Assessment of Piezoelectric Sensors for the Acquisition of Steady Melt Pressures in Polymer Extrusion

fluids

Article Assessment of Piezoelectric Sensors for the Acquisition of Steady Melt Pressures in Polymer Extrusion

Sónia Costa, Paulo F. Teixeira *, José A. Covas * and Loic Hilliou *

Institute for Polymers and Composites/i3N, University of Minho, 4800-058 Guimarães, Portugal; [email protected] * Correspondence: [email protected] (P.F.T.); [email protected] (J.A.C.); [email protected] (L.H.); Tel.: +351-253510320 (L.H.)

Received: 26 February 2019; Accepted: 1 April 2019; Published: 3 April 2019

Abstract: Piezoelectric sensors have made their way into polymer processing and rheometry applications, in particular when small pressure changes with very fast dynamics are to be measured. However, no validation of their use for steady shear rheometry is available in the literature. Here, a rheological slit die was designed and constructed to allow for the direct comparison of pressure data measured with conventional and piezoelectric transducers. The calibration of piezoelectric sensors is presented together with a methodology to correct the data from the inherent signal drift, which is shown to be temperature and pressure independent. Flow curves are measured for polymers showing different levels of viscoelasticity. Piezoelectric slit rheometry is validated and its advantage for the rheology of thermodegradable materials with viscosity below 100 Pa·s is highlighted.

Keywords: piezoelectric; pressure transducers; extrusion; rheology

1. Introduction Accurate readings of steady melt pressure are important to monitor flow conditions during polymer extrusion and for rheometry experiments involving pressure flows. For example, it is well-known that the installation of flush-mounted pressure gauges along a slit die wall allows the assessment of shear viscosity up to relatively high shear stresses, with no need of the Bagley correction for non-viscometric flow effects at the edges of the die [1]. However, the conventional melt pressure transducers of the diaphragm type are bulky and have large front dimensions (typically a diameter of 7.8 mm and process connections with M18 (× 1.5) according to DIN 3852-1592, or 1/2-20 UNF), which may impact on the practical possibility of fixing them on small and/or curved flow channels. In the case of slits, consecutive transducers along the length maybe set apart more than desired and there may be little space for additional transducers. Indeed, if a microscope is also inserted in the slit, it is possible to image the structure of the material undergoing shear flow, thereby giving way to rheo-optical characterization [2]. Piezoelectric sensors have remarkable sensitivity, fast response and reduced size compared to conventional melt pressure sensors. They are often used in injection molding to measure instantaneous pressures along the production cycle. When mounted in customized miniaturized systems (such as capillary rheometry dies), and implementing oversampling techniques, piezoelectric sensors were used to establish relationships between rapid pressure fluctuations with small amplitudes and distortions found on the surface of the extruded materials [3–9]. As a result of these studies, slit dies equipped with piezoelectric transducers are now commercially available as accessories to capillary rheometers. Using these devices, it was possible to predict extrusion instabilities for a series of commercial polyethylenes [10]. A similar piezoelectric set-up was coupled to a laboratory screw

Fluids 2019, 4, 66; doi:10.3390/fluids4020066 www.mdpi.com/journal/fluids Fluids 2019, 4, 66 2 of 12 extruder to demonstrate the feasibility of applying high sensitivity detection systems to practical polymer processing [6]. Unlike conventional diaphragm sensors, piezoelectric sensors exhibit a drift of the signal with time. The drift is inherent to both the charge amplification and transducer-to-amplifier cabling, which are needed to convert the transducer signal into volts. Therefore, it is necessary to adopt data treatment procedures to account for the drift of the piezoelectric signal and for the non-linearity of the transducer with pressure [11] or temperature [12]. Recently Kádár et al. [5] used piezoelectric sensors in a slit die attached to a capillary rheometer to estimate the first normal stress difference of polymer melts, N1, via the so-called ‘pressure hole effect’ [13]. The method is very demanding for the pressure transducers, as small differences between the readings of two sensors are to be measured [14]. Kádár et al. [5] assumed the drift in the voltage Vdrift to be a linear function of time t,

Vdrift(t) = V0 + st, (1) where V0 is the value of the voltage at time 0 defining the start of the recording, and s is the slope that depends on the testing temperature and the pressure applied on the piezoelectric transducer. Eventually, a flow curve was obtained which compared reasonably well with small amplitude oscillatory shear data in a Cox-Merz representation, but a single slope was used to correct the signal drift recorded during the application of a ramp of steady shear rate steps, which correspondingly generated a ramp of pressures. A direct comparison between the flow curves measured with piezoelectric sensors and conventional pressure transducers during steady shear has not yet been reported in the literature. Thus, the use of piezoelectric sensors for steady shear rheometry remains to be validated. This work proposes a methodology to correct the drift together with temperature and pressure effects. A modular slit die was designed and constructed in order to incorporate both piezoelectric sensors and conventional pressure transducers in a mirror-like arrangement along the channel, thus enabling the direct comparison between the flow curves acquired with the two types of transducers.

2. Experimental

2.1. Materials An extrusion grade low density Polyethylene (ALCUDIA® LDPE 2221FG, from Repsol, Spain) with a density of 0.922 g/cm3, a melt flow index of 2.1 g/10 min (190 ◦C/ 2.16 kg) and a processing temperature range between 150–180 ◦C was used for the assessment. This polymer has excellent thermal stability, thus minimizing the eventual influence of thermal degradation in the experiments. Two biodegradable polymers, a polyhydroxybutyrate (PHB P309 from Biomer®, Krailling, Germany) and a Polybutylene adipate terephthalate (PBAT, ecoflex® F Blend C1200, from BASF, Ludwigshafen, Germany) were also used to compare the operability windows of conventional and piezoelectric transducers.

