Multilayer Sheet Coextrusion: Analysis and Design

Multilayer Sheet Coextrusion:

Analysis and Design*

Evan Mirsoulis Department of Chemical Engineering

University of Ottawa Ottawa, Ontario, Canada KIN 984

ABSTRACT A numerical simulation of muUilayer coextruswn

pOws has been undertaken for polymer melts used in producing muUilayered plastic sheets. Viscosity data and other material propertis are used for typ ical melts and adhesives applied in coextrusion. In- dustrial designs have been employed for feedblock geometry and multimanifold vane jlat dies. The analysis is based on the lubrication approximation theory (LAT), which treats the flow locally as fuUy developed. A Newton-Raphson iterative scheme is employed to solve the equations for apressure-driven JIow of N number of layers (N < 11). For a given total flow rate and flow rate ratios (or correspond-

ingly total sheet thickness and individual layer thicknesses), the solution provides the intetjiace locations and individual pressure drops that each extruder has to supply. The shear stresses at the channel walls are checked as a criterion for proper design. The die design or melt combinations are altered to produce smooth shear stresses with no humps or dis- continuities at the points of confluence. Adiabatic temperature rises are also computed based on the pressure drops in the system. Such an analysis provides a quick qualitative as well as quantitative in- sight into the proper design and melt combinations for multilayer sheet coextrusion.

INTRODUCTION

Multilayer coextrusion is practiced increasingly today for many commercial plastics products.’ Up to 11 layers can be used in many combinations. Figure 1 shows a nine-layer structure and typical processing temperatures.2 The outer “skin” layers of polyether-

‘Financid support from the Natural Sciences and Engineering Research Council of Canada (NSERC) is gratefully acknowledged.

Advances in Polymer Technology, Vol. 8, No. 3, 225-242 (1988) 0 1988 by John Wiley & Sons, Inc.

imide (PEI) provide high and low temperature impact strength and high heat resistance. The polycarbonate (PC) or poly(ethy1ene terephthalate) (PET) interme- diate layers would be the volume or “bulk layers. The innermost ethylene vinyl alcohol (EVOH) layer provides the “barrier.” Also adhesive materials AD 1 and AD2 (such as ionomers, i.e., polymers in combination with metallic complexes) are used as bonding agents or tie layers to avoid slippage between adjacent layers.>’ A list of high performance and barrier poly-

CCC 0730-6679/88/030225- 18$04.00

MULTILAYER SHEET COEXTRUSION

FIGURE 1 A nine-laver structure *and typical processing temperatures for multilayer sheet coextrusion (from Ref. 2).

SKIN ADHESIVE

BULK ADHESIVE BARRIER

ADHESIVE BULK

ADHESIVE SKIN

mers along with typical processing temperatures can be found elsewhere.’ StoneburneP gives a list of several tie layers and their appropriate use with polymer combinations.

With the increased interest in coextrusion there has also come the proliferation of equipment. Because of the rapidly changing market conditions and the introduction of new polymers, the design of coextrusion equipment has become more involved. It is now im- perative to select coextrusion dies or feedblocks that are designed with versatility in mind. Therefore, any changes made to the line to accommodate different resins or layer thicknesses should be easy to make, so as not to cause long production delays or high scrap rates.

The industrial design of flat coextrusion dies has been based so far on trial-and-error practical experi- ence. Much progress has been made and new feedblock technology can provide capabilities to coextrude materials with viscosity ratios up to 40:l. It is also possible to coextrude materials with melt temperature differences as high as 80°C without causing damage or thermal degradation to a heat-sensitive material. The layer thicknesses can also be adjusted so as to produce minimal skin layers of 2% to obtain certain surface properties while retaining the heat seal properties of a bulk layer.7

In a typical multilayer sheet coextrusion system both a feedblock and a multimanifold die are used to combine inner (barrier) and outer melt streams. Figure

FIGURE 2 Cloeren coextrusion system uses both feedblock and multimanifold die to combine inner (barrier) and outer melt streams (from Ref. 8).

SELECTOR PLUG 7

A LDPE B ADHESIVE 1 C EVOH (Barrier)

41 / II A D ~ U S T A B L E \ , ~

D ADHESIVE2 E RECLAIM/SCR

0 C D E

ADJUSTABLE FEEDBLOCK VANE 3-LAYER VANE DIE i 5-LAYER FEEDBLOCK

AP

226 VOL. 8, NO. 3


2 shows such a system developed by the Cloeren Com- any,^'' which consists of the following pieces of equipment (all externally adjustable):

0 a selector plug used to change layer sequence as desired (i.e., from B/C/D/E/D structure to a D/E/ B/C/D structure)

0 flow dividers used to proportionally change the geometry of the individual flow channels with re- spect to the throughput of polymer passing through the feed channel

0 die vanes used to combine very low melt flows in outer layers with much higher flows of inner layers or vice versa

0 distribution pins used to compensate for high thickness or viscosity ratios of the polymers being combined at the points of confluence that would otherwise result in distorted interfaces and products

0 multimanifold vane die used to directly feed the polymers into the individual manifolds of the die prior to confluence; because the polymers are sep- arate and distributed across the full die width before contact and they also flow in a continuously diminishing cross sectional area, there is no chance for layer distortion to take place.

