the rheology of concentrated slurries: experimental...

THE RHEOLOGY OF CONCENTRATED SLURRIES: EXPERIMENTAL EVALUATION AND THE EFFECTS ON POLYMER PROCESSING

Mark D. Wetzel Florence, Oregon, 97439

John C. Howe, Michael T. Sterling DuPont, Wilmington, Delaware 19803

Gregory A. Campbell Castle Associates, Jonesport, Maine 04649

Abstract Highly filled polymer compounds can present

processing challenges, including high screw shaft torque, energy consumption, die pressure and melt temperature rise. Previous theoretical development and experimental evaluations of highly filled polymer melts showed that the rheology can be described with a percolation model [1-4]. This paper re-evaluates a batch mixer characterization method used to measure the effects of filler concentration on melt processing. The experimental results are compared with capillary rheometer measurements using several low-density polyethylene resins, calcium carbonate and titanium dioxide. The theoretical treatment of the rheology as a particulate percolating system with power-law behavior is used to analyze rheometer and batch mixer data. The effects of resin molecular weight, filler type and size on rheology and melt processing are described.

Introduction Campbell and Forgacs used percolation theory to

model the viscosity of concentrated suspensions [4]. Other researchers investigated the effects of particles on viscosity where a percolation threshold ranged from 16 to 52 vol. %, depending on the fluid characteristics, particle type and size [1-3]. Batch mixers have been used extensively to examine dispersive mixing of solid fillers in polymer melts. Recently, a 15 cc conical twin-screw batch mixer was used to study the rheological effects of fillers in polymer compounding [1,3]. An axial force measurement was made with a cantilever mounting of the mixer barrel linked to a force transducer. The reactive force of the tapered screws pumping the material into the recirculation loop was related to the viscosity of the blend during processing.

For the work presented in this paper, a 15cc conical twin screw batch mixer supplied by Xplore Instruments BV, Netherlands was used to evaluate the effects of melt viscosity of several polymers filled with different particulate solids or a mixture of fillers. The axial barrel force and a melt thermocouple measurement were recorded to quantify the process response to filler concentration and operating conditions. Titanium dioxide, TiO2, and calcium carbonate, CaCO3, powders were pre-dispersed in Low Density Polyethylene, LDPE,

or Linear LDPE, LLDPE, with different molecular weight distributions using a compounding twin-screw extruder. The masterbatches were letdown in the bath mixer to different filler concentrations. The effects of the filler type, size and loading on melt viscosity and process response were analyzed with resin rheology constitutive equations and the percolation model.

Material Systems and Masterbatches Table 1 lists the commercially available

polyethylene (PE) resins and particulate solids used in the experiments. The LDPE/TiO2 system published previously was used to re-evaluate the batch mixer characterization method [1]. Three LLDPE polymers made with the UNIPOL™ process (catalyst not specified) with melt index values of 160, 20 and 0.7 were used to explore CaCO3 filled compounds. The ~45µm 40-UL CaCO3 grade had no surface modifier applied, while the ~5µm 5-FL material did have a surface treatment. Published particle size values are listed in the table.

Table 1. Polymers and Fillers used.

Masterbatches containing 65 vol. % of the fillers

listed in Table 2 were prepared on a Coperion ZSK-18mm Mega-lab 10 barrel, 41 L/D, twin-screw extruder fitted with a conventional powder dispersive mixing screw. Polymer pellets were metered into the first barrel using a loss-in-weight feeder. Filler powder was fed into a twin-screw side stuffer in barrel #5 with a second loss-in-weight feeder. The extruder screw speed was 250 RPM. The throughput was set to 6.8 kg/hr (15 lb/hr), but was reduced to 4.55 kg/hr (10 lb/hr) for the high viscosity LLDPE and the LDPE/TiO2 system. Barrel temperatures were profiled from 170 to 200ºC. For the

Polymerρ

(g/cc)

Melt Index (g/10min)

(190ºC, 2.16kg) TMP (°C)

Power Law Index (high shear

rates)Equistar LDPE Petrothene NA-206 0.918 13.5 ~110 0.341Dow LLDPE DNDA-1082 0.933 160.0 125 0.700Dow LLDPE GRSN-9820 NT-7 0.924 20.0 123 0.598Dow LLDPE GRSN-2070 NT 0.920 0.7 121 0.393

Fillerρ

(g/cc) d50 (µm)Surface Modifier

Chemours Ti-Pure R-104 TiO2 3.900 0.25 YesOMYACARB 40-UL CaCO3 2.700 45.00 NoOMYACARB 5-FL CaCO3 2.700 5.00 Yes

SPE ANTEC® Anaheim 2017 / 1144

CaCO3 system, masterbatches containing a 70/30 blend of 40-UL/5-FL were compounded in an attempt to determine the effects of particle size combinations on reducing the melt viscosity at high filler loadings. Packing theory calculations and experiments suggested that the maximum packing density could be increased with mixed fillers with a particle diameter ratio of 7 or greater [5], which could reduce the viscosity relative to the pure particle compositions with a small particle component of 15 to 30% [6].

Table 2. ZSK-18mm Compounded Masterbatches.