2.2. Experimental Set-Up A double slit rheometrical die for in-process characterization, recently developed by the authors [15], was modified and used in this study. It includes three modules: a central body (module 1) where the inlet circular channel from the extruder is progressively converted into a slit, which is then divided into perpendicular measurement (module 2) and extrusion (module 3) channels. The flow rate in the measuring slit is varied by a valve positioned at its entrance, whereas a second valve balances the flow rate in the extrusion slit to keep a constant pressure at the die inlet. Thus, rheometrical measurements can be performed while maintaining constant extrusion conditions (feed rate and screw speed). The initial design, construction, and rheological validation have been reported elsewhere [15]. For the present study, a new measurement channel (module 2) was developed. The new module comprises two halves bolted together. In one part, three conventional melt pressure transducers flush Fluids 2019, 4, 66 3 of 12 mountedFluids 2019, can 4, x FOR beinserted, PEER REVIEW while in the other part three piezoelectric transducers can be also flush3 of 12 mounted at the same axial position, see Figure1. The measurement channel presents a cross section of 10be mm also width flush bymounted 0.8 mm at height. the same axial position, see Figure 1. The measurement channel presents a cross section of 10 mm width by 0.8 mm height.

Figure 1. Schematic view of the double slit rheometrical die (a) and cross section view of the measurementFigure 1. Schematic channel (moduleview of 2)the (b ).double slit rheometrical die (a) and cross section view of the measurement channel (module 2) (b). Two piezoelectric transducers from the Kistler Group, Winterthur, Switzerland (Kistler 6182B (PS 1)Two and apiezoelectric Kistler 6189A transducers (PS 2), see mainfrom characteristicsthe Kistler Group, as provided Winterthur, by the Switzerland manufacturers (Kistler in Table 6182B1) were(PS 1) used. and PSa Kistler 2 has the6189A ability (PS to2), perform see main simultaneously characteristics as pressure provided and by temperature the manufacturers measurements in Table and1) were was used. mounted PS 2 closerhas the to ability the die to exit. perform In order simultaneously to minimize pressure the signal and drift, temperature as well as measurements the influence ofand external was mounted electromagnetic closer to noise,the die the exit. sensors In order were to separatelyminimize the shielded signal bydrift, means as well of aas copper the influence mesh coveringof external the electromagnetic wires. Two conventional noise, the sensors pressure were transducers separately Dynisco shielded PT422A by means (0-3000 of a PSI, copper Dynisco mesh Inc.,covering Franklin, the MA,wires. USA) Two with conventional a sensitivity pressure of ±0.5% transducers and a front Dynisco diameter PT422A of 7.8 mm(0-3000 were PSI, used Dynisco (PT 1 mountedInc., Franklin, upstream MA, and USA) PT with 2 mounted a sensitivity downstream). of +/−0.5% These and a transducers front diameter are sensitiveof 7.8 mm to were variations used (PT in the1 mounted temperature upstream in the rangeand PT of 2± moun0.005ted MPa downstream). for ±1 ◦C. All These sensors transducers were flush are mounted sensitive in to the variations double slitin diethe andtemperature adequate in fixing the range was verified. of +/−0.005 MPa for +/−1 °C. All sensors were flush mounted in the double slit die and adequate fixing was verified. Table 1. Characteristics of the melt pressure transducers. Table 1. Characteristics of the melt pressure transducers. Characteristics Kistler 6182 B Kistler 6189A PT422A Characteristics Kistler 6182 B Kistler 6189A PT422A Front diameter 2.5 (mm) 2.5 (mm) 7.8 (mm) RangeFront diameter 0–200 (MPa) 2.5 (mm) 0–200 2.5 (MPa) (mm) 7.8 (mm) 0–21 (MPa) Sensibility, x Range −2.5 (pC/bar) 0–200 (MPa) −6.6 0–200 (pC/bar) (MPa) 0–21 (MPa) 0.5% Operating temperatureSensibility, range: x −2.5 (pC/bar) −6.6 (pC/bar) 0.5% ◦ ◦ Sensor, cable,Operating connector temperature box range: 0–00 ( C) 0–200 ( C) ◦ ◦ ◦ At the frontSensor, of the cable, sensor connector box < 450 ( C) 0–00 (°C) < 450 0–200 ( C) (°C) 0–400 ( C) At the front of the sensor < 450 (°C) < 450 (°C) 0–400 (°C) As a validation strategy, and in order to avoid the inherent fluctuations of pressure and flow rate in screwAs extruders,a validation the strategy, double slit and die in was order attached to avoid on the the barrel inherent of a Rosandfluctuations RH10 of capillary pressure rheometer and flow (Malvernrate in screw Instruments, extruders, Malvern, the double UK), slit see die Figure was2. attached on the barrel of a Rosand RH10 capillary rheometer (Malvern Instruments, Malvern, UK), see Figure 2. Fluids 2019, 4, 66 4 of 12 Fluids 2019, 4, x FOR PEER REVIEW 4 of 12

