Chaotic Mixing in Extrusion-Based Melt Spinning of Fibers

M96-C1, page 1 Chaotic Mixing in Extrusion-Based Melt Spinning of Fibers Michael S. Ellison (leader), Bridgette L. Gomillion; David A. Zumbrunnen (Co-PI), Jiong Wang. Goal Statement The ultimate goal of this research is the development of a new, industrially relevant device and process wherein useful structures, such as submicron filaments, evolve directly within a major phase melt that can be subsequently extruded to form fibers or parts with internal reinforcements and enhanced physical properties. Abstract Chaotic mixing of thermoplastics has been used recently to produce, in small quantities within batch mixers, polymer blends with either interconnected fibrillar or lamellar microstructures. The novel microstructures evolved directly in the melt from initially coarse minor phase bodies due to the recursive stretching and folding characteristics that typify chaotic responses. Enhanced physical properties have been attributed to the novel microstructures. The results with batch mixers suggest that new, structured blends of potential importance to industry can be produced if chaotic mixing conditions can be established in a practical continuous flow device. Experimental and computational research in support of the design of such a device is reported. Introduction Blending of polymers is an economical and effective method to obtain products with desired properties. In addition to polymer selection, blend morphology is one of the most important factors determining the properties of a blend. The morphology is controlled by a number of factors including composition, viscosity ratio, interfacial tension, elasticity, and shearthinning effects. Unfortunately, dispersions of fine droplets is the morphology most commonly obtained when blending is performed in single or double screw extruders or in batch mixers. This blend morphology is not necessarily optimal for providing property enhancement. Recently, polymer blends have been created in special batch mixers by combining coarse molten polymer bodies by chaotic mixing [Zumbrunnen, et al. (1996), Liu and Zumbrunnen (1996)]. Both lamellar and fibrillar morphologies were created and have been shown to provide enhanced physical properties (Liu and Zumbrunnen, 1997). For example, the toughness of polystyrene was improved by 69% due to the in-situ formation of minor phase fibrils by the addition of only 9% by volume of low density polyethylene. During chaotic mixing, minor phase bodies are stretched and folded into thin lamellae. These lamellae may eventually divide into fibrils because of interfacial instabilities. In effect, chaotic mixing provides a unique processing environment in which structures are developed in-situ instead of being broken down as occurs in common mixing. Chaotic mixing has been investigated in the past chiefly as a means to understand mixing processes in general. Most investigations have focused on confined two dimensional flows, with

M96-C1, page 2 only a few venturing into three-dimensional unconfined flows. Given the successes of earlier work in obtaining blends having attractive morphologies using batch mixers, this study is being conducted to assess whether similar morphologies can be created in a continuous flow device. In particular, a device is being designed which, in conjunction with an extruder, can directly produce blends with either fibrillar or lamellar microstructures. This device operates in a continuous flow instead of a batch mode and has therefore been dubbed a continuous flow chaotic mixer (CFCM). Flow visualization techniques, as well as microscopic examination of solidified specimens, will be used to study the formation of the minor phase structures as they evolve. A parallel computational study will disclose the requisite conditions for chaotic mixing to occur in the CFCM and will also demonstrate morphological changes for comparison to the experimental results. Finally, the stability of the blend morphology to flow in a capillary will be assessed. Experimental Plan The design of the CFCM has been derived from two cavity (batch) mixers in which chaotic mixing has been well documented. One mixer is referred to as the eccentric cylinder cavity mixer and the other as the dual vortex mixer. Although based on the design of these mixers in order to provide continuity with prior work, the CFCM allows molten polymer to continuously enter and exit the mixer so that large quantities of materials can be produced for greater industrial relevance. The CFCM will be able to operate in the two configurations shown in Figure 1. In Figure 1a, mixing occurs due to the periodic rotation of the inner cylinders (rods) each of radius R i according to a specific protocol, while the outer cylinder of radius R o remains fixed. In Figure 1b, the alternate configuration for the CFCM is shown based on an eccentric cylinder cavity. Polymer melt fills the space between the cylinders which are rotated periodically to induce chaotic advection. Inner cylinder placement for both configurations is parametrized by the cylinder eccentricity e [= d/ (R o - R i )], where d is the distance between the centers of the inner and outer cylinders. Melt of the major phase polymer enters the CFCM from a standard extruder while the minor phase is injected into the CFCM such that morphology development occurs only in the CFCM. Frontal views of the CFCM are shown for both configurations in Figure 2. The outer cylinder is suspended from the top by an upper cylinder support block and stabilized on the bottom by a lower cylinder support block. The lower cylinder support block incorporates a converging channel to direct the flow into the monofilament spinneret. The cross-sectional view of this block is shown in Figure 3 and key dimensions for the CFCM are listed in Table 1. The outermost cylinder, shown with inlet and outlet hose connections, provides containment for a fluid which will be circulated to maintain the melt at a suitable processing temperature. An injection port at the top of the upper support block allows the introduction of the minor phase. The cylinders are made of glass so as to enable visual recording of the mixing processes occurring with the CFCM.

