Reprinted from American Laboratory October 2009 Technical Article by Tien T. Dao, Allan X. Ye, Ali A. Shaito, Nick Roye, and Kaj Hedman

Capillary Rheometry: Analysis of Low-Viscosity Fluids, and Viscous Liquids and Melts at High Shear Rates

heology is defined as the study of the vertical capillary die when no instrument The basic components of a capillary rhe- flow and deformation of fluids. Based driving force is applied, and 2) low-pressure ometer consist of a barrel, ram (piston), Ron the need to quickly and accurately readings from the transducer during the capillary die fitted inside the barrel, pres- set and control processing conditions, opti- measurement. Many times the measured sure gauge, and force transducer (Figure mize product performance, and/or ensure pressure signal can reach the low-end limit 1). The material is located within the bar- product acceptance, accurate rheological of the pressure transducer used. rel, and then the ram (or piston) attached measurements have become essential in the with a force transducer pushes the material characterization of any flowable materials. Another concern is the required length- through the capillary die at a specified rate. By utilizing rheological measurements on to-diameter ratio (L/D) of the die for the Above the die inside the barrel is a pres- new materials, process conditions can easily measurement to be rigorous. According to sure transducer, which allows for the mea- be determined, and the final product prop- Macosko,3 an L/D of 60 or higher is required surement of the gauge pressure ΔP within erties and performance can be predicted. to eliminate the die entrance/exit effects of the barrel of the capillary rheometer. The Historically, many processes impart high- low-viscosity fluids at high-shear-rate range. force transducer attached to the ram can be shear deformation and/or high-shear-rate This constraint requires that a die with a substituted for the pressure transducer and conditions on a material. Obtaining reliable very small diameter and long length be pro- is used as the measured signal ΔP inside the and accurate data under these conditions duced, which is difficult, if not impossible, barrel. However, any friction in the system has sometimes proven to be problematic to fabricate based on normal machining not associated with the sample resistance and difficult. techniques. In addition, other concerns may to flow is also included in the measured arise in the measurement of low-viscosity output. Using the measured pressure ΔP Traditionally, capillary rheometers have fluids at high shear rates, including viscous been used to measure the shear viscosity heating of the sample during testing, and and elasticity of viscous materials at high high-kinetic-energy effects. a shear rates. More recently, extensional vis- cosity has been obtained through the work A force balance of the translation mechan- of Cogswell et al.1 The interest in high ical system shows that the measured pres- shear rates stems from the mode of defor- sure drop ΔP in the capillary die includes mation a material will undergo in processes the following components: 1) pressure drop like extrusion, film blowing, and injection due to viscous dissipation (the sample’s molding. The design and operational prin- viscosity) within the capillary Pvisc, 2) pres- ciple of a capillary rheometer are condu- sure needed to obtain the kinetic energy of cive to providing rheological data under the testing fluid Pkin, 3) pressure loss due to these unique processing conditions. The end effects including the entrance and exit moving piston/die arrangement produces pressure loss Pent and Pexit, and 4) pressure high shear rates on the order of 107 s–1. A drop for viscoelastic fluids associated with measure of elasticity can be determined elastic energy Pelastic. The overall measured b by measuring expansion of the sample at pressure drop can be written as follows3: the die exit, called die swell. Melt fracture 2 can be studied by observing the extrudate. ΔP = Pvisc + Pkin + Pent + Pexit + Pelastic Extensional viscosity can be obtained as noted above. As a result, capillary rheom- The kinetic energy pressure contribution eters are widely used in both research envi- for a capillary die is given by: ronments and quality control laboratories. 