Figure 2. Schematic view (a) and photograph (b) of the experimental set-up. 1: double slit die. 2: Figure 2. Schematic view (a) and photograph (b) of the experimental set-up. 1: double slit die. 2: conventional pressure transducers. 3: piezoelectric sensors. 4: power supply. 5: charge amplifier. 6: conventional pressure transducers. 3: piezoelectric sensors. 4: power supply. 5: charge amplifier. 6: analog-to-digital converter (ADC) card. 7: terminal block for 25-Pin. 8:D-SUB Cable. 9: strain gage analog-to-digital converter (ADC) card. 7: terminal block for 25-Pin. 8:D-SUB Cable. 9: strain gage indicator. 10: capillary rheometer. indicator. 10: capillary rheometer. The double slit die is independently heated using two temperature controllers OMRON E5CSV (OmronThe Corporation, double slit die Tokyo, is independently Japan). In order heated to acquire using two the signalstemperature from the controllers piezoelectric OMRON sensors, E5CSV the following(Omron Corporation, equipment was Tokyo, used: Japan). In order to acquire the signals from the piezoelectric sensors, the following equipment was used: -- Two charge amplifiers,amplifiers, a Kistler 5155A 2241 for PS 11 andand aa KistlerKistler 5155A5155A 22A122A1 (with(with separateseparate channelschannels to acquire to acquire pressure pressure and temperature) and temperature) for PS for 2. Two PS 2. amplification Two amplification ranges ranges are available are available which dependwhich on dependthe maximum on the maximumcharge delivered charge deliveredby the transducer, by the transducer, namely up namely to 20000 up to pC 20000 (which pC corresponds(which correspondsto 10 V in Range to 10 VI) and in Range up to I) 5000 and pC up to(which 5000 pCcorresponds (which corresponds to 10 V in toRange 10 V II in for Range larger II amplification).for larger amplification). -- Two power supplies (Matrix MPS-5LK-2, deliveringdelivering a voltage between 18–30 V DC)DC) toto feedfeed thethe amplifiersamplifiers and command and command functions. functions. -- Two analog-to-digital converter (ADC) boards (NI-9215 from NationalNational Instruments)Instruments) drivendriven byby custom-writtencustom-written LabVIEW™ LabVIEW routines™ routines to digitize to digitize the the amplifiers amplifiers outputs outputs and and enhance enhance the sensorsensor sensitivitysensitivity with withon-the-fly on-the-fly oversampling oversampling techniques techniques [16–18]. [16– 18]. -- Two DIN-RailDIN-Rail MountMount Terminal Terminal Blocks Blocks for for 25-Pin 25-Pin D-SUB D-SUB Modules Modules and and two two 25-Pin 25-Pin Shielded Shielded D-SUB D- SUB cables (from National Instruments, Austin, TX, USA) in order to interface the power supply, thethe amplifier,amplifier, and the and ADC. the ADC.

EachEach conventionalconventional pressure pressure transducer transducer was was connected connected to ato Dynisco a Dynisco 1390 1390 strain strain gage gage indicator, indicator, with analogwith analog retransmission retransmission output accuracyoutput accuracy span of ± span0.2%. of The +/− strain0.2%. gageThe indicatorstrain gage is also indicator connected is also to a dataconnected acquisition to a data system acquisition NI-9215 fromsystem National NI-9215 Instruments from National (see FigureInstruments2) and driven(see Figure by custom-written 2) and driven LabVIEWby custom-written™ routines. LabVIEW™ The piezoelectric routines. sensorThe piezoelect PS 1 andric the sensor conventional PS 1 and the pressure conventional transducer pressure PT 1 weretransducer connected PT 1to were the sameconnected data acquisitionto the same system data acquisition NI-9215 while system PS 2NI-9215 and PT while 2 were PS connected 2 and PT to 2 thewere second connected data acquisitionto the second system data NI-9215,acquisitio forn system time synchronization. NI-9215, for time synchronization.

2.3.2.3. Experimental ProcedureProcedure

2.3.1.2.3.1. Calibrations ConventionalConventional transducerstransducers and piezoelectric transducers were coupled to a Terwin T1200T1200 MkllMkll hydraulichydraulic comparisoncomparison testtest pump.pump. Calibration curv curveses were constructed by reporting thethe pressurepressure returnedreturned byby thethe transducerstransducers asas aa functionfunction ofof thethe pressurepressure setset byby thethe testtest pump.pump. ForFor thethe piezoelectricpiezoelectric transducers, the calibration was performed with the charge amplifiers set in the Range II. In this case, the voltage returned by the transducers are converted into pressure using the following equation:

PS 1 = PS 2 = (Vcor * 50) / x (2) Fluids 2019, 4, 66 5 of 12 transducers, the calibration was performed with the charge ampliﬁers set in the Range II. In this case, the voltage returned by the transducers are converted into pressure using the following equation:

PS 1 = PS 2 = (Vcor ∗ 50)/x (2) where x is the sensibility given by the manufacturer (see Table1) and Vcor is the output voltage V(t) corrected from the drift, namely Vcor(t) = V(t) − Vdrift(t).

2.3.2. Pressure Measurements and Flow Curves The whole set-up is switched on at least 30 min prior to any measurement to allow for a stabilized temperature in both capillary barrel and double slit die, and to warm up the electronics, therefore reducing the signal drift. The slit is then fed with melt (maintaining constant the piston velocity) for a period of 1 min and the material is left to relax until the pressure readings, PT 1 and PT 2, stabilize. Then, the zero balance of the conventional transducers is adjusted in order to define a zero pressure and to adjust the 80% span. The data acquisition by the ADC starts and the amplifier is switched on to record the piezoelectric drift Vdrift(t) over two minutes. This time is needed for measuring a consistent slope s. Afterwards, 6 successive incremental step increases of the piston velocity are performed in order to ramp up the corresponding shear rates. In each ramp the piston velocity varied from 10 mm/min to 60 mm/min, corresponding to apparent shear rates ranging from 27 s−1 to 165 s−1. The shear rate was step increased only after steady state pressures were read from the graphic display provided under the LabVIEW™ environment. At the end of the ramp, the piston is retracted and the drift monitored for two minutes. The flow curves were constructed using the following analysis for slit rheometry [1], where the pressure drop dP = PS 1 − PS2 or dP = PT 1 − PT 2 and the volumetric . flow rate, Q, are used to determine the wall shear stress σ and the shear rate γ, respectively, with the following equations: H dP σ = (3) 2(1 + H/W) dx where W and H are the width and height of the flow channel respectively, and dx is the distance . between transducers PS 1 and PS 2 or PT 1 and PT 2. The apparent shear rate γa is:

. 6Q γ = (4) a WH2 where Q is obtained in an indirect way by measuring the weight of the extrudate. This methodology is preferred to the use of the piston speed for Q determination, as it can readily be extended to in-line rheometry during extrusion application. The true wall shear rate was calculated from:

. . . γ d ln γ γ = a 2 + a (5) 3 d ln σ

3. Results and Discussion Figure3 presents the time evolution of the voltage V acquired by transducer PS 1 mounted in an empty slit (no pressure applied), in order to assess the drift inherent to this measuring system. In Figure3a, the effect of switching on the amplifier on the recorded voltage is evident: the signal jumps to a value V0 before drifting with time. As expected [5], the signal presents a drift that follows Equation (1). Thus, the voltage can be corrected to give a flat signal Vcor(t) = V(t) − Vdrift(t), as shown in the inset to Figure3a. Both jump to V0 and drift are due to the closing of the electronic circuit (both amplification and pressure sensing), and as such should be independent of the pressure and temperature at the tip of the sensor [19]. Fluids 2019, 4, x FOR PEER REVIEW 6 of 12 Fluids 2019, 4, x FOR PEER REVIEW 6 of 12 Fluids 2019, 4, 66 6 of 12

Figure 3. Drifts measurements with piezoelectric sensor PS 1 in an empty slit. (a) Time dependence Figure 3. Drifts measurements with piezoelectric sensor PS 1 in an empty slit. (a) Time dependence of of Figurethe voltage 3. Drifts delivered measurements by the ch witharge amplifier.piezoelectric The sensor arrow PS indicates 1 in an theempty time slit. at which(a) Time the dependence amplifier the voltage delivered by the charge amplifier. The arrow indicates the time at which the amplifier is is ofswitched the voltage on. The delivered inset in by (a the) displays charge theamplifier. corrected The voltage arrow indicatesVcor(t). (b )the Reproducibility time at which of the the amplifier slope switched on. The inset in (a) displays the corrected voltage Vcor(t). (b) Reproducibility of the slope of of isthe switched drift Vdrift on.(t) −TheV0. inset in (a) displays the corrected voltage Vcor(t). (b) Reproducibility of the slope the drift Vdrift(t) − V0. of the drift Vdrift(t)−V0. Figure 3b shows the measurements of three consecutive independent drift measurements (drift Figure3b shows the measurements of three consecutive independent drift measurements (drift 1, 1, 2, andFigure 3) and 3b showsa drift the measurement measurements performed of three consafterecutive 3 h (drift independent 4). The slope drift smeasurements does not change (drift 2, and 3) and a drift measurement performed after 3 h (drift 4). The slope s does not change significantly significantly1, 2, and 3) in and the athree drift consecutive measurement measurements, performed after in fact 3 hthere (drift is 4).almost The anslope overlap s does of notthe changedata. in the three consecutive measurements, in fact there is almost an overlap of the data. Drift 4 deviates Driftsignificantly 4 deviates in slightly the three from consecutive the previous measurements, measurements, in fact but thereit reflects is almost only aan difference overlap of of the 0.0019 data. slightly from the previous measurements, but it reflects only a difference of 0.0019 MPa from the MPaDrift from 4 deviates the average slightly of fromthe consecutive the previous drifts measurem (usingents, the butsensibility it reflects of onlythe manufacturer a difference of in 0.0019 the average of the consecutive drifts (using the sensibility of the manufacturer in the conversion). In order conversion).MPa from Inthe order average to checkof the for consecutive any effect driftsof pressure (using onthe V sensibilitydrift(t), the piezoelectric of the manufacturer sensors werein the to check for any effect of pressure on Vdrift(t), the piezoelectric sensors were individually mounted on a individuallyconversion). mounted In order onto acheck calibrator for any and effect several of pressure pressures on wereVdrift(t) successively, the piezoelectric applied. sensors Figure were 4 calibrator and several pressures were successively applied. Figure4 reports the time evolution of the reportsindividually the time mounted evolution on ofa calibratorthe output and voltage several V(t) pressures during thewere ramping successively up of applied.pressure Figurein the 4 output voltage V(t) during the ramping up of pressure in the calibration pump. The inset in Figure4 calibrationreports the pump. time Theevolution inset in of Figure the output 4 displays voltage the V(t)pressure during dependence the ramping of theup slopeof pressure s, recorded in the displays the pressure dependence of the slope s, recorded with sensor PS 1. The error bar associated to withcalibration sensor PS pump. 1. The The error inset bar in associated Figure 4 displaysto each data the pressurepoint results dependence from the oferror the computedslope s, recorded from each data point results from the error computed from the fit of Equation (1) to V(t) in each pressure thewith fit of sensor Equation PS 1. (1) The to V(t)error in bar each associated pressure tostep. each The data data point show results that in from the appliedthe error pressure computed range, from step. The data show that in the applied pressure range, there is no significant effect of the pressure on therethe fitis noof Equationsignificant (1) effect to V(t) of inthe each pressure pressure on the step. drift The of data the piezoelectricshow that in sensor.the applied pressure range, the drift of the piezoelectric sensor. there is no significant effect of the pressure on the drift of the piezoelectric sensor.

Figure 4. Time evolution of the output voltage V(t) (solid line) of the PS 1 sensor during the ramping

Figureup of pressure4. Time evolution (circles) inof thethe calibrationoutput voltage pump. V(t) The (solid inset line) displays of the PS the 1 pressuresensor during dependence the ramping of the upslopeFigure of pressures for 4. theTime PS(circles) evolution 1. in the of thecalibration output voltage pump. V(t)The (solidinset displaysline) of the the PS pressure 1 sensor dependence during the rampingof the slopeup ofs for pressure the PS 1.(circles) in the calibration pump. The inset displays the pressure dependence of the Figureslope 5s forrepresents the PS 1. the calibration curves for PS 1 and PS 2. Each data point and error bar result respectivelyFigure 5 fromrepresents the average the calibration and standard curves error for ofPS five 1 and measurements PS 2. Each data similar point to and the oneerror displayed bar result in respectivelyFigureFigure4. The from slopes5 represents the returned average the by calibrationand the standard linear curves fits error to thefor of dataPS five 1 indicateandmeasurements PS 2. that Each the datasimilar response point to oftheand the one error piezoelectric displayed bar result insensorsrespectively Figure is 4. nicely The from slopes linear the average forreturned the rangeand by standard ofthe pressures linear error fits tested.of to five the measurements In data addition, indicate the similar that computed the to responsethe slopes one displayed of do the not significantlyin Figure 4. differThe slopes from thereturned constants by calculatedthe linear fits with to the the sensibilities data indicate reported that the in theresponse calibration of the Fluids 2019, 4, x FOR PEER REVIEW 7 of 12