A three-layer vane die is shown schematically in Fig- ures 3 and 4. Such die design equipped with internal vanes is said to permit discrepancies in materials flows of as much as 400:l. Typical specifications for such dies are an output capacity up to 60 kg/h, sheet width from 7 to 30 cm, and a lip opening of 0.2 cm."

While the industrial design has seen tremendous progress and improvement since the early ' ~ O S , the theoretical analysis has lagged behind. Han''.13 has

FIGURE 3 Cloeren vane die for three-layer sheet coextrusion claimed to permit discrepancies in materials flows of as much as 400:l (from Ref. 11).

initiated the analysis of coextrusion using the equations for fully developed pressure-driven flow in slits and capillaries. Quite recently the finite element method (FEM) has also been applied for a full analysis of the flow field in double-layer coextrusion from a capillary die14 and in the wire-coating process.'' Heng and Mitsouli~'~ have shown that a simplified analysis based on the lubrication approximation theory (LAT), which treats the flow field locally fully developed, can be successfully used as a tool for design purposes to meet certain criteria in coextrusion. These are: (a) relatively flat interfaces in the axial direction; (b) lack of recir- culation; and (c) smooth development of shear stresses at the die walls to avoid excessive stress buildup or stress jumps.

The use of FEM in the analysis of multilayer coextrusion can be prohibitive due to the great demand in computer storage and time. A typical case of five- or

ADJUSTABLE VANE f

ADJUSTABLE LIP

FEED INLET

MELT STREAM

FIGURE 4 Side view of Cloeren vane die for three-layer sheet coextrusion (from Refs. 10 and 11).

ADVANCES IN POLYMER TECHNOLOGY 227

MULTILAYER SHEET COlZTRUSION

seven-layer mextrusion in the whole flow domain would require an iterative solution with the number of unknowns in the order of 103-104. This can be very time- and resource-consuming even in today's super- computers. On the other hand, the judicious use of LAT can provide the desired quantitative information in a matter of seconds. It is therefore the purpose of this paper to set the procedure for the use of LAT in multilayer coextrusion and show the results from the analysis and design of sheet coextrusion systems.

LUBRICATION APPROXIMATION THEORY

The theory and assumptions for the LAT can be found in the textbooks by Han12p'3 and Middleman. l6

Referring to Figure 5 we can distinguish between flow in individual channels before confluence [Figure 5(a)] and combined flow in a die channel of more than one fluids [Figure 5(b)]. In the latter case and for N layers there will be (N - 1) interfaces which are unknown a priori. For each layer mass conservation gives the individual flowrate Qi according to

(individual channel) Qi = w I," v,(y) dy (la)

(die channel) Qi = w

FIGURE 5 Notation for flow analysis in flat channels: (a) individual channel; (b) die channel for combined flow of N layers. Note that layer #1 is the upper and layer #N is the lower fluid.

0 X L=._ FLOW DIRECTION

( b )

where w is the channel width in the third dimension and yL and yu the heights of the lower and upper channel walls, respectively.

The individual flowrates Qi are determined by overall mass conservation for a given mass production rhte m, sheet width w, and individual thicknesses of the finished sheet. If we take density differences between ambient and melt conditions into account, we have

N N

where V is the average linear speed of production, pi the ambient density of layer i, and hi the ambient (cold) thickness of layer i. The superscript (a) refers to ambient conditions.

The linear speed V is then given by

At melt (hot) conditions, the individual flowrates Qi are given by

Qi = wVhhf") phf")/pi (4)

or, using Eq. (3),

i = 1

Note that Eq. (5) gives the volumetric flowrate at melt conditions for layer i. Since the analysis is not 3- dimensional but restricted only to x-y domain, it is necessary to work with QT = Qi/w, i.e., the cross- sectional flow rate for each layer. In what follows, Q is understood to be the cross-sectional flow rate Q*, where the asterisk has been dropped for simplicity.

According to LAT, the equations of motion reduce at each axial position x to

where the pressure gradient ap/dx = 5 is a constant (i.e., it does not depend on cross-flow direction y).

The boundary conditions at the solid walls are assumed to be the no-slip conditions, i.e.,

228 VOL. 8, NO. 3


where VL and Vu are the lower and upper wall velocities (set to zero if the walls are stationary), while at the (N - 1) interfaces there is continuity of the velocities and the shear stresses, i.e.,

where ai is the position of the ith interface (i = l,N - 1).

The shear stress T~~ is related to the velocity gradient through a viscosity function q

avX 7xy = q - = qixy

a Y (9)

where +xy is the shear rate. The viscosity function for polymer melts depends on + and T, the temperature. It can be a constant (Newtonian fluids) or obey a power law or some other nonlinear relationship (e.g., a quadratic dependence on + in a log-log domain and an exponential dependence on T as given in the paper by Basu17).