2 Pkin = ρv Capillary rheometers are versatile and widely used in the rheological measurement where ρ is the density of the fluid, and v of viscous materials where the die sizes nor- is the average velocity of the flow. The mally range from 0.5 to 2.0 mm. However, well-known Bagley correction includes capillary rheometers suffer from several lim- both viscous and elastic components and itations when attempting to measure fluids is used to account for the entrance and Figure 1 a) Schematic of complete capillary with viscosity lower than 1 Pa s: 1) sam- exit pressure effects of non-Newtonian rheometer, and b) closeup of the die structure with ple flow by gravity through the traditional viscoelastic fluids. variables. Figure 2 SmartRHEO capillary rheometer. Figure 3 Viscosity of HDPE at 190 °C using a NOVA rotational rheometer and SmartRHEO capillary rheometer. and known controlled flow rate, one can calculate the viscosity of the test sample. By controlling the velocity of the ram, one algorithm permits automatic, operator-free HDPE and PDMS samples were evaluated can control the shear rate of the sample use of the capillary rheometer. using the ESP mode. These automated ESP through the die and calculate the viscosity results were then compared with the tradi- of the sample at fixed, control shear rates. tional manual-testing mode. By varying the components of the capillary Samples rheometer, the range of shear rates and A commercial, fractional melt index testing condition can be extended to fit extrusion-grade high-density polyethylene Instruments the requirement of the experimenter. (HDPE) was evaluated at 190 °C to demon- A SmartRHEO capillary rheometer was strate the capability of the instrument for test- used to measure the rheological properties Operation of a capillary rheometer is sim- ing high-viscosity materials. To demonstrate of samples over a wide range of shear rates ple but can be more time consuming than the instrument’s ability to measure medium- and test conditions. SmartRHEO is the a rotational rheometer. This is because the viscosity samples, a polydimethylsiloxane most technically advanced laboratory cap- larger sample charge requires more time to (PDMS) gum was evaluated at 105 °C. Both illary rheometer for the determination of reach thermal equilibrium. In addition, it the HDPE and PDMS were then compared the flow behavior of a wide range of materi- can take significant time for the sample to to small amplitude oscillatory shear (SAOS) als. The rheometer can measure shear rates attain steady-state flow at each shear rate. results obtained with a NOVA rheometer from 0.01 to over 10,000,000 s–1, with force Further, the operator must assess when the (REOLOGICA ­Instruments) (Figure 3) at capability from 0.1 to 50 kN. A wide vari- measured stress/force or shear rate reaches comparable shear rates/frequencies using the ety of die sizes and L/Ds are available. Cor- steady state for a particular point in the Cox-Merz rule. rosion-resistant sample chambers, pistons, measurement before changing to the next and dies are also offered. Temperature con- measurement point. A low-viscosity Newtonian oil, along with a trol is better than ±0.1 °C. Other options modified oil, were evaluated to demonstrate include: 1) automatic cleaning, 2) nitrogen This paper describes the SmartRHEO cap- the system’s ability to measure low-viscosity blanket, 3) pressure-volume-­temperature illary rheometer (REOLOGICA Instru- fluids at high shear rates. The role of the system, 4) thermal conductivity system, 5) ments, Bordentown, NJ) (Figure 2). The modifier is to raise the zero shear viscosity slit die geometry, 6) die swell, 7) stretch- data presented demonstrate the instru- while also imparting pseudoplastic, shear- ing unit, and 8) extension viscosity by the ment’s ability to measure not only high- thinning behavior to enhance flowabil- Cogswell method. The VisualRheo soft- viscosity materials at high shear rates, but ity and providing elasticity, leading to an ware can be run in manual, plateau, and also low-viscosity fluids. The ability to test increase in lubricity at high shear rates. automatic ESP mode. The ESP mode is low-viscosity fluids extends the usefulness a significant time saver, allowing experi- of the capillary rheometer to a wider range To demonstrate the utility and accuracy ments to be run without user intervention. of materials. In addition, the Equilibrium of the ESP algorithm in the SmartRHEO’s Other available features in the software Stress Prediction (ESP) instrument control VisualRheo operational software, both the are the Weissenberg-Rabinowitsch and Figure 4 NOVA rotational rheometer.

