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synopsisTwo experimental studies of the melt spinning of fibers have been carried out using low-density polyethylene and polystyrene. First, isothermal spinning experiments were carried out and the relationship between the fiber kinematics and drawdown force was studied. The data were correlated by using the following two methods: (1) the concept of a non-Newtonian elongational viscosity and (2) a nonlinear integral theory of viscoelastic fluids. In the second experiment, the spinline temperature profile of a monofilament fiber being pulled down from a spinneret through stagnant air was measured and the heat transfer coefficient computed. A correlation between the local Nusselt number and a fiber Reynolds number was obtained. An integral boundary layer analysis of forced convection heat transfer from a descending fiber was carried out.

Correlation has been obtained between dragreducing characteristics for turbulent flow in a pipe and measurable properties of several polymer solutions. Several concentrations of high molecular weight polymethyl methacrylate in toluene, high molecular weight polyisobutylene in both toluene and cyclohexane, medium molecular weight polyisobutylene in cyclohexane and benzene and low molecular weight polystyrene in toluene were studied. Data obtained in these nonpolar solvents and literature data for more polar solvents were successfully correlated as the ratio of measured friction factor to purely viscous friction factor vs the modified Deborah number VT1/DO.2, where Tl is the first-mode relaxation time of the solution estimated by the Zimm theory. A shift factor which is a function of intrinsic viscosity 11(4[7]] -1) allowed all the data obtained with nonpolar solvents to be correlated as a single function. For these systems, most of the data fit a single curve to within ± 5 percent of the average friction factor ratio. The shift factor did not give a unique function of the data for the more polar systems.

The piezoelectric impact probe of Wells et al. was used to compare measurements of turbulence intensity in a pipe of purely viscous solvents with viscoelastic polymer solutions and to compare with measurements made with hot-film anemometer probes. An equation was derived which shows the form of normal and shear stress contributions to measured fluctuating impact pressure in viscoelastic fluids. The equation indicated that for viscoelastic fluids, low values of intensities of turbulence can be obtained by neglecting normal and shear stress effects. Experimental measurements showed that turbulence intensities measured at the pipe center with the piezoelectric probe were the same as those measured with a hot-film wedge probe for viscoelastic solutions, but that as the wall was approached, the piezoelectric probe values were low for the viscoelastic solutions. Nomenclature e x = unit vector in the axial direction in cylindrical coordinates e r = unit vector in the radial direction in cylindrical coordinates £0 = unit vector in the tangential direction in cylindrical coordinates g(x) = function of the shear stress fluctuations I = displacement vector p f -fluctuating component of pressure P = pressure P = time-averaged value of P P p = pressure measured by impact tube pt = fluctuating component of pressure measured by piezoelectric probe Pt = total pressure measured by piezoelectric probe Pt = time-averaged value of P t P w = static pressure at the wall r = radial coordinate R = tube radius u f = fluctuating velocity component in the axial direction U_ = velocity in the axial direction U = time-averaged value of U v' = fluctuating velocity component in the radial direction V = velocity vector in cylindrical coordinates x = longitudinal coordinate X c = characteristic time of the flow p = density AI = viscosity (Tl • = deviatoric normal stress aii = time-averaged deviatoric normal stress

values.The mass transfer between fluid elements is considered to be caused mainly by coalescence and dispersion, and thus the overall mass transfer coefficient may be dependent on frequency of coalescence and dispersion, contact time, and contact area of fluid elements. Although U might be expected to vary with agitation speed, we assumed U to be a constant. The values of p were computed for parametric values of U, with k = 1.10, B = 0.10, K = 0.10, Z1 =297, and I 2 = 1.0. In Figure 4, the calculated values of P are plotted vs. the period T together with the experimental results by using f = 0.5 for bafflled and 0.25 for unbaffled vessels. A comprehensive geometrical model has not been made. For periods greater than 10 sec., the calculated reaction rates are relatively insensitive to period but are dependent upon the mass transfer rate. At small periods, the reaction rates is insensitive to the mass transfer rates. The analytical and experimental methods for the chloral hydrate system indicate sufficient concurrence to merit reporting the simple approaches used for the model.