METHOD OF SOLUTION

The solution of the equation of motion [Eq. (6)] along with the appropriate boundary conditions [(7)- (S)] must be achieved by some numerical method, since even in the case of N Newtonian layers analytical solutions are either impossible (N > 2) or difficult to obtain1s (N = 2). The unknowns consists of:

0 A, an integration constant which corresponds to the position at which the maximum in velocity occurs, i.e., the position of zero shear stress 5, the pressure gradient which is assumed constant in the cross-flow direction y ai, the (N - 1) interface locations

The number of unknowns is then (N + 1) for N layers, and we need (N + 1) knowns to get a unique solution. These are:

0 Q, the total flow rate 0 Vu or VL, the upper or lower wall velocity

Qi/Qi+ 1, the (N - 1) flow rate ratios

For the case of individual channels only A and 5 must be solved for and the two knowns are the individual flow rate Qi and Vu or VL, the wall velocity.

Note that either wall velocity can be considered as the known since the other is used as the initial point of calculations (initial-value problem).

The iterative technique employed in the present analysis is a full Newton-Raphson scheme which ex- hibits a quadratic convergence within two to three iterations.

The vector of the unknowns {x} = {A 5 a1 ci2 - - *

aN-l}T must satisfy the system of (N + 1) equations {F} = 0, where

where QT,=t is the total set flow rate and Qi,calcd is the calculated individual flow rate for layer i. In the above we have taken VL as the initial value for starting the calculations.

Applying the Newton-Raphson method, we get

where (k + 1) is the present iteration, k is the previous iteration, and [J] is the Jacobian matrix with entries aFi/axj (1 = l ,N + 1, j = l,N + 1). Nu- merical differentiation has been used for the evalua- tion of the partial derivatives in the Jacobian while a standard IMSL subroutine (LEQTlF) has been used for the solution of the linearized system of (N + 1) equations. The whole process is extremely fast in a digital computer even for a large number of y divi- dions (100 cross-flow intervals have been used for each layer).

For the current axial position x the solution then provides A, 5, and a i , the interface locations. Nu- merical integration (Simpson's rule) then allows the determination of the cross-flow profiles for the shear stresses, shear rates, and velocities. The results are used as an initial estimate for the next axial position x + dx, until the die exit has been reached. Numer- ical integration along the domain length L of all pres-



sure gradients allows the determination of the overall pressure drop APi for each layer according to

APi = Pen - P,, = -lL (") dx (12) dx i

where P, is the entry pressure and P,, is the exit pressure which is set to zero. The pressure gradients are also used to calculate the adiabatic temperature rise for each layer as it proceeds towards the exit according to

Then the viscosity for each layer is corrected according to its temperature dependence.

The results of this work have been obtained using the program LATMULTI developed for multilayer coextrusion of plastics flowing in either planar or an- nular geometries and based on the Lubrication Ap- proximation Theory (LAT) . l9 LATMULTI uses as in- put:

0 geometric configurations of the flow channels 0 operating requirements (operating temperatum, sheet

width, mass flow rate, and either layer flow rates or thicknesses)

0 material properties for each layer (e.g., density, specific heat, and viscosity data)

On output the following information is obtained:

0 axial distributions of pressure drops, shear stresses,

0 velocity, shear stress, shear rate, and viscosity pro-

0 interface development from the points of conflu-

0 overall pressure drop for each layer along the flow

and temperature rises for each layer

files at any axial location

ence to the exit

domain

Note that the program can also be used for axisym- metric geometries (annuli, rods, wires, etc.) by switching through a flag from Cartesian into cylin- drical coordinate system.

A series of tests have been conducted against either analytical or other numerical solutions available in the l i terat~re , '~ . '~ . '~ and the accuracy of the program and the numerical method have thus been well established.

MATERIAL PROPERTIES

It is generally true that a detailed rheological in- vestigation of the materials used in multilayer coextrusion in lacking. Apart from Han's investigations for two-layer coextrusion, 12~13*20 the information found in the literature is very sparse and sporadic, especially for barrier and tie layers. Due to this lack of thorough measurements for viscosity and other material properties, we have taken here data from various sources and in some cases where no data could be found we have assumed reasonable values. Table I contains the relevant information for the resins used in the calculations along with their sources.

The data for LDPE and HDPE (two compatible resins that need no tie layers6) are taken from Basu. l7

The viscosity function is of the form

with

log + = al + a2(10g T) + a3(log T ) ~ (14c)

where p is a Newtonian viscosity and TN a shear stress value below which the materials behave as Newtonian fluids.

The temperature dependence of the viscosity is ex- pressed as

Figure 6 provides the viscosity curves for LDPE and HDPE at 170 and 220°C.

The viscosity data for PC, EVOH and AD2 are taken from Rice.' Additional data for PC and EVOH resins given by Collins and Teutsch22 indicate that, up to 100 s-I, these resins have approximately a constant viscosity and are therefore modelled as New- tonian fluids. However, the temperature dependence follows an Arrhenius relationship:

where E is the activation energy, R, is the ideal gas constant, and T and To are given in K. The values for the other material properties were taken from the Mod- ern Plastics Encyclopedia."

