Fiber spinning viscoelastic

It is appropriate at this time to introduce viscoelastic flow analysis. Fiber spinning is one of the few processes that can be analyzed using analytical viscoelastic models. Here, we follow the approach developed by Denn and Fisher [4], Neglecting inertia, we can start with the momentum balance by modifying eqn. (6.79) as,... 

Figure 6.20 Comparison between experimental and computed velocity profiles during fiber spinning using Denn and Fisher s viscoelastic model [4].

White JL (1964) Dynamics of viscoelastic fluids, melt fracture, and the rheology of fiber spinning. J Appl Polym Sci 8 2339-2357... 

There is a special case when viscosity is low for homogeneous fiber spinning but higher than that required for jet breakup. In this case, beads are formed on fibers as droplets. At some places the liquid jet springs back and becomes twitched in specific locations because of the viscoelastic-behavior of the solution. A SEM micrograph of typical beaded fibers is shown in Figure 10.9 [79]. Usually, the charge density is relatively low. 

Data on extensional stresses in fiber melt spinning, and their constitutive modeling for both isothermal and nonisothermal fiber spinning, can be found in the several books referred to earlier. Further modeling elforts are discussed by Denn.(66) However, it is fair to say that no totally acceptable rheological model has so far been found to quantitatively explain viscoelastic fiber-spinning results. The question of rheological constitutive equations is examined briefly in Section 7. 

Our analysis of fiber spinning in this chapter will be based on an inelastic rheological model of the stresses. This rheological description appears to be adequate for polyesters and nylons, which comprise the bulk of commercial spinning applications, and our spinning model is essentially the one used in industrial computer codes. This is a process in which melt viscoelasticity can sometimes play an important role, however, and we will revisit the process in Chapter 10. 

Fiber spinning, discussed in Chapter 7, is a process in which the residence time is short hence, transient viscoelastic effects are likely to be important. Our starting point for a steady-state thin filament analysis is Equation 7.26 ... 

The book begins with introductory material and a brief review of fundamentals, after which the first part focuses on analytical treatments of basic polymer processes extrusion, mold filling, fiber spinning, and so forth. The thin gap (lubrication) and thin filament approximations are employed, and all analyses in this part are for inelastic liquids. An introduction to finite element calculation follows, where full numerical solutions are compared to analytical results. Polymer rheology is then introduced, with an emphasis on relatively simple viscoelastic models that have been used with some success to model processing operations. Applications in which melt viscoelasticity is important are then revisited, followed by a chapter on stability and sensitivity that focuses on melt spinning and a chapter on wall slip and extrusion... 

The analysis of electrospinning process is based on the slender-body theory. It is widely used in fiber spinning of viscoelastic liquid. To simplify the mathematical description, a few idealizing assumptions are made. The jet radius R decreases slowly along the axial direction dR Z) dZ fluid velocity x> is uniform in the cross section of the jet. 

Other examples of viscoelastic materials are synovial fluid, molten polymers (with thread-forming properties used in fiber spinning or film blowing), and "bouncing putty" or "nutty putty," which will flow if stretched slowly, but bounces if struck hard against a hard surface. 

Ishizuka, O., Koyama, K. Rheology and dynamics of melt spinning viscoelastic polypropylene and polyeth-ylenes. In High-Speed Fiber Spinning. Science and Engineering Aspects, Ziabicki, A., Kawai, H., eds. John Wiley Sons, New York, 1985, pp. 383-429. 

Better agreement with experiments was achieved by Phan-Thien (1978), who solved the fiber-spinning problem using the PTT viscoelastic model (see Eq. 3.45). In this case the constitutive equation was fitted to data for LDPE and PS and the solutions to the fiber-spinning problem were compared to experimental data. 

As in the fiber-spinning section, we first gain extensive understanding of the film blowing process by analyzing the simplest case, that of the isothermal Newtonian film blowing case. Then, we discuss some points about the nonisothermal film blowing for Newtonian and viscoelastic materials. The stability analysis of this process is introduced, and some overall remarks are presented at the end of this section. 

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