M96-C1, page 3 Figure 1. Cross-sectional views of the continuous flow chaotic mixer The drive system (not shown) for the inner cylinder(s) is composed of stepper motors and their allied control system. The control system monitors the rotation of the cylinders. Rotational rates and displacements are programmable. Table 1. Key dimensions of the CFCM Inside diameter, outer cylinder Outside diameter, outer cylinder Outside diameter, inner cylinder(s) Length 10.80 cm 12.00 cm 2.70 cm variable from 50.8 to 101.6 cm

M96-C1, page 4 Injection port Upper support block assembly Inlet hose connection Outer cylinder Vertical supports Outer cylinder jacket Outlet hose connection Lower support block Monofilament spinneret Inner cylinders Figure 2. Frontal views of the CFCM: (a) dual vortex geometry (b) eccentric cylinder geometry The CFCM will be mated with the spin head of our existing pilot scale melt spinning line. The setup is shown in Figure 4. Once the CFCM is filled with a thermoplastic melt of the major phase, chaotic mixing will be induced by periodically rotating the cylinders (Figure 1) according to a specific protocol to be determined from computational simulations. A minor phase thermoplastic (pigmented tracer) will be injected at a port near the inlet of the CFCM such that morphology development occurs only within the CFCM. The resulting blends will be discharged directly from the lower support block or through a spinneret to produce monofilament. Mixing conditions within the CFCM will be recorded photographically and the minor phase morphology

M96-C1, page 5 in microtome Figure 3. Cross-sectional view of the lower support block with converging channel slices of solidified filament extrudate will be examined by optical and electron microscopy. The monofilament will be quenched and wound at different speeds to assess the effect of the drawdown speed on the fiber microstructure and properties. The experimental study will utilize mixing chambers of varying lengths (ranging from 50.8 to 101.6 cm) and different material flow rates to investigate the effect of residence time on the stability of the formed structures in the minor phase. The converging flow angle in the lower support block (Figure 3) will also be varied with and without the spinneret in place to assess the influence of converging flow on the stability of the final structures exiting the CFCM. The composite formation aspect of the experimental study will proceed in two steps. We will use the same thermoplastics as in previous batch chaotic mixing experiments in order to demonstrate that structures formed in these studies can be obtained in a continuous flow process; hence, the first phase of the current project will utilize polystyrene as the major component and low density polyethylene as the minor component. The mixer parameters (mixing protocol, mixer length and converging angle) that are important for the formation and stabilization of the morphology in this system will be optimized. In addition, the impact of drawdown speed will be studied to assess it s role in morphological development. The second phase of the project is the production of materials with enhanced properties. Polymers selected for this aspect of the investigation will be chosen based on the desired properties of the blend. Although there is no single theory that describes the influence of viscoelasticity on droplet (minor component) deformation, studies indicate that droplets in a viscoelastic medium are harder to break up relative to droplets in a Newtonian system. The viscosity and elasticity ratios, dynamic interfacial tension coefficient, critical capillary number and blend composition all influence the ability of the droplet (minor component) to deform into fibrils. The mixer parameters that are important for the formation and stabilization of the morphology as a function of the blend properties mentioned above will be optimized. The morphology of the as-spun fibers will be examined using scanning electron microscopy, by freeze-fracturing and by selective dissolution of the major phase. Computational Model In order to establish chaotic mixing in the CFCM, the cylinders of the mixer must be rotated periodically according to specific protocols. These protocols for continuous flow devices are not presently known but may be determined by computational simulations in the manner done

M96-C1, page 6 previously for batch mixers (e.g., Miles, et al., 1995). In these simulations, the velocity field is determined so that the motion of individual fluid particles comprising minor phase bodies can be tracked. Under chaotic mixing conditions, particles do not follow specific paths periodically. Instead, neighboring particles move rapidly away from each other. These characteristics cause minor phase bodies in a melt to become stretched, as mentioned previously, and are detectable by constructing phase space trajectories and Poincaré sections, and also by calculating Lyapunov exponents. Algorithms for these tools are currently being developed. Extruder Tracer injection port Hopper Spin Head CFCM Control Cabinet Figure 4. Experimental setup The computational fluid mechanics code PHOENICS (version 2.2.1) has been employed to solve the Navier-Stokes equations and compute the velocity fields in three-dimensional space and for each instant of time. PHOENICS is based on the SIMPLE [Semi-Implicit Method for Pressure Linked Equations (Patankar, 1980)] algorithm to solve discretized representations of the momentum equations over a finite volume of a computational cell. In this algorithm, the discretized equations are first solved with an approximated pressure field to obtain estimated velocities at mesh points within a fixed computational grid. Conservation of mass is then applied to develop corrections to the velocity and pressure fields. This procedure is implemented interactively until a converged velocity field results for a specific time. In order to prevent the generation of unrealistic velocity fields, a staggered grid is used in which scalar variables are calculated at the center of a computational cell while velocity components are calculated at points located on the faces of each cell.

