A Novel Vibrating-Wire Viscometer for High-Viscosity Liquids at

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A Novel Vibrating-Wire Viscometer for High-Viscosity Liquids at Moderate Pressures Marc J. Assael* and Sofia K. Mylona Laboratory of Thermophysical Properties & Environmental Processes, Chemical Engineering Department, Aristotle University, Thessaloniki 54124, Greece ABSTRACT: The design and operation of a new vibrating-wire viscometer for the measurement of high-viscosity liquids (50 to 125) mPa·s, and up to 18 MPa are described. The design of the instrument is based on a complete theory so that it is possible to make absolute measurements. The viscosity of liquid diisodecyl phthalate (DIDP) is measured at temperatures between (293 and 363) K and pressures between (0.1 and 18) MPa with an absolute uncertainty of ± 1.5 %.

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(c) Paredes et al.11 in 2009 employed a rotational automated viscometer Anton Paar Stabinger SVM3000, and a rolling-ball viscometer Rusk 1602-830 for high pressures to measure the viscosity of DIDP from (303.15 to 373.15) K up to 60 MPa. The measurements were performed in a relative way with an uncertainty of less than ± 4 % (at 95 % confidence level). (d) The measurements of Harris and Bair6 in 2007, were performed using three different falling body viscometers at temperatures from (273.15 to 373.15) K and pressures up to 1 GPa, in a relative way with an expanded uncertainty of ± 2 %. The work described in this paper aims to produce a third absolute viscosity set under pressure, performed in a novel vibrating-wire instrument operated in the free decay mode. It will also fill a gap in the moderate pressure range available viscosity values.

INTRODUCTION

All viscometers employed in accredited viscosity measurements must be calibrated through a chain of reference fluids to an international primary standard.1 Alternatively, the International Association for Transport Properties, IATP (former Subcommittee of Transport Properties of the International Union of Pure and Applied Chemistry, IUPAC) has been considering the possibility of recommending other, well-specified in purity and easily accessible fluids, as viscosity standards.2 The viscosity of water at 293.15 K and 0.101325 MPa of (1.0016 ± 0.0017) mPa·s is still the only internationally accepted value.3 To measure the viscosity of more viscous fluids found in industrial applications, IATP instigated a project on the “Investigation of a new high-viscosity standard”. Indeed, based upon a critical review of measurements4−8 performed at atmospheric pressure for this purpose, diisodecyl phthalate (DIDP, C6H4(COOC10H21)2) was recently proposed9 as an industrial standard reference liquid for the calibration of viscometers operating in the viscosity range (50 to 125) mPa·s at the temperatures of (293.15, 298.15, and 303.15) K, with an uncertainty of ± 1 % (at 95 % confidence level). In the case of DIDP viscosity measurements performed under pressure there are only four sets of data available: (a) The measurements of Peleties and Trusler8 were performed in 2011 in a new absolute vibrating wire viscometer operated under steady-state forced mode, with an uncertainty of ± 2 % (at 95 % confidence level). The measurements were performed at (298.15 to 373.15) K, and up to 140 MPa. (b) Al Motari et al.10 employed also in 2007 a vibrating wire viscometer and performed measurements at (298.15 to 423.15) K, and pressures up to 70 MPa, with an uncertainty of ± 2.5 % (at 95 % confidence level). © XXXX American Chemical Society

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WORKING EQUATIONS

A complete review of the theory of the vibrating-wire viscometer, operated in the free-decay mode, has been given by Retsina et al.12,13 and Papadaki.14 It was shown that under appropriate conditions, the viscosity, η (mPa·s), of a fluid of density, ρ (kg·m−3), is calculated from the logarithmic decrement, Δ (−), its value, Δο (−) in vacuum, and the frequency, ω (rad/s), of the oscillation of a wire of radius, R (m), and density, ρs (kg·m−3), immersed in the fluid. Furthermore, the displacement of the wire from its equilibrium position as a function of time, in one mode, is given by the equation Received: December 11, 2012 Accepted: March 7, 2013

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dx.doi.org/10.1021/je301306e | J. Chem. Eng. Data XXXX, XXX, XXX−XXX

Journal of Chemical & Engineering Data y = εRe(i −Δ)ωt

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(1)

The final working equations are Δ=

(ρ /ρs )k′ + 2Δ0 2[1 + (ρ /ρs )k]

(2)

where k = −1 + 2 Im[A]

and

k′ = 2Re[A] + 2Δ Im[A] (3)

and ⎧ 2K1(s) ⎫ ⎬, A = (i − Δ)⎨1 + s K 0(s) ⎭ ⎩ s=

(i − Δ)Ω ,

and

Figure 1. Working region for measuring the viscosity of DIDP.

with ρωR2 Ω= η

smaller resistance and hence a larger current on the bridge.14 For this reason the bridge resistances had to be changed accordingly.