Rheology Measurements and Models The melt viscosity of the LLDPE resins, the CaCO3

masterbatches and batch mixer letdown samples were measured in accordance with ASTM D 3835 using a Dynisco LCR 7001 capillary rheometer. The diameter of the die was confirmed before the start of each test using a Meyer Gage Company Class X GO/NOGO gage which has a tolerance of ± 0.0003 in. The barrel temperature was calibrated at least once a quarter following the procedure in ASTM D 3835 using a calibrated Hart Scientific model 1502A thermometer readout equipped with a NIST-traceable SDI model A1143-01 temperature probe. The combined accuracy of the readout and probe is better than 0.1°C. The viscosity of each LLDPE resin was tested at 170, 190 and 210°C and at shear rates from 250 to 1 s-1 using a 1.0 mm diameter die with L/D = 30 and a 180 degree inlet angle. The melt time was 300 s. A 1.5 kN or a 10 kN load cell was used to measure the force generated by pushing the molten polymer through the die. The KARS software implementation of the steady-state algorithm procedure in ASTM D 3835 was used to determine that each data point was taken at steady-state flow conditions. The test was performed in duplicate at all temperatures with a fresh sample loading for each test. The test-to-test repeatability, expressed in the terms of the repeatability coefficient of variation, was less than 3% at all shear rates. To confirm the melt stability, as part of the shear rate sweep, the first shear rate in the sweep was repeated. The calibration of the LCR 7001 was confirmed by testing the viscosity of a polypropylene standard at shear rates from 250 to 10 s-1.

The repeatability coefficient of variation was less than 2%.

A Cross constitutive model was used to predict viscosity as a function of shear rate for the LDPE and LLDPE resins:

η( !γ ) = 0η

1+ λ !γ 1−n (1)

where h0 is the zero-shear viscosity, n is a power-law exponent and l is a relaxation time [7]. Assuming that the time-temperature superposition principle held, the WLF relationship was used to model the effect of temperature with a shift factor aT:

η0 T( )η0 Tref( )

= aT =10−C1 T−Tref( )C2+ T−Tref( )⎡

⎣⎢⎢

⎤

⎦⎥⎥ (2)

where C1 and C2 are model parameters and TRef is the reference temperature, 125°C (LDPE) or 190°C (LLDPE) [7]. Figure 1 shows LDPE capillary rheometer viscosity data from [8] as a function of shear rate and temperature along with model prediction curves. Equation 1 and 2 coefficients for all viscosity data were estimated using time-temperature superposition data shifts to a Cross model master curve and a set of Generalized Reduced Gradient (GRG) nonlinear constrained minimizations with the Microsoft Excel Solver. For the LDPE/TiO2 system analysis, viscosity estimates shown in the figure were extrapolated to the batch mixer experimental melt temperatures of 185°C to 195°C.

Figure 1. NA-206 LDPE viscosity data and model.

Figure 2 through Figure 4 plot the melt viscosity data and Cross model fits for the 1082 (160 MI), 9820 (20 MI) and 2070 (0.7 MI) LLDPE resins. The low molecular weight 1082 shear rates were limited to values above those used for the batch mixer analysis. All resins, especially at higher shear rates, exhibit power-law behavior. The Cross model fits the power-law and transition regions with sufficient accuracy for the analysis. The viscosity models were used to extrapolate to the operating conditions of the mixer.

Masterbatch Polymer Filler

Loading (vol. %)

MB-1 LLDPE 1082 MI 160 OMYA 40-UL (CaCO3) 65%MB-2 LLDPE 1082 MI 160 OMYA 5-FL (CaCO3) 65%MB-3 LLDPE 1082 MI 160 40-UL/5-FL 70/30 Blend 65%MB-4 LLDPE 9820 MI 20 OMYA 40-UL (CaCO3) 65%MB-5 LLDPE 9820 MI 20 OMYA 5-FL (CaCO3) 65%MB-6 LLDPE 9820 MI 20 40-UL/5-FL 70/30 Blend 65%MB-7 LLDPE 2070 MI 0.7 OMYA 40-UL (CaCO3) 65%MB-8 LLDPE 2070 MI 0.7 OMYA 5-FL (CaCO3) 65%MB-9 LLDPE 2070 MI 0.7 40-UL/5-FL 70/30 Blend 65%MB-10 LDPE NA-206 MI 13.5 Ti-Pure R-104 TiO2 65%

999.7 760.3

556.6

100

1000

10000

1 10 100 1000 10000

Vis

cosi

ty (P

a.s)

Shear Rate (1/s)

125 °C 125 °C Cross 135 °C 135 °C Cross 145 °C 145 °C Cross 185 °C Cross DSM Channel Est.

Cross Model Coefficients: η0 = 8,000 Pa.s at TRef = 125ºC λ = 0.2911 sec n = 0.3883

WLF Temperature Coefficient: C1 = 1.00, C2 = 57.86


Figure 2. 1082 LLDPE MI 160 viscosity data and model.

Figure 3. 9820 LLDPE MI 20 viscosity data and model.

Figure 4. LLDPE 2070 MI 0.7 viscosity data and model.

Capillary rheometer measurements were made on the LLDPE/CaCO3 masterbatch letdown samples processed with the Xplore batch mixer. Figure 5 through Figure 7 show the melt viscosity data for masterbatch letdowns with CaCO3 concentrations at 10, 30 and 60 vol. %. For the 160 MI 1082 LLDPE, both CaCO3 grades and the 70/30 blend increased the melt viscosity with a significant jump at 60 vol. %. The viscosities exhibited power-law behavior over the shear rate range of interest and had similar profiles, regardless of particle size or surface treatment. The 20 MI 9820 LDPE had a

similar trend with filler loading. However, the ~5µm 5-FL surface treated CaCO3 reduced the viscosity as compared with the ~45µm 40-UL untreated grade. The 70/30 blend did not decrease the viscosity as suggested by packing theory. For the 0.7 MI 2070 LLDPE, the batch mixer reached torque or force limits and could not process 60 vol. % compositions. Trends in viscosity changes were similar to those of the 20 MI LLDPE.

Figure 5. LLDPE 1082 MI 160 / CaCO3 melt viscosity.

Figure 6. LLDPE 9820 MI 20 / CaCO3 melt viscosity.

Figure 7. LLDPE 2070 MI 0.7 / CaCO3 melt viscosity.