For the adhesive layer AD1 we have adopted the

230 VOL. 8, NO. 3


TABLE I Material Properties Used in the Calculations

AD1 Material CXA b p e a Y LDPE” HDPE” Pc EVOH AD2 309520 PEI

Ambient density p“’ 0.918 0.954 1.2121 1.15” 0.942’ 0.9421 1 .272’

Density (at TO) 0.8772 - 0.8732 - 1 .o” 1 .o” 0.75’ 0.75” 0.75’ (g/cm3)

P (g/cm3) 0.00059To O.oo0291To

C p (J/g K) 0.003376To Specific heat (at TO) 2.079 + 3.5 2. 12‘ 2.1” 2.121 2.0720 2.1.

Reference temperature 220 220 3005 232’ 2325 21020 3702 To (“C)

Newtonian viscosity 2546 209800 6005 15005 24005 7500” 20” )L (Pa s)

stress T~ (Pa) Newtonian shear loo0 loo0 - - - loo0 -

Viscosity constant al -0.2843 - 11.95 - - - - 10.459 - Viscosity constant a2 - 1.338 2.405 - - - 2.273 - Viscosity constant a3 0.3269 5.073 X 10-4 - - - 0.0 - Shift factor b (K-l) 0.00948 0.01266 - - - 0.019” - Temperature factor - - 11786.40’ 8334.065 3427.84’ - 1oooO.o”

WRg (K)

‘Value assumed.

values given by Chin et al.*’ for their CXA-3095 resin (an ethylene-based multifunctional polymer made by DuPont). The viscosity data are modeled using Eqs. (14) and (15).

Finally for the polyetherimide (PEI) resin made under the trade name ULTEM and used as a skin layer under very high temperatures, we were unable to find any other data except for density. We have assumed then a Newtonian behavior with an Arrhenius-type temperature dependence for our calculations. In view of the high processing temperatures and the low viscosity incurred, such an approximation appears reasonable.

RESULTS AND DISCUSSION

Cloeren Multimanifold “Vane” Die

We proceed with the analysis in a typical “vane” die designed by the Cloeren Company. The design

specifications are given in Figure 7 and Table 11. Note that the geometry has been read off as faithfully as possible from the commercial brochure, l 1 and it is not exactly symmetric. The die is designed such that there is a continuously diminishing cross-sectional area from the manifold to the die land. Such dies are claimed to produce distortion-free layers even for polymer combinations with viscosity ratios of 400:l and greater.”

The operating requirements are for a sheet width of 30 cm, a thickness of 0.2 cm at ambient temperature, and a mass production rate of 16.67 gls (60 kgl h). For these conditions the analysis is carried out for a layer of LDPE sandwiched between two layers of HDPE, or HDPWLDPWHDPE. Thus the coextruded sheet will have HDPE as the skin layer for its surface properties while LDPE will be the bulk layer for its heat seal proper tie^.^ Note that LDPE and HDPE need not have tie layers6 and that having the less viscous LDPE enclosed by the more viscous HDPE does not

ADVANCES IN POLYMER TECHNOLOGY 23 1


~ ~~~ ~~

FIGURE 6 Viscosity curves for LDPE and HDPE (data taken from Basu").

Viscosity Curves

Id

'\'. HDPE

10' .

necessarily cause layer distortion due to the use of the special vane die.8

For the total thickness h = 0.2 cm, the individual thicknesses may be varied as desired. Three cases have been examined: (I) hl/hZ/h3, 0.02/0.16/0.02; (11) hl/

The first two cases are symmetric in output but the third is asymmetric. Also note that case 11 represents

h2/h3,0.004/0.192/0.004; 0 h1/hZ/h3,0.10/0.08/0.02.

a skin layer of 2%, which is an extreme example from practice.' All melts are considered entering at 220°C.

The results from the calculations at 220°C are summarized in Table 111 and Figures 8-12. Figure 8 shows the interface developments for each case. Obviously, the best combination is for case I, where level interfaces exist running parallel to the main flow direction. The worst case is the asymmetric case III, where the

FIGURE 7 Die design for a Cloeren three-layer CLOEREN'S DIE DESIGN vane die" (see ;; 4 . 0

u also data in Table - It). 3.0

& 2.0

2 1 . 0

g 0.0

c

n

0 - 1 . 0

0 -2.0

(r -3.0

- 4 . 0

0

-1 < - c

W w

0.0 2.0 4 . 0 6.0 8.0 10.0 12.0 1 4 . 0

A X I A L C O O R D I N A T E . x (ern)

232 VOL. 8 , NO. 3


upper interface is bent to accommodate the higher flow rate of the upper layer. Further evidence is presented in Figure 9, where the shear stresses at the upper and lower walls are plotted vs. axial distance. The asymmetric case III shows that, right after the point of confluence, there is an undesirable “jump” in the shear stress at the upper wall, while the other two cases show a continuous smooth stress build-up towards the die exit. Cases I and II show the same distributions but different absolute values for the maxima.

A look at the pressure distributions of each layer for case III in Figure 10 illustrates the fact that extra pressure has to be supplied for the upper layer HDPE to accommodate the higher flow rate. Note how the pressures equalize after confluence. The other two cases have pressure distributions not greatly different for each layer. The corresponding adiabatic temperature rises due to individual pressure drops are shown in Figure 11. As expected under the conditions of simulation, a small temperature rise of less than 1°C occurs for each layer.

Finally, Figure 12 shows the velocity profiles at the die exit along with the interfaces (dashed lines) for cases I and III. Points to notice are the asymmetry for case 111 and the faster speed of the less viscous LDPE in the middle.