(4)

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In the above equations, ε (−), denotes the ratio of amplitude of oscillation over the wire radius, while Ko and K1 are modified Bessel functions of zero and first order. The new instrument is designed to measure the viscosity of fluids in the range of (2 to 100) mPa·s, and densities of (600 to 1000) kg·m−3. The temperature of operation is (250 to 400) K and the pressure is (0.1 to 30) MPa. To derive eqs 2 to 4, the following design criteria must be obeyed:12−14 1. infinite length of wire, negligible acial effects: R≪L

EXPERIMENTAL SECTION The aforementioned criteria define uniquely the design parameters of the viscometer to be employed for the measurement of the viscosity of DIDP. The vibrating wire, 1 (see Figure 2), is made of 300 μm diameter tungsten wire

(5)

2. infinite fluid, no enclosure:

R c/R > 30

(6)

3. Mach number, compressibility of the fluid:

ωεR /c ≪ 1 4. small displacement of the wire: εR ≪ 1 ⇒ ε ≪ 1

(7)

(8)

5. Reynolds number, laminar flow:

εΩ ≪ 1

(9)

In the above equations, Rc is the radius of the fluid’s enclosure, and c is the speed of sound in the liquid. It can further be shown12−14 that, combining the last two criteria, one obtains ⎛η⎞ 1 ω ≫ 10−2⎜ ⎟ 2 ⎝ ρ⎠R ⎛η⎞ 1 ω ≪ 104⎜ ⎟ 2 ⎝ ρ⎠ R

(10) Figure 2. The vibrating-wire viscometer. (11)

(Goodfellow Cambridge Ltd. UK), with a length of 50 mm and a frequency in vacuum of about 1 kHz. The wire is squeezed tight between two SS 316L plates, 2 and 3, at either end. The plates are isolated from their support by the use of ceramic washers, 4 and 5 (Dynamic Ceramic, UK). In our previous vibrating-wire instrument,15 constant tensioning of the wire was ensured by hanging at its bottom a large weight. This made the instrument very sensitive and large in volume. In our new vibrating-wire instrument, constant tensioning of the wire is achieved by keeping the two supports separated by two 3 mmdiameter tungsten rods, 6 and 7 (Goodfellow Cambridge Ltd. UK). Thus the length of the wire is unaffected by temperature changes as the rods expand in the same way as the wire. While

Finally, an additional criterion arises from the requirement to determine the logarithmic decrement and hence the viscosity, with an uncertainty of ± 0.1 % or better.

0.01 ≤ Δ ≤ 0.08

(12)

The aforementioned criteria, eqs 10 to 12, and eq 7, in connection with the working equations, define the working region of the new viscometer. (see Figure 1). Hence, for a tungsten wire oscillating typically with an angular frequency ω = 6000 rad/s the required radius for the measurement of the viscosity of DIDP is 150 μm. It should also be mentioned that employing a large diameter wire results in a B


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of ± 0.5 %, while the precision and reproducibility were better than ± 0.1 %. To ensure the continuing good operation of the new viscometer, a 100 μm-diameter tungsten wire was employed and the viscosity of toluene (99.9 % Panreac, CAS number 108-88-3, see also Table 1), was measured at