Figure 8 plots power law index n estimates at shear rates above 100 s-1 for the masterbatch letdowns. For most states, n decreased with increasing CaCO3

63.97 62.25 59.64

10

100

10 100 1000 10000

Vis

cosi

ty (P

a.s)

Shear Rate (1/s)


Cross Model Coefficients: η0 = 60 Pa.s at TRef = 190ºC λ = 0.005 sec n = 0.3


545.4

456.4

379.1

100

1000

10 100 1000

Vis

cosi

ty (P

a.s)

Shear Rate (1/s)


Cross Model Coefficients: η0 = 2,250 Pa.s at TRef = 190ºC λ = 2.2842 sec n = 0.6787

WLF Temperature Coefficients: C1 = 2.51, C2 = 274.41

3083.6 2092.3

1419.5

100

1000

10000

10 100 1000

Vis

cosi

ty (P

a.s)

Shear Rate (1/s)


Cross Model Coefficients: η0 = 2,062,651 Pa.s at TRef = 190ºC λ = 5,638 sec n = 0.4398


10

100

1000

10000

1 10 100 1000

Vis

cosi

ty (P

a.s)

Shear Rate (1/s)

LLDPE 1082 (160 MI)

1082/40UL 30%

1082/5FL 10%

1082/5FL 30%

1082/5FL 60%

1082/40UL/5FL 10%

1082/40UL/5FL 60%

T = 190oC

LLDPE 1082

10% 40-UL 10% Blend 30% 5-FL

30% 40-UL

60% 5-FL

60% Blend

100

1000

10000

100000

1 10 100 1000

Vis

cosi

ty (P

a.s)

Shear Rate (1/s)

9820 (MI 20) 9820/40UL 10% 9820/40UL 30% 9820/40UL 60% 9820/5FL 10% 9820/5FL 30% 9820/5FL 60% 9820/40UL/5FL 10% 9820/40UL/5FL 30% 9820/40UL/5FL 60%

T = 190oC

LLDPE 9820

10 vol. % 30 vol. %

60 vol. %

60% 5-FL

60% Blend 60% 40-UL

30% Blend

30% 40-UL 30% 5-FL

100

1000

10000

100000

1 10 100 1000

Vis

cosi

ty (P

a.s)

Shear Rate (1/s)

2070 (MI 0.7) 2070/40UL 10% 2070/40UL 30% 2070/5FL 10% 2070/5FL 30% 2070/40UL/5FL 10% 2070/40UL/5FL 30%

T = 190oC

LLDPE 2070

10 vol. % 30 vol. %

Xplore (DSM) limited to maximum of 30 vol. % CaCO3.


concentration, especially above the percolation threshold, fc. The change in n was the lowest for the high molecular weight 2070 0.7 MI LLDPE system.

Figure 8. LLDPE / CaCO3 letdown power law estimates.

The Campbell-Forgacs filler percolation model was used to fit batch mixer letdown sample capillary rheometer data and mixer force measurement viscosity estimates [1,3,4]. The percolation model has the form

1---

===÷÷÷÷

ø

ö

çççç

è

æ

ffff

hhh f

m

cm

fr ea (3)

for f ≥fc , where the f is the filler volume concentration, fc is the percolation threshold, fm is the maximum filler packing and hf is the fluid viscosity. Below fc, a Batchelor relationship was used

21 ffhhh f KAaf

r ++=== (4)

where the A is the usually the Einstein coefficient, 2.5, and the default value for K is 6.2. Applying the concentration shift factor, af, to the zero-shear viscosity, constitutive Eq. 1 becomes

η( !γ,T,φ) =aTaφ( ) 0η

1+ λ aT !γ( )1−n (5)

To compare rheometer data with batch mixer viscosity estimates, the percolation model was fit to viscosity values at 190ºC and 50 s-1. Both fc and fm were fitting parameters. Figure 9 through Figure 11 plot LLDPE/CaCO3 masterbatch letdown sample measurements and percolation model predictive curves where sufficient data were available. Since shift factor Eqs. 3 and 4 have different forms, there is a discontinuity at fc. Although samples were limited at high filler concentrations, the 1082 160 MI and 9820 20 MI compounds showed significant increases in viscosity consistent with the percolation theory. The effect of CaCO3 concentration above fc was much more pronounced with the low molecular weight resin system with hr of 33 to 35 for the 160 MI LLDPE and hr of 4 to

10 with the 20 MI resin. Since the batch mixer could not process high CaCO3 loadings in 2070 0.7 MI LLDPE, the model prediction is an extrapolation above fc. However, since the batch mixer exceeded its torque or force limits, the melt viscosity increase was likely to trend similar to other systems above 30 vol. %.

Figure 9. LLDPE 1082 MI 160 / CaCO3 MB letdown

percolation model at 50 s-1.

Figure 10. LLDPE 9820 MI 20 / CaCO3 MB letdown


Figure 11. LLDPE 2070 MI 0.7 / CaCO3 MB letdown


0.200

0.300

0.400

0.500

0.600

0.700

0.800

0.900

0% 10% 20% 30% 40% 50% 60%

Pow

er L

aw n

(> 1

00s-1

)

CaCO3 Volume %

MB-4 9820/40-UL MB-5 9820/5-FL MB-6 9820/Blend MB-2 1082/5-FL MB-3 1082/Blend MB-7 2070/40-UL MB-8 2070/5-FL MB-9 2070/Blend

20 MI

160 MI

0.7 MI

33.64

35.46

0.0

5.0

10.0

15.0

20.0

25.0

30.0

35.0

40.0

0% 10% 20% 30% 40% 50% 60%

η/η

f

CaCO3 Volume %

MB-1 40-UL MB-2 5-FL MB-3 70/30 Blend MB-2 Model Percolation

(≥ φC)

Batchelor (fit) (< φC)