Fluidspiezoelectric 2019, 4, x FOR sensors PEER REVIEWis nicely linear for the range of pressures tested. In addition, the computed7 of 12 slopes do not significantly differ from the constants calculated with the sensibilities reported in the piezoelectriccalibration certificate sensors is supplied nicely linear by the for manufacturer, the range of namely pressures 50 /tested. x = 20 forIn addition,PS 1 and 50the / computedx = 7.58 for FluidsslopesPS 20192 (see do, 4, Tablenot 66 significantly 1 for x). The differ intercepts from theto the constant origins for calculated the linear with fits theare sensibilities0.28 ± 0.03 and reported 0.096 7±in of0.001 the 12 calibrationfor PS1 and certificate PS2, respectively. supplied by These the manufacturer, intercepts are namelysmaller 50than / x =those 20 for found PS 1 forand the 50 /conventional x = 7.58 for ± ± PStransducers 2 (see Table (0.415 1 for ±x ).0.015), The intercepts which suggest to the origina better for sensitivity the linear forfits piezoelectricare 0.28 0.03 sensors and 0.096 in the 0.001 low- certiﬁcate supplied by the manufacturer, namely 50/x = 20 for PS 1 and 50/x = 7.58 for PS 2 (see forpressure PS1 and range. PS2, respectively. These intercepts are smaller than those found for the conventional Tabletransducers1 for x). (0.415 The intercepts ± 0.015), towhich the origin suggest for a the better linear sensitivity ﬁts are 0.28 for ±piezoelectric0.03 and 0.096 sensors± 0.001 in the for PS1low- andpressure PS2, respectively. range. These intercepts are smaller than those found for the conventional transducers (0.415 ± 0.015), which suggest a better sensitivity for piezoelectric sensors in the low-pressure range.

Figure 5. Calibration curves for PS 1 and PS 2, fitted with a linear function. Figure 5. Calibration curves for PS 1 and PS 2, ﬁtted with a linear function.

In order toFigure estimate 5. Calibration the eventual curves effect for PS of1 and the PS melt 2, fitted temperature with a linear on function. Vdrift, experiments were In order to estimate the eventual effect of the melt temperature on V , experiments were performed with the piezoelectric transducers mounted on the heated doubledrift slit die, but with no performed with the piezoelectric transducers mounted on the heated double slit die, but with no materialIn order in the to slit estimate cavity. Figurethe eventual 6 reports effect the temperatureof the melt dependencetemperature of on the V slopedrift, experiments s computed wereusing materialperformed in the with slit the cavity. piezoelectric Figure6 reports transducers the temperature mounted dependenceon the heated of thedouble slope slits computeddie, but with using no Equation (1) from Vdrift transients recorded with PS 2. Equationmaterial (1)in the from slitV cavity.drift transients Figure 6 recorded reports the with temperature PS 2. dependence of the slope s computed using Equation (1) from Vdrift transients recorded with PS 2.

Figure 6. Average drift slope s as function of temperature. Figure 6. Average drift slope s as function of temperature. Each point and error bar in the figure correspond to an average value and error computed from five measurements.Each point and For errorFigure the bar temperature 6.in Average the figure drift range correspond slope tested s as function in to Figure an average of6 temperature., which value corresponds and error computed to the range from recommendedfive measurements. by the For manufacturer, the temperature no noteworthy range tested variation in Figure of s6,with which temperature corresponds is to perceived. the range Thisrecommended result,Each point together byand the witherror manufacturer, the bar data in the displayed figure no noteworthy correspond in Figure variation4 ,to confirms an average of s that with valueV temperaturedrift andis essentially error is computed perceived. due to from the This five measurements. For the temperature range tested in Figure 6, which corresponds to the range electronicresult, together imperfections with the ofthe data whole disp piezoelectriclayed in Figure acquisition 4, confirms system that [11 V,12drift,19 is]. essentially due to the recommendedelectronicFigure7 imperfections presents by the manufacturer, the of time the whole evolution no piezoelectric noteworthy of the outputs variationacquisition of of the systems with piezoelectric temperature [11,12,19]. and is conventionalperceived. This transducersresult, together recorded with during the data the disp rampinglayed up in of Figure piston 4, velocities. confirms that Vdrift is essentially due to the electronic imperfections of the whole piezoelectric acquisition system [11,12,19]. Fluids 2019, 4, x FOR PEER REVIEW 8 of 12

Fluids 2019Figure, 4, x FOR 7 PEERpresents REVIEW the time evolution of the outputs of the piezoelectric and conventional8 of 12 transducers recorded during the ramping up of piston velocities. Figure 7 presents the time evolution of the outputs of the piezoelectric and conventional transducersFluids 2019, 4 ,recorded 66 during the ramping up of piston velocities. 8 of 12