M96-C1, page 7 Numerical solutions can be determined with the finite volume method for conservation equations that can be placed into the general form, t ( ρφ) ( ρ φ) ( Γ φ) + div u = div grad + S The four terms in this partial differential equation account for unsteadiness, advection, diffusion, and sources. The dependent variable can represent a variety of quantities such as the mass fraction of a chemical species or temperature. In this study, the component flow velocities in three dimensional space are the dependent variables. The principal assumptions in the simulations are (i) Newtonian fluid, (ii) laminar flow, (iii) constant property fluids, (iv) negligible interfacial tension between phases, and (v) immiscible phases. The assumptions of Newtonian behavior and laminar flow are deemed appropriate since processing in the CFCM will occur at low Reynolds, Deborah, and Weissenberg numbers. Neglecting interfacial tension restricts the model's applicability to the mixing of similar polymers or to initial morphological changes in large minor phase bodies. However, this assumption will not constrain the primary objective of the computer simulations. Protocols for cylinder motion that provide chaotic mixing everywhere in the CFCM will be established using a single fluid. This procedure has been followed in a related study with batch mixers and was found to provide good results (Liu and Zumbrunnen, 1996). Two-phase simulations can be performed for blends having different viscosities but a small interfacial tension either due to molecular similarity or the addition of compatibilizing agents. The two-phase simulations will provide an indication of how interfaces between two fluids alter the flow field and thereby potentially change the mixing protocol necessary to achieve chaotic mixing conditions. Because the cylinder surfaces are not aligned to the coordinate axes of common orthogonal coordinate systems, a body-fitted-coordinate (BFC) system has been designed and used to construct the computational mesh. The finite volumes in a structured BFC grid remain topologically Cartesian. Thus, they retain six faces and eight corners, and cells that were originally adjacent remain adjacent. Compared to Cartesian and cylindrical coordinate systems, a BFC system requires more memory storage and computational expense. The computational grid and the BFC system is shown in Figure 5 for a grid coarser than the one actually used. The velocity field within the domain can be solved for any specified rotations of the inner and outer cylinders and for a given flow rate of polymer melt moving along the CFCM axis.

M96-C1, page 8 Figure 5. Computational grid for the determination of the instantaneous velocity fields in the eccentric cavity CFCM. The mesh in the x-y plane is shown for clarity in Figure 6. It is clear that the BFC grid is essentially a Cartesian grid that has been selectively deformed to conform to the boundaries of the physical system. Figure 2. Computational grid in the x-y plane. In preparation for the computational simulations, the model has been implemented to determine the velocity field for Stokes flow conditions with no axial flow component. Examples of results from these simulations are shown in Figure 3 in terms of streamlines. These results will be compared to previous two-dimensional solutions as one means to validate the model. Tests for grid size sensitivity, iteration tolerance, and numerical accuracy are also being performed before the model is used to simulate chaotic mixing in the CFCM.

M96-C1, page 9 (a) (b) (c) (d) Figure 3. Streamline patterns in the eccentric cylinder apparatus for different speeds of the outer and inner cylinders : (a) v out = 0, (b) v in = 0, (c) vout = 3 vin, (d) vout = 3 vin. References Liu, Y. H. And Zumbrunnen, D. A., Emergence of Fibrillar Composites Due to Chaotic Mixing of Molten Polymers, Polymer Composites, Vol. 17, pp. 187-197, 1996. Liu, Y. H. and Zumbrunnen, D. A., "Toughness Enhancement in Polymer Blends Due to the In- Situ Formation of Fine-Scale Extended Structures at Low Minor Phase Concentrations by Chaotic Mixing," Proceedings of the International Mechanical Engineering Congress and Exposition, Materials Division, ASME, New York, 1997 (in press). Jana, S. C., Metcalf, G., Ottino, J. M., Experimental and computational studies of mixing in complex Stokes flows: the vortex mixing flow and multicellular cavity flows, J Fluid Mech., Vol. 269, pp 199-246, 1994. Kusch, H. A. and Ottino, J. M., Experiments on mixing in continuous chaotic flows, J Fluid Mech., Vol. 236, pp 319-348, 1992. Miles, K. C., Nagarajan, B., and Zumbrunnen, D. A., Three-Dimensional Chaotic Mixing of Fluids in a Cylindrical Cavity, Journal of Fluids Engineering, Vol. 117, pp. 582-588, 1995. Ottino, J. M., The Kinematics of Mixing: Stretching, Chaos, and Transport, Cambridge Patankar, S. V., Numerical Heat Transfer and Fluid Flow, McGraw-Hill, New York, 1980. Zhang, D. F. And Zumbrunnen, D. A., Influences of Fluidic Interfaces on the Formation of Fine- Scale Structures by Chaotic Mixing, Journal of Fluids Engineering, Vol. 118, pp. 40-47, 1996. Zumbrunnen, D. A., Miles, K. C., and Liu, Y. H., Auto-Processing of Very Fine-Scale composite Materials by Chaotic Mixing of Melts, Composites Part A, Vol. 27A, pp. 37-47, 1996.