From the above analysis of the three different cases and for a given design, it becomes obvious that the best results are obtained when a symmetric sheet is produced with the vanes adjusted in a symmetric way. To avoid the stress jumps in the case of producing an asymmetric-in-thickness sheet, one of the vanes will have to be adjusted or the melt temperature will have to be changed. From a series of runs for different operating temperatures, it was found that temperature variations are not as important as changes in geometry. Therefore, the adjustment of the die vanes is quite crucial for producing defect-free coextruded sheets.

Cloeren Nine-Layer Feedblock/“Vane” Die/Die Insert System

We proceed with the analysis in a highly sophis- ticated coextrusion equipment developed by the Clo- eren Company that handles nine layers. It uses a five- layer feedblock (primary feedblock), a two-layer insert feedblock (secondary feedblock), and a three- layer “vane” die.*v9 The design specifications are given in Figure 13 and Table IV. Again the geometry has been read off as faithfully as possible from Figure 8 of Ref. 2 and it is considered symmetric. The combination of melts corresponds to the arrangement of

TABLE I1 Design Speci6cations for a Cloeren Three-Layer “Vane” Die8

Point Layer 1 Layer 2 Layer 3

A (0, 3.5) (0, 0.45) (0, -2.6)

B (7.6, 3.5) (6.1, 0.45) (6.8, -2.6) B’ (6.48, 2.75) (6.1, -0.45) (7.6, -3.5) C (9.1, 1.75) (6.5, 0.6) (7.6, -2.25) C’ (7.6, 2.26) (6.5, -0.6) (9.1, -1.8) D (11.0, 0.3) (10.8, 0.15) (10.8, -0.15) D’ (10.8, 0.15) (10.8, -0.15) (11.0, -0.3) E (13.15, 0.1) b b

F (14.8, 0.1) b b

A’ (0, 2.75) (0, -0.45) (0, -3.5)

E’ b b (13.15, -0.1)

F’ b b (14.8, -0.1)

‘(x,y) are p i n t coordinates in cm. V o be determined by the solution.

Figure 1 where an EVOH-barrier layer is sandwiched between two layers of adhesive (AD2), with PC being the bulk layer. The bulk layers are further adhered to the skin layers of PEI through another adhesive material (ADl). The material properties are given in Ta- ble I, and the operating temperatures are those shown

TABLE I11 Three-Layer Sheet Coextrusion for

HDPE/LDPE/HDPE (1/2/3)”

case I 1 2 3

case I1 1 2 3

Case m 1 2 3

0.02 0.16 0.02

0.004 0.192 0.004

0.10 0.08 0.02

1.88 1.72 1.81

1.33 1.37 1.30

2.40 1.82 1.98

220.7 220.9 220.7

220.5 220.7 220.5

220.9 220.9 220.7

- 0.062 0.034 0.062

-0.047 0.035 0.047

-0.075 0.032 0.063

%I = 16.67 as, w = 30 cm, h = 0.2 cm, To = 220°C.



FIGURE 8 Interface development for different thickness requirements in threelayer sheet coextrusion HDPV LDPWHDPE (1/2/ 3): (case I) (hjlhd h3, 0.02/0.16/0.02); (case 11) (hllhdh3, 0.004/0.192/0.004); (case 111) (hllhdh3, 0.1 0/0.08/0.02). Same data as in Table 111.

- E

," 1 . 1

- 0 . 7

2 0.3 n 0 - 0 . 1

-I -0.5

A

W

< r

- (L

0 0

< u I

& - 0 . 9 W >

- 1 . 3

C L O E R E N ' S DIE O E S I C N

- E

-2 1 . 1

- 0 . 7

2 0.3 n 0 -0 .1

--1 -0.5

W + < - (L

0 0

< 0 - & - 0 . 9 W w

- I . 3

9 . 7 10 .7 11.7 12.7 13.7 1 4 . 7

9 . 7 10 .7 11.7 12 .7 13.7 14 .7 - E 1. 1

- 0 . 7 B?

- 1 . 3 LY I

9 . 7 10.7 1 1 . 7 12.7 13.7 14.7

A X I A L C O O R D I N A T E . x (cm)

in Figure 1. For lack of other evidence, we have assumed the temperatures of the adhesive layers as being in between the temperatures of the adjacent layers, i.e., To(AD1) = 330°CandTo(AD2) = 250°C.

The operating requirements are for a sheet width of 30 cm, a thickness of 0.12 cm at ambient temperature, and a mass production rate of 16.67 g/s (60 kgl h). The individual thicknesses may be varied as de-

sired. We have chosen the arrangement (hl/h2/h3/h4/

O.OllO.Ol), with 1 being PEI and 5 being the barrier EVOH. The arrangement is thus symmetric. We wish to examine the suitability of this design with regard to shear stress developments along the channel walls.

The results from the simulation are summarized in Table V. Figure 14 shows the interface developments

hSlhdh-Jh81h9, 0.0 110.0 110.0210.0 110.0210.0 110.021

234 VOL. 8, NO. 3


0 . 0 8

% 0 . 0 6

G a

2 0.04 v)

a v)

0 .02 c

0.00 < W I @ -0.02 _I

_f < =-0.04

-0 .06

- 0 . 0 8

cases I and 111

in Figure 8). - . - . - ( I ) (same conditions as

- - (111) -

- 3 ,

-.....-.-........--------.-----------------~-------~-------~ -.