T = 190oC, 50 s-1

φC = 0.10

φm = 0.797 5-FL: 5µm

70/30 Blend

ηr =1+3.88φ +19.13φ2

1−−

−

===⎟⎟⎟⎟

⎠

⎞

⎜⎜⎜⎜

⎝

⎛

φφφφ

ηη

η φm

cm

fr ea

8.35

4.13

9.78

0.0

2.0

4.0

6.0

8.0

10.0

12.0

14.0

0% 10% 20% 30% 40% 50% 60%

η/η

f

CaCO3 Volume %

MB-4 40-UL MB-5 5-FL MB-6 70/30 Blend MB-4 Model

Percolation (≥ φC)


T = 190oC, 50 s-1

φC = 0.21

φm = 0.92

5-FL: 5µm

40-UL: 45µm

70/30 Blend

ηr =1+1.33φ + 4.53φ2

1−−

−

===⎟⎟⎟⎟

⎠

⎞

⎜⎜⎜⎜

⎝

⎛

φφφφ

ηη

η φm

cm

fr ea

0.0

1.0

2.0

3.0

4.0

5.0

6.0

7.0

8.0

9.0

10.0

0% 10% 20% 30% 40% 50% 60%

η/η

f

CaCO3 Volume %

MB-7 40-UL MB-8 5-FL MB-9 70/30 Blend MB-7 Model Percolation

(≥ φC)


T = 190oC, 50 s-1

φC = 0.24

φm = 0.97

40-UL: 45µm

ηr =1+1.58φ + 4.88φ2

1−−

−

===⎟⎟⎟⎟

⎠

⎞

⎜⎜⎜⎜

⎝

⎛

φφφφ

ηη

η φm

cm

fr ea

Batch mixer limited to maximum of 30 vol. % CaCO3. Percolation fit lacks sufficient data.


Batch Mixer Experiments Melt blending experiments were conducted on a 15

cc conical twin screw batch mixer supplied by Xplore Instruments BV, Netherlands to evaluate the rheological effects of filler concentration in polyethylene. The batch mixer was used to melt and mix PE masterbatches prepared on the ZSK-18mm extruder with PE and to measure the process response as a function of filler concentration and shear rate. The following test protocol was used: 1. Masterbatch letdowns from 10 to 60 vol. % were

made by diluting the 65 vol. % concentrates with additional polymer pellets or granules. PE and the masterbatch were pre-weighed to maintain a fixed material volume of 12 cc. Ingredients were pre-blended and fed as pellet or granule mixtures. Each polymer was processed in the batch mixer as well.

2. Barrel top, center and bottom zone temperatures were set to 190, 190 and 195°C respectively to maintain melt temperatures close the 190°C rheometer reference value. The bottom zone was set to a higher value to compensate for increased heat loss with the metal mass that included the sample valve and recirculation flow channels.

3. After loading the pellets into the mixer at 60 RPM, the material was melted and melt-mixed for about 3 minutes to reach an equilibrium state with sufficient TiO2 distribution to form a homogenous blend.

4. The mixer was then run for 3 minutes at 60 RPM to obtain the steady state barrel force and melt temperature measurements.

5. The screw speed was increased to 120 RPM and the mixer was run for another 3 minutes.

6. The screw speed was increased to 240 RPM and the mixer was run for the final 3 minutes.

7. Barrel force and the melt temperature were recorded at a frequency of 1 sample/second. At each screw speed, 90 seconds of data at steady-state conditions were used to calculate average values and standard deviations.

8. To minimize the experimental workload, only two replicate tests were run for each composition. The mean and standard deviations for force and temperature measurements were calculated for each replicate data set. At the end of each test, extrudate samples were collected for viscosity measurements.

Replicate batch mixer melt time histories for 9820 20 MI LLDPE are shown in Figure 12. Barrel force and the melt temperature thermocouple signals show the material loading, polymer melting and equilibration transitions. Data for analysis were taken after the melting or screw speed transitions were completed to determine the average force and melt temperature with approximately 90 samples at 60, 120 and 240 RPM. The

plots show that the LLDPE exhibited a slight thermal degradation with a negative slope and exponential-like decay in the force as a function of time. Increasing screw speed caused the force and melt temperature to increase. Differences in event times were corrected by time-shifting replicates to the initial melting peak force. While the material volume for each run was constant, there were measurable differences in barrel force levels.

Figure 12. Batch mixer barrel force and melt temperature

for the unfilled 9820 LLDPE polymer.

Figure 13 shows replicate tests of the 50 vol. % 40-UL CaCO3 in 9820 LLDPE letdown process profiles in the batch mixer. While barrel force and melt temperature traces were reproducible, there were slight differences in levels. Relative to the LDPE state, the viscosity of highly filled composition resulted in increased force values and greater deviations in the melt temperature. Average values and standard deviations calculated for the force and temperature measurements for all CaCO3 concentrations are listed in Table 3.

Figure 13. MB-4 9820 LLDPE/50 vol. % 40-UL CaCO3

letdown barrel force and melt temperature.

Average barrel force values listed in Table 3 for MB-4 are plotted as a function of shear

rate and CaCO3 loading in Figure 14. Error bars are ±1 standard deviation for two replicates per state. Barrel

180

182

184

186

188

190

192

194

196

198

200

0

500

1,000

1,500

2,000

2,500

3,000

3,500

0 100 200 300 400 500 600 700 800 900

Mel

t Tem

pera

ture

(ºC

)

Bar

rel F

orce

(N)

Time (Sec)

1 LLDPE 9820 Force 1B LLDPE 9820 Force 1 LLDPE 9820 Tmelt 1B LLDPE 9820 Tmelt

1 Force LDPE

1 TMelt

1B TMelt

1B Force LDPE

60 rpm

120 rpm

240 rpm

Material loading, barrel heat transfer, melting

180

185

190

195

200

205

210

0

1000

2000

3000

4000

5000

6000

7000

8000

0 100 200 300 400 500 600 700 800 900

Mel

t Tem

pera

ture

(ºC

)

Bar

rel F

orce

(N)

Time (Sec)

6 Force 6B Force 6 Tmelt 6B Tmelt

6 Force

6 TMelt

6B TMelt

6B Force

60 rpm

120 rpm

240 rpm


force increased with shear rate and nonlinearly with filler loading. Average melt temperatures are plotted as a function of shear rate and CaCO3 loading in Figure 15. Temperature increased with shear rate over the range of CaCO3 concentrations; 155ºC at 21 s-1, 156ºC at 42 s-1 and 157ºC at 83 s-1. The dissipated energy increased significantly with filler concentration with a temperature change from the LLDPE resin to 50 or 60 vol. %; 1.9ºC at 21 s-1, 3.6ºC at 42 s-1 and 7.6ºC at 83 s-1.