Bagley corrections, advanced curve-fitting module, elongational viscosity module, Figure 5 Viscosity of PDMS at 105 °C using a NOVA rotational rheometer and SmartRHEO capillary wall slip module, and thermal degradation rheometer. analysis module. Data exportation to other Windows programs is included as standard. tested at 190 °C, and the viscosity was of the ­SmartRHEO capillary rheometer. Capillary testing and results measured over a shear rate range from 1 PDMS exhibits less flow instability at For the testing of high- and medium- to 1000 s–1. At rates greater than 1000 s–1, high shear rates, permitting accurate ­viscosity materials at high shear rates, the melt fracture of HDPE occurred, and the data collection at shear rates in excess ­SmartRHEO capillary rheometer was uti- experiment was stopped. Results of this of 5000 s–1. Results of this experiment lized with a 1.0-mm die and a die length of measurement are presented in Figure 3. To are presented in Figure 5. Similar to the 20.0 mm. An L/D of 20 or greater is nor- confirm the capillary data, the HDPE sam- HPDE sample, the PDMS was also tested mally preferred in capillary testing of viscous ple was also evaluated on a NOVA rota- in SAOS using a NOVA rheometer at materials. A standardized procedure was tional rheometer (Figure 4) under SAOS 105 °C. As seen in the figure, the cap- used for all of the capillary testing. First, the at 190 °C. By applying the Cox-Merz rule, illary and rotational data match well, instrument was set to the desired test tem- the steady shear viscosity from the capil- as observed for the HDPE sample. The perature. After the instrument reached the lary rheometer can be directly compared results from Figure 5 show a wider range test temperature, the sample was loaded into with dynamic shear viscosity from the of shear rate, from 0.05 to 5000 s–1, com- the barrel of the capillary rheometer and the rotational rheometer. This comparison is pared to the HDPE sample. test was started. The test was set up so that also presented in Figure 3. As seen in the the sample would be at thermal equilibrium figure, the steady shear viscosity of HDPE To extend the capability of the capillary rhe- for 10 min in the first step of the test. The at 190 °C using the capillary rheometer ometer to measure low-viscosity material, piston was then lowered until it touched the matched the viscosity measurement from a small-diameter die (0.13-mm) with large sample and a maximum load of 0.200 kN the rotational rheometer. By utilizing both L/D (160 and 240) was designed and fabri- was applied. The measuring steps proceeded measurement techniques (rotational and cated.4,5 One concern when testing at high after the loading and movement of the pis- capillary), one can accurately measure the shear rates is viscous heating of the sample. ton with a controlled velocity and shear rate. viscosity of HDPE from low (0.05 s–1 ) to To investigate whether die viscous heating Once the steady-state stress at a particular high shear rates (1000 s–1). could have an effect during sample testing shear rate was reached, a data point was col- at higher shear rates, the Nahme (Na) num- lected, and the next selected shear rate was PDMS was selected as a medium-viscos- ber was calculated. The Na number needs to applied. This step was repeated until all shear ity material. A similar procedure and be less than 1 for die viscous heating to be rates were completed or the sample began to testing method was used for the PDMS neglected. The Na number can be calculated exhibit flow instability (melt fracture). as described for the HPDE above. The by the following equation3: main difference between the two sets of βη γ R2 HDPE was selected as a high-viscosity experiments is that the PDMS was run Na = sample for its ease of use and well-known at 105 °C instead of 190 °C. The tem- 4k rheological behavior in both capillary and perature of 105 °C was chosen to demon- Where β is the temperature sensitivity of rotational measurements. The HDPE was strate the midrange viscosity capability viscosity, η is the viscosity of the fluid, γ is According to Macosko,3 the L/D of the die should be larger than 60 to elimi- nate the entrance and exit effects at the high shear for low-viscosity fluids. Data here indicate that the L/D value for a 0.13-mm die should be greater than 150 to eliminate the need to cor- rect for Bagley, kinetic energy, and entrance and exit pressure contribu- tions. The small-diameter and, more importantly, high L/D requirement of the die make it difficult to manufacture by traditional means. These machining limitations were overcome by the use of some unique engineering concepts and techniques for producing the 0.13- mm die.

Two low-viscosity materials were used for this test—a Newtonian oil and an oil with modifier. A procedure was used that is similar to that used for the HPDE and PDMS materials. However, the temperature was 70 °C and the samples were tested at much higher shear rates (10,000–1,000,000 –1 Figure 6 Comparison of flow curves using a 0.13-mm die for Newtonian oil and modified oil at 70 °C. s ). Steady shear rotational viscosity was measured on a NOVA rheometer. Results are presented in Figure 6, where both the capillary and rotational vis- cosity data of the two oil samples are plotted versus shear rate from 100 to 1,000,000 s–1. The modified oil shows shear thinning at high shear rate com- pared to the Newtonian oil sample. The samples possess very low viscosity, in the range of 13 cP for Newtonian oil and 15 cP for modified oil, respectively. The excellent agreement between the rotational and capillary data under- scores the reliability of the technique. Clearly, utilizing the appropriate test condition, pressure transducer, and customized die, low-viscosity materials can be measured routinely at very high shear rate with the ­SmartRHEO capil- lary rheometer.