1’ ’\ -

-

-

C L O E R E N ’ S D I E

a 1 . 4 - w 1.2 -

1.0 -

0 . 8 -

0.6 -

a 3 v)

a a

0 . 2 0 . 4 t 0 . 0 -1

0 . 0 3 . 0 6 . 0 9.0 A X I A L COOROINATE. x ( c m )

FIGURE 10 Pressure distributions for each layer in case 111 (same conditions as in Figure 8).

1 2 . 0 15.0

in different sections of the equipment. Note that five combined sections have been used with variable step sizes for each section. The solution is still very fast even for such a complicated domain and so many layers (13 CPU seconds for a total of about 7000 points

in University of Ottawa’s AMDAHL-5860 computer). The pressure distributions are shown in Figure 15, where pressure equalization occurs after each point of confluence. The highest pressure is found to be for the barrier layer (EVOH). This is not surprising given



FIGURE 11 Adiabatic temperature rises for each layer in case 111 (same conditions as in Figure 8).

CLOEREN'S D I E

222.0

221.5 - c

W LL 2 221 . o < u W a t W c

220.5

220.0 0.0 3.0 6.0 9.0 12.0 15.0

A X I A L COORDINATE. x ( c m )

FIGURE 12 Cross-flow velocity profile at the die exit for cases I and 111 (same conditions as in Figure 8). Dashed lines correspond to interfaces.

0.10

0.08

0.06

a 0 . 0 4

.. - W

z 2 0.02

p 0.00 ... 0 0

0 -0.02

2 -0.04

& -0.06

-1 <

c u

CLOEREN'S D I E

0.0 1.0 2.0 3.0 4.0 5.0 6 . 0 7.0 VELOCITY. vx ( c n / a )

the lowest temperature of 220°C. The outermost layers of PEI and AD1 show the lowest pressure drops due to the highest temperatures. The pressure drops are used to calculate the adiabatic temperature rise for each layer. Figure 16 shows these results. Again due to the relatively mild conditions of extrusion (highest

shear rate at exit = 160 s-') and the high operating temperatures, temperature rises are less than 2°C (highest rise for EVOH with a AT = 1.8"C).

The velocity profile at the exit is shown in Figure 17, along with the interface positions. Most of the sheet comes out with a pluglike profile due to the less

236 VOL. 8, NO. 3


CLOEREN'S DIE DESIGN

FIGURE13 Design specifications for a Cloeren nine-layer coextrusion systerr?*8 (see also data in Table IV).

5-LAYER FEEDBLOCK 2-LAYER DIE INSERT SYSTEM 3-LAYER "VANE" DIE EXIT ;; 4 .0

3.0 0 - I; 2.0

z 1.0 + < - 0

0 0 LII 0 . 0

0 -1.0

0 -2 .0

(L -3.0 w

_I -2

I

+

0 . 0 3.0 6.0 9.0 12.0 15.0 18.0 21 .o A X I A L COORDINATE. x ( cn )

viscous layers near the walls which act as lubri- cants. The absolute maximum shear rate .;U occurs at the exit die walls having a value .;U = - 163.2 s-' (layer l), while .;Urn,, = 163.2 8' at the exit lower wall (layer 9). The corresponding shear stresses are

- 0.0033 and 0.0033 MPa, respectively, due to sym- metry.

Finally, the shear stress distributions along the outer die walls are shown in Figure 18. Due to the many changes in the geometry, there are several local max-

TABLE IV Design Specifications for a Cloeren Nine-Layer Coextrusion S y ~ t e r n ~ ? ~ a

Point Layer 1 Layer 2 Layer 3 Layer 4 Layer 5

A (10.8, 3.65) (8.55, 2.35) (0, 2.9) (0, 1.7) (0, 0.35)

B (11.45, 3.65) (10.5, 2.35) (1.5, 2.9) (1.0. 1.7) (0.5, 0.35) A' (10.8, 3.15) (8.55, 1.65) (0, 2.4) (0, 1.2) (0, -0.35)

B' (11.45, 3.15) (13.2, 1.65) (1.5, 2.4) (1.1. 1.2) (0.5, -0.35) C (11.6, 3.37) b (1.9, 2.58) (2.6, 0.25) (2.55, 0.05) C' (11.6, 2.9) (13.55, 1.5) (1.9, 1.8) (2.55, 0.05) (2.55, -0.05) D (13.1, 2.1) b (3.15, 0.6) (3.2, 0.25) D' (13.05, 1.8) (14.0, 1.75) (3.2, 0.25) b

E (13.55, 2.2) b (4.2, 0.35) E' b (15.05, 1.75) b

F (14.0, 1.95) b (13.15, 0.35) F' b (15.55, 1.55) b

G (16.25, 1.95) b (14.15, 0.125) G' b (18.3, 0.075) b

H (16.85, 1.6) (14.9, 0.125) H' I (18.35, 0.15) (16.2, 0.28) I' J (19.95, 0.05) (17.2, 0.125) J' K (20.6, 0.05) (18.3, 0.075) K'

b b

b b

b b

b b

'(x,y) are point coordinates in cm. Symmehy assumed for layers 6, 7, 8 and 9. q o be determined by the solution.