Figure 7. Time evolution of outputs (voltages) measured during the stepwise ramp in the piston velocity of the capillary rheometer fed with a low density polyethylene (LDPE) at 150 °C. (a)— Figure 7. Time evolution of outputs (voltages) measured during the stepwise ramp in the piston velocity FigurePiezoelectric 7. Time (PSevolution 1) and ofconventional outputs (voltages) (PT 1) transducers measured duringlocated theupstream. stepwise (b )—Piezoelectricramp in the piston (PS 2) of the capillary rheometer fed with a low density polyethylene (LDPE) at 150 ◦C. (a)—Piezoelectric velocityand conventional of the capillary (PT 2) rheometer transducers fed located with adownstream. low density polyethylene (LDPE) at 150 °C. (a)— (PS 1) and conventional (PT 1) transducers located upstream. (b)—Piezoelectric (PS 2) and conventional Piezoelectric (PS 1) and conventional (PT 1) transducers located upstream. (b)—Piezoelectric (PS 2) (PT 2) transducers located downstream. andThe conventional double slit (PT rheometer2) transducers was located fed downstream.with LDPE at 150 °C. The transients of face-mounted transducers show a satisfactory matching along the time scale. The piezoelectric signals show the The double slit rheometer was fed with LDPE at 150 ◦C. The transients of face-mounted expected drifts before the inception of melt flow, and after stopping and retracting the piston of the transducersThe double show slit a satisfactoryrheometer was matching fed with along LDPE the timeat 150 scale. °C. TheThe piezoelectrictransients of signals face-mounted show the capillary rheometer. The piezoelectric data were corrected by computing Vcor(t) using either Vdrift(t) transducersexpected drifts show before a satisfactory the inception matching of melt along ﬂow, the andtime after scale. stopping The piezoelectric and retracting signals the show piston the of expectedmeasured drifts before before actuating the inception the piston of melt or flow,Vdrift(t) and measured after stopping at the end and of retracting the ramp. the The piston steady of the state the capillary rheometer. The piezoelectric data were corrected by computing Vcor(t) using either values of Vcor(t) recorded for each piston velocity were then converted into pressure using the capillaryV (t) measuredrheometer. before The piezoelectri actuating thec data piston were or Vcorrected(t) measured by computing at the end Vcor of(t) theusing ramp. either The V steadydrift(t) calibrationdrift curves, see Figure 5. The resulting presdriftsures PS 1 and PS 2 are plotted in Figure 8 as a measuredstate values before of V actuating(t) recorded the piston for each or pistonVdrift(t) velocitymeasured were at the then end converted of the ramp. into pressureThe steady using state the function of the corpiston velocities, together with the pressures PT 1 and PT 2 measured with the valuescalibration of Vcor curves,(t) recorded see Figure for each5. The piston resulting velocity pressures were then PS 1 converted and PS 2 areinto plotted pressure in Figureusing 8the as conventional transducers. Experiments performed at 180 °C are also reported in Figure 8. Each curve calibrationa function curves, of the pistonsee Figure velocities, 5. The togetherresulting withpressures the pressures PS 1 and PTPS 12 andare plotted PT 2 measured in Figure with 8 as thea in Figure 8 is the result of the average of two ramps performed to check for data reproducibility. The functionconventional of the transducers. piston velocities, Experiments together performed with the at pressures 180 ◦C are PT also 1 reportedand PT 2 in measured Figure8. Each with curve the corresponding error bars for each data point are smaller than the symbols used to represent the data. conventionalin Figure8 is transducers. the result of Experiments the average ofperformed two ramps at performed180 °C are also to check reported for data in Figure reproducibility. 8. Each curve The The error resulting from the reproducibility is larger (ranging from 0.02% to 3.4% for piezoelectric incorresponding Figure 8 is the errorresult bars of the for average each data of pointtwo ramps are smaller performed than theto check symbols for data used reproducibility. to represent the The data. sensors and 0.02% to 1.2% for conventional transducers) than the error from the pressure reading correspondingThe error resulting error bars from for the each reproducibility data point are is sm largeraller (ranging than the fromsymbols 0.02% used to to 3.4% represent for piezoelectric the data. (ranging from 0.13% to 0.3% for piezoelectric sensors and 0.16% to 0.5% for conventional Thesensors error andresulting 0.02% from to 1.2% the forreproducibility conventional is transducers) larger (ranging than from the error0.02% fromto 3.4% the for pressure piezoelectric reading transducers). sensors(ranging and from 0.02% 0.13% to to1.2% 0.3% for for conventional piezoelectric transducers) sensors and 0.16%than the to 0.5%error for from conventional the pressure transducers). reading (ranging from 0.13% to 0.3% for piezoelectric sensors and 0.16% to 0.5% for conventional transducers).

Figure 8. Comparison between the pressures obtained with the piezoelectric sensors and conventional Figure 8. Comparison between the pressures obtained with the piezoelectric sensors and conventional transducers for each piston velocity. (a) LDPE at 150 ◦C. (b) LDPE at 180 ◦C. Initial slope and final transducers for each piston velocity. (a) LDPE at 150 °C. (b) LDPE at 180 °C. Initial slope and final slope refer to the values of s used in the fitting of Vdrift before actuating the piston or at the end of slope refer to the values of s used in the fitting of Vdrift before actuating the piston or at the end of the Figurethe ramp 8. Comparison in piston’s between velocity. the Average pressure indicatess obtained that with drift the correction piezoelectric is performed sensors and by computingconventional the transducersaverage of initialfor each and piston final slopesvelocity.s. (a) LDPE at 150 °C. (b) LDPE at 180 °C. Initial slope and final slope refer to the values of s used in the fitting of Vdrift before actuating the piston or at the end of the Data in Figure8 indicate a moderate mismatch between the pressures returned by the two types of transducers, albeit their contour being virtually identical. Piezoelectric sensors measured somewhat Fluids 2019, 4, x FOR PEER REVIEW 9 of 12