Figure 14. MB-4 LLDPE 9820 / 40-UL CaCO3 letdown

average barrel force. Error bars are ± 1 s.

Figure 15. MB-4 LLDPE 9820 / 40-UL CaCO3 letdown

melt temperature. Error bars are ± 1 s.

For the purpose of analysis, batch mixer shear rates were estimated as a function of screw speed by calculating an average channel depth of the screws. The average channel shear rate can be approximated by

( )rpmNmNhD

ChanChan ==pg! (6)

where D is the screw tip diameter, N is the screw speed and h is the channel depth. Dimensions were measured at 13 locations down the tapered length of the screw. The average values were used to estimate D and h. A constant 0.1mm tip to barrel gap was assumed to calculate the clearance shear rates. Shear rate estimates as a function of screw speed are shown in Figure 16. The channel shear rate expression has slope mChan =

0.346. Using the shear rate estimates, melt viscosities were calculated from the barrel force data using the approximation

( )Chan

BarrelFFkg

gh!

! » (7)

where FBarrel is the force measurement and kF is a mixer and material system specific constant calculated to be 23.3 for LDPE/TiO2, 9.7 for 9820 LLDPE/CaCO3, 7.0 for 1028 LLDPE/CaCO3 and 15.8 for 2070 LLDPE/CaCO3 to match capillary rheometer unfilled viscosity values at the mixer melt temperature and 21 s-1. The LDPE/TiO2 kF value used in previous publications was 28.5 [1,3].

Figure 16. Xplore 15cc batch mixer shear rate estimates.

Figure 17 plots the melt viscosity estimates from the barrel force data as a function of shear rate and filler concentration. Error bars are ±1 standard deviation for the two replicate viscosity estimates from the force values measured at each state. The difference between viscosity estimates at the three shear rates increased significantly with filler loading. This was due, in part to the increase in melt temperature. However, the rectangular channel shear approximation is likely to be incorrect for self-wiping screws. Energy dissipation in the clearances was also likely to be significant increasing the “effective” shear rate.

0

1000

2000

3000

4000

5000

6000

7000

8000

0% 10% 20% 30% 40% 50% 60%

Bar

rel F

orce

(N)

CaCO3 Volume %

60rpm (21 1/s) 120rpm (42 1/s) 240rpm (83 1/s)

Xplore torque/power limits reached for 60 vol. % CaCO3 at 120 and 240 rpm.

184

186

188

190

192

194

196

198

200

0% 10% 20% 30% 40% 50% 60%

Mel

t Tem

pera

ture

(o C)

CaCO3 Volume %

60rpm (21 1/s) 120rpm (42 1/s) 240rpm (83 1/s)

Tavg @60rpm = 186ºC, ΔT = 1.9ºC



20.8

41.5

83.1

SRch = 0.346*RPM

SRclr = 6.823*RPM

0

500

1000

1500

2000

2500

3000

0

10

20

30

40

50

60

70

80

90

100

0 30 60 90 120 150 180 210 240 270

Aver

age

Cle

aran

ce S

hear

Rat

e (1

/s)

Aver

age

Cha

nnel

She

ar R

ate

(1/s

)

Screw Speed (RPM)

Channel Clearance


Figure 17. MB-4 letdown melt viscosity estimates from

barrel force measurements.

In Figure 18, the force measurement viscosity estimates are plotted as a function of shear rate and CaCO3 loading along with the percolation model curve fitted at 21 s-1 using the Batchelor relationship below fc = 0.239 and with a maximum packing fm = 0.989, the upper constraint limit used for the Excel Solver minimization.

Figure 18. MB-4 9820 20 MI LLDPE / 40-UL CaCO3

mixer relative viscosity estimates and percolation model curve fitted at 21 s-1.

Figure 19. MB-4 LLDPE 9820 / 40-UL CaCO3 batch

mixer viscosity estimates vs. model predictions using 21 s-1 data.

The percolation model predictions are plotted against the force measurement viscosity estimates in Figure 19 using the Batchelor model with A = 1.04 and K = 5.4 below fc. The model, fitted to 21 s-1 data, makes reasonable predictions of the viscosity change as a function of filler concentration for all shear rates. However, prediction errors increase at high filler loadings at 42 and 83 s-1.

The focus of the analysis was on high loadings above the percolation threshold. Relative viscosity estimates are plotted in Figure 20 for the 9820 20 MI LLDPE letdowns with ~45µm 40-UL, ~5µm 5-FL and the 70/30 filler blend letdowns as a function of shear rate and CaCO3 concentration. The table inset lists the model parameter estimates with fc ranging from 0.14 to 0.22 and fm from 0.78 and 0.8. Percolating behavior and the trends with filler type and concentration are consistent with capillary rheometer measurements. While absolute values are different the relative viscosities at 60 vol. % are similar, with the 40-UL mixer value of 5.59, rheometer 8.35, the 5-FL mixer 3.47, rheometer 4.13, and the filler blend mixer 6.18, rheometer 9.78. Like the rheometer, the batch mixer estimates reflect the differences between the untreated 40µm and the surface modified 5µm CaCO3 grades.

0

500

1000

1500

2000

2500

3000

3500

0% 10% 20% 30% 40% 50% 60%

Vis

cosi

ty (P

a.s)

CaCO3 Volume %

60rpm (21 1/s) 120rpm (42 1/s) 240rpm (83 1/s)

( )γ

γη!