FIGURE 14 Interface development in various sections of a Cloeren nine- layer coextrusion system. Same data as in Table V. (a) Five-layer

layer die insert systemlthree-layer ”vane” die; (c) nine- layer ”vane” die.

feedblock; (b) two-

CLOEREN’S DIE DESIGN

4.0

3 . 0

2 2.0 0 - A

. 1.0 W c < z a

0 0 0

A

I

IL 0 . 0

2 -1 .0 - c LL W >

-2 .0

-3.0

-4.0 I 0 . 0 1.0 2.0 3 . 0 4.0 5.0 6.0

A X I A L COORDINATE. x (cm)

TABLE V Nine-Layer Sheet Coextrusion in Cloeren Nine-Layer

FeedblocWVane” Die/Die Insert System”

h, TO., AP, T-,, T-,*

1 (cm) (“C) (MPa) (“C) (MPa)

1 (PEI) 2 (ADl) 3 (W 4 (AD2) 5 (EVOH) 6 (AD2) 7 (pc) 8 (ADl) 9 (PEI)

0.01 370 0.01 330 0.02 290 0.01 250 0.02 220 0.01 250 0.02 290 0.01 330 0.01 370

0.09 0.18 2.32 2.39 3.00 2.39 2.32 0.18 0.09

370.1 330.2 291.3 251.7 221.8 251.7 291.3 330.2 370.1

-0.0033 - 0.0023 -0.0018 -0.0009 -0.OOO4

0.0009 0.0018 0.0023 0.0033

%I = 16.67 g/s, w = 30 cm, h = 0.12 cm

ima and minima. However, it is obvious that stress jumps appear which are undesirable. Some modifications in the design would therefore be necessary to improve the stress field.

238

After a series of trial runs, a new design has been found that meets these requirements. Figure 19 shows the extra modifications made (dashed lines), while in Figure 20 the stress distributions are presented. Evi- dently, smooth stress buildups have been achieved as desired. However, the overall results do not differ substantially from the previous ones and will not be repeated here.

CONCLUSIONS

The lubrication approximation theory (LAT) has been used to study the combined flow of many layers inside coextrusion equipment. In particular, industrial designs have been used for multimanifold “vane” dies and feedblock geometries which are employed in the production of multilayered plastic sheets. The materials considered are typical polymer melts such as LDPE, HDPE, PC, and EVOH and also two adhesive resins and a polyetherimide material (PEI) used as a skin layer in coextrusion of a nine-layer sheet. They are modeled as Newtonian or shear-thinning fluids with an exponential dependence of viscosity on tem-

VOL. 8, NO. 3


FIGURE 14 Continued

C L O E R E N ' S DIE O E S I G N C L O E R E N ' S D I E D E S I G N

1.2 - E

2 0 . 8 ,.

w 0 . 4 c < z I

g 0 . 0 0 0 0

A - 0 . 4 < u - t

W z n - 0 . 8

- I . 2 8 . 6 1 0 . 6 1 2 . 6 14.6 1 6 . 6 18 .6 2 0 . 6 17 .2 1 7 . 6 18 .0 18.4 18 .8 1 9 . 2 1 9 . 6 2 0 . 0 2 0 . 4 20 .8

A X I A L COORDINATE. x ( c m ) A X I A L COORDINATE. x ( c m )

3 . 2

2 . 8

- ; 2 . 4 5 a 2 . 0

W LL 7 1.6

a 1 . 2

ul W

IY

0 . 8

0 . 4

0 . 0

C L O E R E N ' S D I E

AD1 R , 0 . 0 3.0 6 . 0 9.0 1 2 . 0 15.0 18.0 2 1 . 0

A X I A L COORDINATE. x Lcm)

FIGURE 15 Pressure distributions for each layer in a nine-layer coextrusion system (same conditions as in Figure 14).

perature according to data available in the literature. The LAT simplifies greatly the conservation equa-

tions from partial differential into ordinary thus al- lowing a solution which is both fast and reasonably accurate despite the limitations of treating a 2dimen- sional domain as locally 1-dimensional. The results are expected to be less accurate when large angles are

encountered (greater than lo"), as is the case of flow in converging channels before confluence. However, these channels are rather large compared to the die channels where most of the pressure drop and the shearing occurs. As a result, the errors involved by using LAT are rather small, and they do not influence the overall performance criteria for die design.



FIGURE 16 Adiabatic temperature rises for each layer in a nine-layer coextrusion system (same conditions as in Figure 14).

C L O E R E N ' S DIE 400.0

380.0

. . I , I ,

200.0 1 0 .0 3.0 6.0 9.0 12.0 15.0 18.0 21.0

A X I A L C O O R D I N A T E . x ( c m )

FIGURE 17 Cross-flow velocity profile at the die exit in a ninalayer coextrusion system (same conditions as in Figure 14): (---) interfaces.

