinguish it from true time-dependent disruption arising from anelastic behaviour of the cell walls. Anelastic behaviour, or time-dependent elasticity, is thought to arise from a restructuring of the fabric of the cell wall material at a molecular level. Anelasticity is stress induced and requires energy which is dissipated as heat, and if it is excessive it can weaken the structure and cause its breakage. 

The main objectives of this article are (i) to give an account of the simple theory related to spin-lattice relaxation-rates, in a language that is directed, as far as possible, to the practising chemist rather than to the theoretician (ii) to caution against uncritical use of this simple theory for systems that are strongly coupled, or undergoing anisotropic reorientation, or both (hi) to introduce the pulse n.m.r. experiments that are used to measure spin-lattice relaxation-rates, and to stress the precautions necessary for accurate... 

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