! BarrelF Fk≈ kF = 9.7

0.0

1.0

2.0

3.0

4.0

5.0

6.0

7.0

8.0

9.0

0% 10% 20% 30% 40% 50% 60%

η/η

f

CaCO3 Volume %

60rpm (21 1/s) 120rpm (42 1/s) 240rpm (83 1/s) Percolation Model @ 21 1/s Percolation

(≥ φC)


φC = 0.239

φm = 0.989

ηr =1+1.04φ + 5.4φ2

1−−

−

===⎟⎟⎟⎟

⎠

⎞

⎜⎜⎜⎜

⎝

⎛

φφφφ

ηη

η φm

cm

fr ea

0

500

1000

1500

2000

2500

0 500 1000 1500 2000 2500

Vis

cosi

ty M

odel

(Pa.

s)

Viscosity from Force Experiment (Pa.s)

60rpm (21 1/s) 120rpm (42 1/s) 240rpm (83 1/s)

1−−

−

===⎟⎟⎟⎟

⎠

⎞

⎜⎜⎜⎜

⎝

⎛

φφφφ

ηη

η φm

cm

fr ea

ηr =1+1.04φ + 5.4φ2

φC = 0.239

φm = 0.989

(< φC)


Figure 20. MB-4, 5 and 6 LLDPE 9820 / CaCO3 batch

mixer viscosity estimates and model curves.

Following the same approach, batch mixer experiments were run with the low viscosity 1028 160 MI LLDPE as exemplified in Table 4. Figure 21 plots viscosity data and estimates for the 1028 160 MI LLDPE letdowns with ~45µm 40-UL, ~5µm 5-FL and the 70/30 filler blend letdowns as a function of shear rate and CaCO3 concentration.

Figure 21. MB-1, 2 and 3 LLDPE 1028 / CaCO3 batch

mixer viscosity estimates and model predictions.

The table inset lists the model parameter estimates with fc ranging from 0.14 to 0.22 and fm from 0.78 and 0.8. For the low viscosity LLDPE, the treated 5-FL CaCO3 increased the viscosity at high loadings relative to the untreated 40-UL and the 70/30 blend. The model fits with 21 s-1 batch mixer data captured the trends with small differences in fc and fm. Batch mixer estimates were lower than rheometer values.

Method and Analysis Limitations The highly filled polymers used in the experiments

exhibited rheological percolation and a rapid rise in viscosity with increasing solids concentration above fc. The experiments, model forms and fitting routines are very sensitive to filler concentration at high loadings. The batch mixer test method was re-evaluated to

determine if it is robust and accurate as a viscosity measurement tool. Figure 22 plots LDPE/TiO2 data and the fitted percolation model curve using from the ANTEC 2016 paper [1]. The same system was run in the present work, but under different conditions. A 65 vol. % masterbatch was produced on the ZSK-18mm extruder. Letdowns of MB-10 were made on the batch mixer at the same conditions used for the LLDPE/CaCO3 systems. Table 5 lists batch mixer force data and viscosity estimates using a kf value for Eq. 7 of 23.3 verses 28.5 in the previous work. The force values were approximately double in this work. This could be due to the dispersion state of the masterbatches, where the 65 vol. % concentrate was difficult to make on the extruder with submicron TiO2 particles. Furthermore, new screws were used in the batch mixer, reducing leakage flows over the flight tips, increasing the force.

Figure 22. ANTEC 2016 NA-206 LDPE/ TiO2 batch mixer

viscosity estimates and model predictions [1].

In the present work, the TiO2 letdown concentration was extended to 60 vol. %, but fewer compositions were run to minimize the experimental workload. Figure 23 plots the MB-10 batch mixer letdown force viscosity estimates and the percolation model curve fitted to the 21 s-1 data. The viscosity estimates are about double those of the previous experiment. A definitive cause of the differences between experiments cannot be identified. Reproducibility requires that the same materials be used on the same equipment, run under identical conditions and preferably with the same operator or identical protocols.

5.59

3.47

6.18

0.0

1.0

2.0

3.0

4.0

5.0

6.0

7.0

0% 10% 20% 30% 40% 50% 60%

η/η

f

CaCO3 Volume %

MB-4 40-UL MB-5 5-FL MB-6 70/30 Blend MB-4 Model MB-5 Model MB-6 Model

5-FL: 5µm

40-UL: 45µm

70/30 Blend

MB4 MB5 MB6φm 0.989 0.989 0.930φc 0.239 0.400 0.270A 1.04 0.52 0.50K 5.40 4.68 9.00

Capillary Rheometer @ 190°C, 50 s-1

40-UL 8.35 5-FL 4.13 Blend 9.78

19.34

26.0

19.86

0.0

5.0

10.0

15.0

20.0

25.0

30.0

0% 10% 20% 30% 40% 50% 60%

η/η

f

CaCO3 Volume %

MB-1 40-UL MB-2 5-FL MB-3 70/30 Blend MB-1 Model MB-2 Model MB-3 Model

5-FL: 5µm Capillary Rheometer @ 190°C, 50 s-1

5-FL 33.64 Blend 35.46

MB1 MB2 MB3φm 0.784 0.797 0.791φc 0.219 0.142 0.200A 4.24 3.88 3.00K 0.00 19.13 8.00

0.00

1.00

2.00

3.00

4.00

5.00

6.00

0% 10% 20% 30% 40% 50% 60%

η/η

f

TiO2 Volume %

50rpm (18 1/s) 100rpm (35 1/s) 200rpm (70 1/s) Percolation Model

Percolation (≥ φC)

Batchelor (< φC)

225.45.01 φφη ++=r

T = 155oC, 18 s-1

φC = 0.36 φm = 0.98

1−−

−

===⎟⎟⎟⎟

⎠

⎞

⎜⎜⎜⎜

⎝

⎛

φφφφ

ηη

η φm

cm

fr ea


Figure 23. MB-10 NA-206 LDPE/ TiO2 batch mixer

viscosity estimates and model predictions.