ramp in piston’s velocity. Average indicates that drift correction is performed by computing the average of initial and final slopes s. Fluids 2019, 4, 66 9 of 12 Table 2. Differences (in %) between the pressures measured with piezoelectric (PS) and conventional transducers (PT), and between the corresponding computed viscosities. larger values than the conventional sensors upstream, whereas the opposite occurs downstream. Temperature Sensors Initial slope Final slope Average slope Generally, the method of drift correction (s fitted at the beginning or at the end of the ramp, or s Pressure Viscosity Pressure Viscosity Pressure Viscosity computed from the average of these two values) does not impact significantly on the results, as the PT 1 vs. PS 1 2.4–3.0% 1.9–3.1% 2.2–3.0% 150 °C 6.7–9.3% 9.1–11% 8.0–10% mismatch betweenPT conventional 2 vs. PS 2 and 0.4–1.0% piezoelectric measurements 1.6–3.6% remains in the 0.8–2.0% range of 0.4% to 4% (see Table2). This conclusionPT 1 vs. PS 1 is consistent 2.5–4.0% with the results0.0–0.8% displayed in Figures1.3–2.3%4 and6 where the 180 °C 6.7–12% 5.0–7.1% 5.6–9.2% drift is shown to bePT independent 2 vs. PS 2 of 1.0–1.5% both pressure and temperature. 2.3–3.9% Overall, the 1.7–2.7% numbers reported in Table2 compare well with the 2% scatter reported in the pressure measurements of a conventional transducerData in used Figure for the8 indicate capillary a moderate rheometry mismatch of a low-density between polyethylenethe pressures atreturned 150 ◦C[ by20 ].the two types of transducers, albeit their contour being virtually identical. Piezoelectric sensors measured somewhatTable 2. largerDifferences values (in %)than between the conventional the pressures measuredsensors withupstream, piezoelectric whereas (PS) andthe conventionalopposite occurs downstream.transducers Generally, (PT), and betweenthe method the corresponding of drift correction computed (s fitted viscosities. at the beginning or at the end of the ramp,Temperature or s computed Sensors from the average Initial Slopeof these two values) Final does Slope not impact Averagesignificantly Slope on the results, as the mismatch betweenPressure conventional Viscosity and piezoelectric Pressure measurements Viscosity Pressure remains Viscosity in the range of 0.4% to 4% (seePT Table 1 vs. PS2). 1 This2.4–3.0% conclusion is consistent1.9–3.1% with the results displayed2.2–3.0% in Figures 4 and 150 ◦C 6.7–9.3% 9.1–11% 8.0–10% 6 where the drift isPT shown 2 vs. PS to 2 be 0.4–1.0%independent of both pressure 1.6–3.6% and temperature. 0.8–2.0% Overall, the numbers PT 1 vs. PS 1 2.5–4.0% 0.0–0.8% 1.3–2.3% reported180 in◦C Table 2 compare well with the6.7–12% 2% scatter reported in5.0–7.1% the pressure measurements5.6–9.2% of a PT 2 vs. PS 2 1.0–1.5% 2.3–3.9% 1.7–2.7% conventional transducer used for the capillary rheometry of a low-density polyethylene at 150 °C [20]. The data with the average slope method for drift correction displayed in Figure 8 were inserted in EquationsThe data with(3)–(5) the to average compute slope the method flow curves for drift shown correction in Figure displayed 9. The in Figureimpact8 wereof the inserted mismatch in Equationsbetween the (3)–(5) pressure to compute readings the of flow both curves type of shown transducers in Figure on9. the The resulting impact of flow the mismatchcurves is evident between in theFigure pressure 9. The readings pressure of mismatch both type produces of transducers a vertic onal the shift resulting between flow the curves flow curves, is evident the indifferences Figure9. Thebetween pressure the mismatchmeasured producesviscosities a verticalbeing larger shift betweenat smaller the shear flow rates curves, than the at differences larger shear between rates. theNonetheless, measured the viscosities discrepancy being between larger at the smaller measured shear viscosities rates than remains at larger in the shear range rates. 5.6% Nonetheless, to 10% (see thealso discrepancy Table 2), which between can be the assumed measured as viscositiesacceptable remainsif one considers in the range the 10% 5.6% experimental to 10% (see alsoerror Table usually2), whichreported can for be assumedrotational as rheometry acceptable [21] if one and considers recently theconfirmed 10% experimental with Newtonian error usually viscosity reported standards for rotational[22] and with rheometry a low density [21] and polyethylene recently confirmed studied with at 150 Newtonian °C [14]. viscosity standards [22] and with a low density polyethylene studied at 150 ◦C[14].