the wire hangs from its top support, it is tensioned by placing a large weight at its bottom, after the bottom plate. The wire is left for a day at this position, and then the bottom support is tightened, the weight removed, and the wire is kept under tension between the two supports. This arrangement made the whole viscometer smaller and easier to use. The oscillations of the wire are induced electromagnetically and detected in a similar fashion. The magnets, 8, used for both of these purposes are mounted in a support, 9, surrounding the wire and made out of magnetized SS 1.2083. The magnets, gold-plated to avoid oxidation, are made from samarium− cobalt, and produce a field of about 1 T at the wire. The viscometer, hanging from the upper closure 10, as shown in Figure 2, is lowered inside the pressure vessel made from SS 304L. Sealing is accomplished by a graphite-carbonfilled PTFE filled with SS 316 springs. The two electrical connections come out of the upper closure, while the pressure vessel is connected at its bottom with the pressure system. Pressure is increased by a AO612W-A-STD (Stansted Fluid Power, UK) air driven pump, and it was recorded with a calibrated PTX-520-0 (Druck Ltd., UK) with an uncertainty of better than ± 0.1 % over its whole range. The temperature of the pressure vessel is recorded by two platinum resistance thermometers W85K3 (Degussa, Germany), calibrated against a Class I platinum resistance thermometers (Tinsley, UK) according to ITS 90, placed one at its top and the other at its bottom. The measurement of the temperature is better than ± 20 mK. The pressure vessel is finally placed in a 20-L bath (60 % v/v ethylene glycol), controlled by a F81-MV (Julabo, Germany) circulator, capable of maintaining the temperature stable and uniform with an uncertainty of ± 10 mK. The oscillations of the wire are initiated by applying two pulses of current opposite sign to the wire. The initial motion then contains a number of harmonics of the fundamental frequency which decay rapidly compared with the decay of the fundamental. It has been found that this symmetric method of initiation is essential to ensure that the zero point of the oscillation is coincident with the rest position of the wire. Following initiation of the motion, the signal induced in the vibrating wire is observed with a bridge in which the wire forms one arm. The out-of-balance signal, amplified by 30 000 times, is then observed with an A/D converter coupled to a microcomputer through Direct Memory Access. This configuration enables sampling of the oscillating signal at a rate of 50 kHz with a resolution of 12 bits. Since the frequency of the oscillation is about 1 kHz, one obtains roughly 50 points per cycle of the wire’s motion. This information is stored for subsequent analysis. Prior to the measurement of the viscosity of fluids, the logarithmic decrement, Δ0, in vacuum was measured, The viscometer was subjected to successive vacuum down to 10−7 MPa (10−3 mbar) and the logarithmic decrement was measured. The extrapolated logarithmic decrement to zero pressure, was found to be equal to 0.00014. It should be noted that the logarithmic decrement in vacuum for the 100 μm diameter wire was equivalently found to be 0.00005. These values were found to be very reproducible and independent of temperature for our temperature range.

Table 1. Samples Information Table chemical name toluene 1-methylnaphthalene (1-MNP) diisodecyl phthalate (DIDP)

source

initial mole fraction purity

purification method

Panreac Merck

0.999 0.94

none none

Merck

0.99

none

Table 2. Measurements of the Viscosity of Toluenea p/MPa

T/K

ρ/kg·m−3

η/mPa·s

0.101 0.101 0.101 0.101 0.101 2.23 4.43 6.42 8.31 10.06 11.85 14.20 15.73 17.83 1.24 2.11 3.96 5.66 7.84 9.86 12.32 14.08 15.90 17.78

293.313 303.043 312.901 322.786 332.408 332.422 332.356 332.317 332.303 332.317 332.342 332.578 332.369 332.669 303.018 302.825 302.734 302.759 302.773 302.683 302.915 302.915 302.940 302.967

867.09 858.06 848.85 839.55 830.41 832.42 834.53 836.38 838.09 839.62 841.15 842.94 844.41 845.88 859.78 859.86 861.40 862.69 864.34 865.93 867.54 868.82 870.11 871.42

0.5897 0.5223 0.4683 0.4215 0.3836 0.3917 0.3988 0.4061 0.4137 0.4189 0.4248 0.4300 0.4358 0.4411 0.5315 0.5351 0.5470 0.5547 0.5627 0.5697 0.5812 0.5871 0.5900 0.6050

a Standard uncertainties u are u(p) = 0.1 %, u(T) = 0.02 K, and u(ρ) = 0.05 %,16 and the combined uncertainty Uc is Uc(η) = 0.5 %.

atmospheric and higher pressures, see Table 2. The density of toluene required for the analysis of the measurements and shown in Table 2, was obtained from the correlation proposed by Assael et al.16 with in uncertainty of ± 0.05 %. In Figure 3, the deviations of our measurements from two reference correlations are shown: (a) In the case of the atmospheric pressure measurements, Santos et al.17 in 2006, proposed a reference correlation with an uncertainty of 0.5 % (at the 95 % confidence level). Our measurements deviate from this correlation by less than this value. (b) In the case of higher pressures, and up to 250 MPa, Assael et al.16 in 2001, proposed a reference correlation with an uncertainty of 2.7 % (at the 95 % confidence level). In this case also the present measurements agree with this correlation to better than 1 %. The aforementioned discussion confirms that the present vibrating-wire viscometer with the 100 μm diameter tungsten