In order to capture the curvature of the viscosity increase at high filler concentrations, more compositions are required that were used in the present experiments. Furthermore, additional replicates are needed to quantify and account for the variability within a compositional state. Also, the apparent shear rate was used in all calculations. Applying a Rabinowitsch correction reduced the LLDPE resin viscosity by 2 to 5%, so it was ignored. Since n decreased with increasing filler concentration, a more comprehensive analysis would require estimating n at each filled composition and applying the correction.

For the LLDPE/CaCO3 systems, it was recognized that the 40-UL grade had no surface treatment while the smaller particle 5-FL material had a surface modifier applied. This changed the surface energy for dispersion. Furthermore, it is likely that an excess of surface modifier may have had a plasticizing effect on the higher molecular weight LLDPE resins, causing a measurable reduction in viscosity as illustrated in Figure 6 and Figure 20. It was assumed that untreated ~45µm particles could be dispersed sufficiently in PE primarily from shear and elongational stresses in the compounding extruder. The smaller ~5µm particles were selected to increase the maximum packing of the 70/30 filler blend; only a surface modified version was commercially available. Dispersion analysis was not conducted in this study.

The percolation model is capable of capturing the effects of filler loading with the rapid increase of melt viscosity, especially at high concentrations. However, the power law index n did change and tended to reduce with increasing filler content as shown in Figure 8. The Cross equation and percolation model do not account for this change. The original percolation theory development assumed the fluid to be Newtonian [4]. The LLDPE resins and filled compounds were non-Newtonian. The percolation model and the parameter fitting minimization employed are sensitive to how many data points are available in order to determine the

percolation threshold and maximum packing values. Model parameters and viscosity estimates are useful when working within one system, but quantitative comparison could be inaccurate. As described earlier, there is a discontinuity between the Batchelor and percolation models due to their form, how much data are available above and below fc. Also, parameter estimates for and fm tended to be high. From packing theory, non-spherical particles and non-monodisperse particle size distributions can enable higher packing densities. Furthermore, the model fitting methods with limited data at high filler concentrations likely contributed to these high values. One cannot draw definitive conclusions to what the actual maximum packing would be for these systems or quantify the morphology from the rheology and batch mixer experiments.

Conclusions Melt blending tests were conducted on a batch

mixer using LLDPE and two different CaCO3 powders to determine the effects of filler size and type, concentration and operating conditions on the process rheological response. The experiments, rheology measurements and viscosity models showed: 1. The experimental method developed using a batch

mixer correlated with capillary rheometer measurements. While batch mixer viscosity estimates did not match the measurement data, the method was able to quantify differences in the process response with polymer molecular weight, filler size and surface treatment.

2. All resins and filled compositions showed shear-thinning power-law like behavior, especially at shear rates near and above the average values estimated for the batch mixer channel. Estimates for the power law exponent n tended to decrease with increasing filler loading, especially at high filler loadings.

3. LLDPE molecular weight had a significant effect on the shape of the increase in viscosity with CaCO3 loading for all combinations tested. The 160 MI LLDPE exhibited little sensitivity to CaCO3 particle size or surface treatment, while the 20 MI LLDPE showed a reduced increase in viscosity for the ~5µm surface treated CaCO3 relative to the untreated ~45µm material and a 70/30 blend of the fillers.

4. The percolation model was used to fit capillary rheometer measurements and batch mixer viscosity estimates for the LLDPE/CaCO3 and LDPE/TiO2 systems. With limitations, the model captured the shapes of the viscosity increases with filler loading on a system-by-system basis. Percolation theory and the experimental method employed are useful tools for gaining insights into the behavior of highly filled polymer systems during melt processing operations.

0.0

2.0

4.0

6.0

8.0

10.0

12.0

14.0

16.0

0% 10% 20% 30% 40% 50% 60%

η/η

f

TiO2 Volume %

60rpm (21 1/s) 120rpm (42 1/s) 240rpm (84 1/s) Percolation Model @ 21 1/s Percolation

(≥ φC)


φC = 0.15 φm = 0.95

T = 186oC, 21 s-1

ηr =1+ 2.53φ +8.33φ2

1−−

−

===⎟⎟⎟⎟

⎠

⎞

⎜⎜⎜⎜

⎝

⎛

φφφφ

ηη

η φm

cm

fr ea


References 1. M. D. Wetzel, D. R. Pettitt, Jr., G. A. Campbell,

“Development of a Predictive Power Law Relationship for Concentrated Slurries, Part 2: Experiment and Processing Implications,” SPE ANTEC 2016, Indianapolis, IN, May 2016.

2. G. A. Campbell, M. E. Zak, J. S. Radhakrishnan, M. D. Wetzel, “Development of a Predictive Power Law Relationship for Concentrated Slurries, Part 1: Theory,” SPE ANTEC, Indianapolis, IN, May, 2016.

3. G. A. Campbell, M. D. Wetzel, “Characterizing the Flow of Slurries using Percolation Theory Based Functions”, Polym Eng Sci. doi:10.1002/pen.24435 Sept. 13, 2016.

4. G. A. Campbell, G. Forgacs, Physical Review A Volume 41, Number 8, 15 April 1990.

5. D. J. Cumberland, R. J. Crawford, “Handbook of Power Technology, Volume 6: The Packing of Particles,” Elsevier, Amsterdam, 1987, pp. 79-118.

6. A. J. Poslinski, R. K. Gupta, et al., Journal of Rheology, 32(B), 751-771 (1988).

7. J. M. Dealy, K. F. Wissbrun, “Melt Rheology and its Role in Plastics Processing,” Chapman & Hall, New York, 1995, 390-409.