Figure 9. Flow curves measured with LDPE at 150 ◦C (solid symbols) and 180 ◦C (open symbols) using theFigure piezoelectric 9. Flow curves (triangles) measured and the with conventional LDPE at 150 (squares) °C (solid pressuresymbols) transducers. and 180 °C (open symbols) using the piezoelectric (triangles) and the conventional (squares) pressure transducers. The operability window of the piezoelectric transducers is now examined by testing materials showingThe different operability levels window of viscoelasticity of the piezoelectric and comparing transducers the resulting is now flow examined curves with by testing those measured materials usingshowing conventional different transducers.levels of viscoelasticity All drift corrections and comparing were performed the resulting using theflow average curves between with those the slopesmeasured recorded using before conventional and after transducers. the ramp in piston All drift velocities. corrections A PBAT were grade performed designed using for film the blowingaverage application was selected for exploring the upper viscoelastic part of the operability window, as this biodegradable material shows significant melt strength. The flow curves were measured at 190 ◦C and are presented in Figure 10. Overall, both sets of data, acquired either with conventional or piezoelectric Fluids 2019, 4, x FOR PEER REVIEW 10 of 12 between the slopes recorded before and after the ramp in piston velocities. A PBAT grade designed for film blowing application was selected for exploring the upper viscoelastic part of the operability window, as this biodegradable material shows significant melt strength. The flow curves were measured at 190 °C and are presented in Figure 10. Overall, both sets of data, acquired either with Fluids 2019, 4, 66 10 of 12 conventional or piezoelectric transducers with an equally high level of precision (error bars are smaller than the symbols size), nicely overlap. This result validates the use of piezoelectric transducerstransducers for with slit anrheometry, equally highat least level for of materi precisionals showing (error barsshear are viscosities smaller thanin the the range symbols 500–1000 size), Pa·snicely at shear overlap. rates This between result 20 validates s−1 andthe 200 use s−1. ofA piezoelectricbio-based and transducers compostable for PHB slit rheometry, was selected at leastfor screeningfor materials low showingviscosity shear materials. viscosities PHB inis the well range known 500–1000 for its Pa ·slimited at shear thermal rates betweenstability 20and s− 1 processability.and 200 s−1. AAs bio-based such, this and is compostablea challenging PHB material was selectedfor capillary for screening rheometry, low and viscosity flow curves materials. of polyhydroxyalkanoatesPHB is well known for itsare limitedscarcely thermal found stabilityin the literature and processability. [23–25]. Indeed, As such, true this wall is a shear challenging rates couldmaterial not forbe computed capillary rheometry, from the data and since flow steady curves st ofate polyhydroxyalkanoates flow was not achieved are for scarcely any piston found velocity in the (seeliterature the inset [23 –in25 Figure]. Indeed, 10). true Thus, wall the shear apparent rates couldviscosity, not beηa, computedis reported from in Figure the data 10 sinceas a function steady state of theflow apparent was not shear achieved rate,for , anyfor the piston two velocity flow curves (seethe measured inset in at Figure 190 °C.10). In Thus, spite the of these apparent difficulties, viscosity, . aη monotonica, is reported shear in Figure thinning 10 as flow a function curve of with the apparentsatisfactory shear error rate, barsγa, foris reported the two flow for curvesthe experiment measured carriedat 190 ◦outC. Inwith spite the of piezo these transduc difficulties,ers up a monotonic to a shear shearrate of thinning 150 s−1. flowIn contrast, curve with larger satisfactory error barserror are obtainedbars is reported with the for conventional the experiment transducers carried out withand thethe piezoflow transducerscurve displays up to an a shear unrealistic rate of 150shear s−1 . thickeningIn contrast, at largerlarger errorshear bars rates. are Thus, obtained this result with theconfirms conventional the good transducers performance and of the piezoelectric flow curve transducersdisplays an for unrealistic detecting shearsmall thickeningpressure variations at larger [3–6]. shear The rates. slope Thus, of the this PHB result flow confirms curve measured the good withperformance the piezoelectric of piezoelectric sensors transducers is larger than for detecting−1, which small suggests pressure the occurrence variations [3of– 6possible]. The slope flow of instabilities.the PHB flow However, curve measured the piezoelectric with the transient piezoelectric in thesensors inset to isFigure larger 10 than does− not1, which show suggestsoscillations the withoccurrence frequency of possible and amplitude flow instabilities. signaling However,the presence the piezoelectricflow instabilities transient as reported in the inset elsewhere to Figure [7]. 10 Therefore,does not showthe steep oscillations slope in with the PHB frequency flow curve and amplitude seems related signaling to the the fact presence that uncorrected flow instabilities apparent as viscositiesreported elsewhereand shear [rates7]. Therefore, are reported the steepin the slopegraph. in In the addition, PHB flow the curve effect seems of thermal related degradation to the fact thaton theuncorrected shear viscosity apparent further viscosities contribute ands to shear an apparent rates are shear reported thinning. in the graph. In addition, the effect of thermal degradation on the shear viscosity further contributes to an apparent shear thinning.

Figure 10. Flow curves measured with polybutylene adipate terephthalate (PBAT) at 180 ◦C (squares) ◦ Figureand polyhydroxybutyrate 10. Flow curves measured (PHB) with at 190polybutyleneC (triangles). adipate Comparison terephthalate between (PBAT) piezoelectric at 180 °C (squares) sensors and(symbols polyhydroxybutyrate and lines in grey) (PHB) and conventionalat 190 °C (triangl pressurees). transducersComparison (symbols between and piezoelectric lines in black). sensors The (symbolsinset represents and lines the in grey) time evolutionand conventional of outputs pressu (voltages)re transducers measured (symbols with PHBand lines by sensors in black). located The insetupstream represents during the the time stepwise evolution ramp of in theoutputs piston (voltages) velocity ofmeasured the capillary with rheometer. PHB by sensors located upstream during the stepwise ramp in the piston velocity of the capillary rheometer. 4. Conclusions

The use of piezoelectric transducers for steady melt pressure measurement has been assessed by directly comparing the flow curves measured with such transducers and with diaphragm transducers conventionally used in capillary rheometry and in polymer extrusion. A modular slit die was designed and constructed to allow for the direct comparison between the pressure data acquired by both types of transducers. Piezoelectric transducers were first calibrated and the drift inherent to the sensors electronics was analyzed as a function of both temperature and pressure. Various methodologies for Fluids 2019, 4, 66 11 of 12 the drift correction were proposed and the results confirmed that the drift does not depend on the temperature nor on the pressure. The pressure data acquired with piezoelectric transducers differ from the data returned by conventional transducers. The difference ranges from 0% to 4% for all shear rates and temperatures tested with a LDPE. Differences in pressure readings result in a maximum 10% difference in the shear viscosities measured with LDPE for all experimental conditions tested. This difference is acceptable given the 10% error usually reported for viscosities measured either with rotational rheometers or capillary rheometers. Accordingly, the results reported here validate the use of piezoelectric transducers for slit rheometry. A better agreement between the shear viscosities measured with the two types of transducers was achieved with a more elastic PBAT. In contrast to this, piezoelectric transducers outperformed conventional transducers for measuring the steady shear viscosity of a biodegradable PHB with values of the order of 20 Pa·s at shear rates of 100 s−1.

Author Contributions: The conceptualization of the whole study was performed by P.F.T., J.A.C., and L.H. Experiments were performed by P.F.T. and S.C. P.F.T., J.A.C. and L.H. analyzed the data. P.F.T. drafted the paper and P.F.T., J.A.C., and L.H. wrote, reviewed and edited the paper. Funding: This research was funded by National Funds through FCT—Portuguese Foundation for Science and Technology, Reference UID/CTM/50025/2013 and FEDER funds through the COMPETE 2020 Programme under the project number POCI-01-0145-FEDER 007688. L.H. acknowledges funding from the FCT Investigator Programme through grant IF/00606/2014. Acknowledgments: The authors are grateful to Miguel Gomes and Jasper Cooremans from the Polymer Engineering Department of University of Minho for support in the set-up of experiments. Conﬂicts of Interest: The authors declare no conﬂict of interest.

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