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CONFIRMATION OF OPERATION In a previous publication15 the full analysis of errors was presented. It was thus shown that the vibrating wire, operated according to the full theory, was characterized by an uncertainty C



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Figure 3. Percentage deviations of the measurements of the viscosity of toluene from reference values: ●, Santos et al.;17 ○, Assael et al. at T = 333.15 K;16 Δ, Assael et al. at T = 303.15 K.16

wire, continues to operate with an uncertainty of better than ± 0.5 %. To ensure that the viscometer continues its excellent operation when the 100 μm diameter wire will be substituted by the 300 μm diameter tungsten wire, 1-methylnaphthalene (1-MNP) was next investigated. Performing a similar analysis to that described previously, see Figure 1, it can be shown that as 1-MNP has a typical viscosity of 1−4 mPa·s, its viscosity can be measured with both wires. The purity of 1-MNP employed was 94 % (Merck, CAS number 90-12-0), while GC−MS analysis showed that the remainder was mostly 2-MNP. The low purity of the sample was not a problem, as the same sample was measured with both wires. The diameter of the tungsten wire employed was measured directly and repeatedly by scanning electron microscopy (SEM), and found to be equal to 302.7 μm. The measurements of the viscosity of 1-MNP are shown in Table 3. The density values employed for the analysis of the measurements, and shown in Table 3, were obtained from the measurements of Caudwell et al.,18 performed with an uncertainty of ± 0.2 % (at the 95 % confidence level). The viscosity values obtained employing the 100 μm diameter tungsten wire were fitted for comparison purposes to the equation ⎛ ⎞ 628.2 ⎟ η /(mPa· s) = 0.06552 exp⎜ ⎝ T /K − 132.8 ⎠

Table 3. Measurements of the Viscosity of 1-MNP as a Function of Temperature at Atmospheric Pressurea T/K 288.349 302.915 312.786 322.733 332.603 342.264 351.737 298.092 302.965 312.889 322.747 332.498 342.353

ρ/kg·m−3 100 μm Diameter Tungsten Wire 1027.1 1016.0 1008.5 1000.9 993.41 985.99 978.67 300 μm Diameter Tungsten Wire 1019.7 1016.0 1008.5 1000.9 993.49 985.92

η/mPa·s 3.720 2.620 2.168 1.786 1.523 1.300 1.148 2.910 2.629 2.160 1.800 1.523 1.314

a

Standard uncertainties u are u(p) = 0.1 %, u(T) = 0.02 K, and u(ρ) = 0.02 %,18 and the combined expanded uncertainty Uc is Uc(η) = 1 % (level of confidence = 0.95).

Et-Tahir et al.,19 performed in a relative way with an uncertainty of ± 2 % (at the 95 % confidence level), are also shown. These measurements also agree with the present data within ± 2 %. The aforementioned discussion, indicates that the new vibrating-wire viscometer with the 300 μm diameter wire, operates with an uncertainty of ± 1 % (at the 95 % confidence level).

(13)

Percentage deviations of our viscosity measurements from the above equation, for both wires employed, are shown in Figure 4. The standard deviation of our measurements from the above equation is ± 1 % (at the 95 % confidence level). In the same figure, measurements of two other investigators are also shown. Caudwell et al.18 measured in 2009 the viscosity of 1-MNP over an extended temperature and pressure range with an uncertainty of ± 2 % (at the 95 % confidence level). Their measurements at atmospheric pressure, agree with the present ones within 2.1 %. Also in Figure 4 the older measurements of

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RESULTS In Table 4, the measurements of the viscosity of liquid diisodecyl phthalate (DIDP), are shown. The DIDP was obtained from Merck (CAS number 26761-40-0) with a purity of 99 %. The sample was directly inserted in the viscometer D



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Figure 4. Percentage deviations of the measurements of the viscosity of 1-MNP as a function of temperature, from the values obtained by eq 13: ●, this work using the 100 μm diameter wire; ○, this work using the 300 μm diameter wire; Δ, Caudwell et al.;18 □, Et-Tahir et al.19

under vacuum. The measurements were fitted for comparison purposes to the equation