Equilibrium stress prediction Figure 7 Viscosity of HDPE at 190 °C using ESP capillary measurement and manual capillary measurement. One of the limitations of capillary test- ing is the time of the testing procedure and the requirement of the presence of the shear rate, R is the radius of the die, and even if the shear rate were increased by 100 an operator to collect data during the k is the thermal conductivity of the fluid. times, the die viscous heating would not experiment. As a result, the ESP soft- have an effect on the measurement. Simi- ware function was developed to elimi- Using a shear rate at 106 s–1 and proper- larly, calculations for the kinetic energy nate the need for operator intervention ties of the tested fluid, the Na number was and Bagley corrections showed both terms during a run; in addition, it speeds up estimated to be 10–7, which is well below 1. to be negligible for the 0.13-mm die in the the experimental measurement process. This value of the Na number confirms that shear rate range 10,000–1,000,000 s–1. For well-behaved materials, i.e., where a software automatically changes to tigate a wide range of materials over a the next shear rate until the end of broad range of shear rates. With custom- the experiment. ized dies, the rheometer can be used rou- tinely to test low-viscosity materials at The comparison between manual very high shear rate. The ease of use and and ESP mode testing is presented in the ESP function will shorten the test- Figure 7. It can be seen that the ESP ing time and reduce the operating cost of function successfully predicted the obtaining rheological results. steady shear viscosity of the sample b without the presence of an operator. In addition, the ESP mode signifi- References cantly reduced the time of the experi- 1. Cogswell, F.N. Converging flow of polymer ment. Figure 8 shows the duration of melts in extrusion dies. Polym. Eng. Sci. the experiment using manual and ESP 1972, 12, 64–73. mode. The ESP mode reduced the 2. Tatum, J.A. An Experimental Investiga- amount of time to perform the experi- tion of the Response of Polymeric Sys- ment by 70%, yet still provided data tems Containing Particles in Extension- comparable to the manual mode. This Dominated Flow Fields; Ph.D. dissertation; Figure 8 Raw data showing pressure versus time for feature will significantly reduce test- Clemson University, SC, 2006. a) manual experiment with a total time of approximately ing time and can be applied for quality 3. Macosko, C.W. Rheology Principles, Mea- 1100 sec, and b) ESP experiment with a total time of control process where time and, more surements and Applications; Publishers, Inc., approximately 400 sec. importantly, operation intervention, New York, NY, 1994. are minimized. 4. Wang, X. Drop-On-Demand Deposition of Complex Fluid on Textiles; Ph.D. dis- stress growth is exponential, the stress sertation; Georgia Institute of Technology, growth curve can be fitted with a spe- Conclusion Atlanta, GA, 2008. cific equation. The steady-state stress The SmartRHEO capillary rheometer can 5. Egorova, N. Using Slit Rheometry in value at the applied shear rate can be be used to investigate rheological properties Characterizing Coating Colour Flow in predicted using the fitted equation con- of a wide range of materials from low-viscos- Blade Coating Process; Ph.D. disserta- stants. By applying a special algorithm ity fluids in the range of 1–10 cP to highly tion; Helsinki University of Technology, and the fitting equation, ESP uses the viscous materials such as HDPE. Also, cap- Finland, 2006. data for the first several seconds to esti- illary rheometry can provide the high-shear- mate the constant for the equation from rate region beyond the limit of rotational which the steady-state value can be rheometers. By applying the Cox-Merz rule, determined without the experimental the range of shear rate measurements can be waiting time to attain steady-state flow. extended from very low shear rate using a Dr. Dao, Dr. Ye, and Dr. Shaito are with HDPE was used to test the ability of the rotational rheometer to very high shear rate ­REOLOGICA Instruments, 231 Crosswicks ESP function. Similar testing conditions using a capillary rheometer. The combina- Rd., Bordentown, NJ 08505, U.S.A.; tel.: 609- as used in the manual control mode test- tion of data from both rheometers gives the ing of the HDPE were used. The major engineer and scientist a much better under- 298-2522; fax: 609-298-2795; e-mail: info@­ difference is that the ESP mode was set standing of the full spectrum of material reologicainstruments.com. Mr. Roye is Western up to measure the data over the first 10 flow behavior. Region Manager, REOLOGICA ­Instruments, sec of each shear rate, and then uses the Valley Village, CA, U.S.A. Dr. Hedman is data to predict the steady-state viscos- The SmartRHEO capillary rheometer is VP Software Development, REOLOGICA ity. After 10 sec of measurement, the versatile and easy to customize to inves- ­Instruments, Lund, Sweden.