Two-dimensional modeling of dry spinning of polymer fibers

doi:10.1016/j.jnnfm.2004.03.003

Journal of Non-Newtonian Fluid Mechanics

Volume 118, Issues 2–3, 5 April 2004, Pages 121-136

https://doi.org/10.1016/j.jnnfm.2004.03.003 Get rights and content

Abstract

Predictions of the dynamics of dry spinning of polymer fibers based on a two-dimensional model are presented. The constitutive equation used to describe the spinning fluid includes both viscous and viscoelastic effects and is based on an equivalent parallel combination of a non-linear Giesekus equation and a simple Newtonian component. Temperature and composition effects are accounted for in the viscosity, glass transition, and zero-shear modulus, and through these, in the associated relaxation time of the constitutive model. Inclusion of the viscous component enables predictions of the distinction between locking-in of the fiber velocity profile due to the rapidly rising viscosity and consequently dropping deformation rate, and fiber solidification due to the occurrence of a glass transition. Predictions of the axial and radial profiles of temperature, composition, stress, and orientation reflect the occurrence of skin-core morphology. Moreover, the single free parameter in the model, representing the ratio of the Newtonian component viscosity to that of the total viscosity, affects the fiber force profiles, and most especially the fiber axial velocity profile, and can therefore be used as a fitting parameter for spinline data.

Introduction

Dry spinning is used to produce man-made fibers from polymers such as cellulose acetate, cellulose triacetate, polymers and copolymers of vinyl chloride, and acrylonitrile. Despite the commercial importance of this processing technology, related modeling studies have received relatively little attention in recent years. Early studies [1], [2], [3], [4] focused on one-dimensional modeling of the initial stages, modeling the first several centimeters along the spin line. Later, Brazinsky et al. [5] performed a simple two-dimensional modeling study on both mass and heat transfer processes, in which constant filament density was assumed. More recently, Sano [6] presented a model which is two-dimensional for the mass transfer process only, but includes the affects of variable filament density. In all of these endeavors, a purely viscous, Newtonian constitutive equation was used to model the rheological behavior of the polymer spin solution. In his thesis study, Koelling [7] employed a Giesekus constitutive equation to model the solution. However, his spinline model predictions for the dimensionless velocity profile did not exhibit the plateau behavior generally characteristic of the process [5]. Interestingly, their predictions were shown to fit one set of experimental velocity profile data. Gou and McHugh [8] developed a one-dimensional model based on a modified form of the Giesekus equation in which a non-linear spring force factor is added to account for finite chain extensibility.

The purpose of this paper is to present a two-dimensional analysis of the dry spinning process that incorporates both viscous and viscoelastic contributions to the constitutive equation, along with effects due to non-constant density. The inclusion of these effects, along with radial and axial variations in the concentration and temperature fields, leads to more accurate predictions of the solidification behavior, skin formation, and chain orientation.

Section snippets

Model development

Fig. 1 illustrates the process variables and some boundary conditions. In the following development, subscripts 1 and 2 refer, respectively, to the polymer and solvent. As seen, an axisymmetric stream of spin dope exits a spinneret of diameter d_s at a mass flow rate W and temperature T_s and is drawn continuously at a take-up speed v_L. The volume fraction of solvent in the spin dope is φ_2s. The extruded dope swells to a diameter larger than the spinneret hole and at the point of maximum die

Material properties and input parameters

Cellulose acetate fibers are most commonly produced by dry spinning, hence, we chose the system cellulose acetate (CA)–acetone for illustration of our model predictions.

Coordinate transformation and non-dimensionalization

The fiber radius R(z) represents a free surface, which reduces with axial distance z. In the computation, the free surface domain is converted to a fixed rectangular domain by normalizing the radial coordinate r with the fiber radius R(z), namely, $r^{∗} = r R(z) .$ As a result, one can show that $∂ ∂r_{z} = 1 R ∂ ∂r^{∗}_{z},$ $∂^{2} ∂r^{2}_{z} = 1 R^{2} ∂^{2} ∂r^{∗2}_{z},$ $∂ ∂z_{r} = ∂ ∂z_{r^{∗}} − r^{∗} R d R d z ∂ ∂r^{∗}_{z} .$

For computational efficiency, all of the variables and properties with dimensions in the model equations are non-dimensionalized. Particularly, a

Temperature profiles and determination of glass transition point

Fig. 4 shows the computed axial temperature profiles at the fiber surface and center as well as the cross-sectionally averaged temperature axial profile. The axial profiles show that the temperature drops very quickly, reaching a local minimum, and then rises dramatically, eventually approaching the ambient temperature. The large drop in the temperature at the beginning reflects the endothermal effect of solvent evaporation. The overlapping of these three temperature profiles suggests a

Conclusions

In this paper, we have shown predictions of the dynamics of dry spinning of polymer fibers based on a two-dimensional model for the temperature, composition, and associated stress profiles. Both viscous and viscoelastic effects are incorporated in the constitutive model for the spin fluid through an equivalent parallel combination of a non-linear Giesekus equation and a simple Newtonian component. Temperature and composition effects are also included in the viscosity, glass transition, and

Acknowledgements

This work has been supported in part by the ERC program of the National Science Foundation under Award No. EEC-9731680 administered through the Center for Advanced Engineering Fibers and Films at Clemson University, and in part by a grant from Celanese Acetate LLC.

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Two-dimensional modeling of dry spinning of polymer fibers

Abstract

Introduction

Section snippets

Model development

Material properties and input parameters

Coordinate transformation and non-dimensionalization

Temperature profiles and determination of glass transition point

Conclusions

Acknowledgements

J. Non-Newtonian Fluid Mech.

Mass transfer during dry spinning of fibers

J. Appl. Polym. Sci.

Studies on dry spinning. I. Fundamental equations

J. Appl. Polym. Sci.

Studies on dry spinning. II. Numerical solutions for some polymer–solvent systems based on the assumption that drying is controlled by boundary-layer mass transfer

J. Appl. Polym. Sci.

Dry spinning process: comparison of theory with experiment

Polym. Eng. Sci.

Drying behavior of acetate filament in dry spinning

Drying Technol.

A comparison of Newtonian and viscoelastic constitutive models for dry spinning of polymer fibers

J. Appl. Polym. Sci.

Separation of elastic and viscous effects in polymer melt extrusion

J. Appl. Polym. Sci.

Elastic behavior of concentrated solutions of acrylonitrile copolymers

J. Appl. Polym. Sci.