C L O E R E N ' S DIE

-I < 2 -0.04

& -0.06 I- cr

-0.08

-0 .10

1

0.0 1.0 2.0 3.0 4.0 5.0 6.0 7.0 V E L O C I T Y . vx (cn/e.)

The flow inside coextrusion equipment takes place usually in a parallel fashion, thus making LAT an excellent tool for the analysis. LAT provides the pressure drop that each individual extruder will have to supply for a certain layer thickness, along with other

quantities of interest, such as adiabatic temperature rise, interface locations, and shear stress distributions along the channel walls. Especially the shear stresses can be checked as a criterion of proper design. Smooth stresses developed along the walls with no abrupt

VOL. 8, NO. 3 240


C L O E R E N ' S D I E

0.004

- a r z 0.002

v) v) Lu E t v)

2 0.000 W 8 v)

_I

_I c 3 -0.002

-0.004 10.0 12.0 14.0 16.0 18.0 20.0

A X I A L C O O R D I N A T E . x (en)

FIGURE^ 8 Shear stress distributions along the outer die walls (same conditions as in Figure 14).

MOD1 FICATIONS L'. POINT I (18.35,0.15)

POINT I1 (l8.30,0.20) POINT 12 (18.45,O.lO)

FIGURE 19 Modifications in the Vane" die design of the Cloeren nine- layer coextrusion system to improve stress fields.

changes or humps and no crossover from positive to negative values along the flow length are deemed as the desired characteristics of good design.

The analysis has shown that symmetric adjustment of the vanes is very important for the outside layers

in order to provide smooth streamlined flows. For the case of many layers the temperatures will have to be adjusted so that the viscosities of adjacent layers do not differ substantially at the interface, thus reducing the undesirable effect of viscosity mismatch.



FIGURE 20 Shear stress distributions alona CLOEREN’S D I E (MODIFIED) the modified out& o. oo4 die walls (same data as in Table V).

a 5 2 0.002 07 v)

W LT

v) +

5 0.000 W 1 v)

J

J < 3 -0.002

-0.004 10.0 1 2 . 0 14 .0 16.0 18.0 20.0

AXIAL COORDINATE. x ( c m )

Finally, it would be highly desirable to have ex- perimental data for pressure drops vs. layer thicknesses from actual operations in order to provide the ultimate test between the present analysis and practice. Of paramount importance is also the collection of good material data, mainly viscosity data for a wide range

of shear rates and temperatures for resins and adhesives used in multilayer coextrusion.

REFERENCES

1. The Cloeren Company, Mod. Plast., (Aug.), (1985). Vol. 62, p. 41. 2. The Cloeren Company, Co-Ex ’85, Tech. Corf., Schot. Bus. Res.,

3. R. A. Weiss, P. K. Agarwal, and R. D. Lundberg, in SPE 42nd

4. D. 1. Bentley, Jr., in SPE 44th ANTEC. Tech. Papers, 1986, Vol.

5. C. E . Rice, in SPE 44th ANTEC, Tech. Papers, 1986, Vol. 32, p.

6. L. A. Stoneburner, in SPE 45th ANTEC. Tech. Papers, 1987, Vol.

7. The Cloeren Company, Mod. Plast., @ec.), (1985). Vol. 62. p. 28. 8. The Cloeren Company, Mod. Plast., (Aug.), (1983), Vol. 60, p. 35. 9. The Cloeren Company, U.S. Pat. 4,152,387 and 4,197,069 (1986).

Princeton. NJ. 1985.

ANTEC. Tech. Papers, 1984, Vol. 30, p. 468.

32, p. 781.

835.

33, p. 837.

10. R. Wocd, Plast. Mach. Equip., (Jul.), (1984). 11. The Cloeren Company, commercial brochure, 1986. 12. C. D. Han, Rheology in Polymer Recessing, Academic Press, New

13. C. D. Han, Multiphase Flow in Polymer Processing. Academic Press,

14. E. Mitsouulis and F. L. Heng, J . Appl. Polym. Sci., 34, 1713 (1987). 15. F. L. Heng and E. Mitsoulis, Int. Polym. Proc.. 1988, to appear. 16. S. Middleman, FwrdarncntaLr of Polymer Processing, McGraw-Hill,

17. S. Basu, Polym. Eng. Sci., 21, 1128 (1981). 18. R. B. Bird, W. E. Stewart, and E. N. Lightfoot, Transport Phenom-

CM. Wiley, New Yo&, 1960. 19. E. Mitsoulis and F. L. Heng, LATMULTI-A Sofrware Package for

Multilayer Coextrusion ofPlastics.” Dept. of Chem. Eng., Univ. of Ottawa, Ottawa, ON, 1987.

20. H. B. Chin, Y. 1. Kim, andC. D. Han, Polym. Eng. Rev., 4, 281 (1984).

21. Modern Plastics Encyclopedia, Mdjraw-Hffl, New Yo&, 1988. 22. P. C. Collins and E. 0. Teutsch, in SPE42ndANTEC, Tech. Papers.

Yo&. 1976.

New Yo&, 1981.

New Yo*, 1977.

1984, Vol. 30, p. 915.

242 VOL. 8, NO. 3

Multilayer Sheet Coextrusion: Analysis and Design

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