8. Niedenzu, P. M., Sedar, Jr., W. T., Wetzel, M. D., “High Solids Viscosity for TiO2 Masterbatch,” SPE Color and Appearance Division RETEC, 2011.

Table 3. MB-4 LLDPE 9820/40-UL CaCO3 batch mixer barrel force and melt temperature data and viscosity estimates.

The batch mixer could not be run at 120 and 240 RPM.

Table 4. MB-1 LLDPE 1028/40-UL CaCO3 batch mixer barrel force and melt temperature data and viscosity estimates.

60 120 240 60 120 240 60 120 240 60 120 24021 42 83 21 42 83 21 42 83 21 42 83

#CaCO3 (wt.%)

φ CaCO3 (vol %)

Force (N)

Force (N)

Force (N)

Tmelt (oC)

Tmelt (oC)

Tmelt (oC)

η Force (Pa.s)

η Force (Pa.s)

η Force (Pa.s)

η Stdev (Pa.s)

η Stdev (Pa.s)

η Stdev (Pa.s)

1 0% 0.0% 1154.4 1863.5 2790.1 185.1 186.9 190.8 539.4 435.3 325.9 1.2 0.6 2.42 25% 10.0% 1343.7 2179.0 3176.8 185.4 187.4 191.7 627.8 509.1 371.1 36.0 19.8 12.23 42% 20.0% 1642.5 2599.3 3751.0 185.8 187.9 192.9 767.5 607.3 438.2 58.1 22.7 16.24 56% 30.0% 2474.8 3706.8 5020.8 185.3 188.3 194.2 1156.3 866.0 586.5 87.7 54.5 26.85 66% 40.0% 3056.5 4417.6 5745.8 186.1 189.5 196.0 1428.2 1032.0 671.2 32.5 14.4 9.56 75% 50.0% 4337.4 5903.7 7130.9 186.6 190.5 198.4 2026.6 1379.2 833.0 38.9 23.3 0.07 81% 60.0% 6457.9 187.0 3017.4 2.5

Avg: 2923.9 3445.0 4602.6 185.9 188.4 194.0 Kforce: 9.7Max: 6457.9 5903.7 7130.9 187.0 190.5 198.4Min: 1154.4 1863.5 2790.1 185.1 186.9 190.8Diff: 5303.5 4040.2 4340.8 1.88 3.58 7.56

Screw RPM:Shear Rate (1/s):

60 120 240 60 120 240 60 120 240 60 120 24021 42 83 21 42 83 21 42 83 21 42 83

#CaCO3 (wt.%)

φ CaCO3 (vol %)

Force (N)

Force (N)

Force (N)

Tmelt (oC)

Tmelt (oC)

Tmelt (oC)

η Force (Pa.s)

η Force (Pa.s)

η Force (Pa.s)

η Stdev (Pa.s)

η Stdev (Pa.s)

η Stdev (Pa.s)

1 0% 0.0% 195.1 307.1 589.4 186.2 187.0 188.2 65.8 51.8 49.7 8.5 1.4 0.42 24% 10.0% 283.0 418.9 750.8 185.7 186.9 188.5 95.4 70.6 63.3 3.6 2.8 1.93 42% 20.0% 338.0 614.4 1087.6 186.3 187.3 189.3 114.0 103.6 91.7 49.7 50.3 41.64 55% 30.0% 494.5 862.3 1518.4 186.3 187.5 190.0 166.8 145.4 128.0 55.3 39.8 32.75 66% 40.0% 558.7 986.6 1675.9 186.3 187.9 191.1 188.4 166.3 141.3 10.6 8.4 5.06 74% 50.0% 1183.3 1976.1 2934.2 186.4 188.6 193.1 399.0 333.2 247.3 18.5 17.4 8.97 81% 60.0% 3772.8 3394.4 4465.0 186.9 189.5 195.5 1272.2 572.3 376.4 605.7 343.8 150.2




Table 5. MB-10 LDPE/TiO2 batch mixer barrel force and melt temperature data and viscosity estimates.

The advice contained herein is based upon tests and information believed to be reliable, but users should not rely upon it absolutely for specific applications since performance properties will vary with processing conditions. It is given and accepted at user’s risk and confirmation of its validity and suitability in particular cases should be obtained independently. The authors and their affiliate entities make no guarantees of results and assume no obligation or liability in connection with its advice. This publication is not to be taken as a license to operate under, or recommendation to infringe, any patents.

60 120 240 60 120 240 60 120 240 60 120 24021 42 83 21 42 83 21 42 83 21 42 83

#TiO2

(wt.%)

φ TiO2

(vol %)Force

(N)Force

(N)Force

(N)Tmelt (oC)

Tmelt (oC)

Tmelt (oC)

η Force (Pa.s)

η Force (Pa.s)

η Force (Pa.s)

η Stdev (Pa.s)

η Stdev (Pa.s)

η Stdev (Pa.s)

1 0% 0.0% 923.6 1133.6 1525.2 154.6 154.9 156.0 1034.4 634.8 427.0 66.4 37.2 21.02 32% 10.0% 1208.3 1642.0 2203.3 185.9 187.2 189.9 1353.2 919.5 616.9 51.8 5.6 9.93 51% 20.0% 1636.3 2211.4 2895.1 185.6 187.4 191.2 1832.6 1238.3 810.6 88.0 34.8 18.74 64% 30.0% 2136.8 2886.3 3708.7 186.2 188.4 192.7 2393.0 1616.2 1038.4 70.3 35.5 20.05 74% 40.0% 3157.4 4179.1 5159.1 185.8 188.6 194.1 3536.1 2340.2 1444.5 105.3 25.3 7.46 81% 50.0% 4949.1 6422.2 7448.4 186.9 190.3 197.4 5542.7 3596.3 2085.4 31.1 40.2 0.07 86% 60.0% 8194.2 186.1 9177.1 0.0




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