Table 4. Measurements of the Viscosity of DIDP as a Function of Temperature at Atmospheric Pressurea T/K

ρ/kg·m−3

η/mPa·s

293.363 298.261 303.121 308.103 313.033 317.925 322.770 327.586 333.239 338.172 342.992 347.961 353.097 358.132 363.188

966.33 962.84 959.38 955.84 952.34 948.86 945.42 942.00 937.99 934.49 931.07 927.55 923.91 920.34 966.33

123.0 88.70 64.37 49.15 37.38 29.60 23.66 19.32 15.72 13.17 11.16 9.553 8.234 7.178 6.272

⎛ ⎞ 728.5 ⎟ η /(mPa· s) = 0.08691 exp⎜ ⎝ T /K − 193.0 ⎠

(14)

Percentage deviations of our viscosity measurements from the above equation, are shown in Figure 5. The standard deviation of our measurements from the above equation is ± 1.5 % (at the 95 % confidence level), which is slightly higher than the instrument’s uncertainty of ± 1 %. This is attributed to the higher viscosity values, inevitably connected to a smaller sampling number of oscillations. In Figure 5 the following can also be noted: (i) Caetano et al.9 proposed in 2008, a reference correlation for the viscosity of DIDP at temperatures between (288.15 and 308.15) K and atmospheric pressure with an uncertainty of ± 1 % (at the 95 % confidence level). Our measurements agree with this correlation within ± 1 %. (ii) Paredes et al. (sample A),11 Harris and Bair (sample A),6 and Al Motari et al. (sample C)10 measured samples of DIDP of exactly the same purity as the one used at this work. All these values agree with the present

a

Standard uncertainties u are u(T) = 0.02 K, and u(ρ) = 0.02 %,11 and the combined expanded uncertainty Uc is Uc(η) = 1.5 % (level of confidence = 0.95).

Figure 5. Percentage deviations of the measurements of the viscosity of DIDP as a function of temperature, from the values obtained by eq 14: ●, this work; ―, Caetano et al.;9 ○, Peleties and Trusler;8 Δ, Paredes et al. (sample A);11 ◊, Paredes et al. (sample B);11 ■, Paredes et al. (sample C);11 ⌽, Fröba and Leipertz;7 △ with a vertical bar, Harris and Bair (sample A);6 □, Harris and Bair (sample B);6 ⧫, Harris and Bair (sample C);6 ⊖, Harris;20 ⊞, Al Motari et al. (sample A);10 ◑, Al Motari et al. (sample B);10 ▲, Al Motari et al. (sample C);10 ◓, Caetano et al.;21 ◐, Caetano et al.;5 ⬓, Correia da Mata et al.22 E



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values calculated with eq 14, within ± 2 %. (iii) The remaining data, consisting of samples of slightly higher purity, also agree with the present values within ± 2 %. The aforementioned discussion indicates that the viscometer employed for high viscosity liquids should be expected to operate with an uncertainty of less than ± 1.5 %. In Table 5, the measurements of the viscosity of DIDP at pressures up to 18 MPa are shown. The density values shown in the same table and employed in the calculation of the viscosity have been obtained from the measurements of Paredes et al.11 (sample Asame purity as present sample), with an uncertainty of better than 0.02 %. In the same table, viscosity values converted to nominal temperatures of (303.15 and 343.15) K, are also shown. These values were fitted to the following equations for comparison purpose, as at 303.15 K

Table 5. Measurements of the Viscosity of DIDP as a Function of Pressurea p/MPa

T/K

2.46 2.46 2.45 4.51 4.51 6.44 6.44 8.39 10.25 10.25 11.19 13.30 15.37 17.31

302.747 302.747 302.747 302.747 302.747 302.747 302.747 302.747 302.747 302.747 302.747 302.747 302.747 302.747

2.43 2.43 2.42 4.26 6.13 7.97 7.97 9.70 9.70 10.95 10.97 13.18 13.18 15.22 15.22 17.13

342.692 342.692 342.692 342.692 342.692 342.667 342.667 342.667 342.667 342.900 342.900 342.900 342.900 342.900 342.900 342.939

ρ/(kg·m−3)

η(T,p)/mPa·s

Tnom = 303.15 K 961.36 70.440 961.36 70.625 961.35 70.144 962.55 74.037 962.55 73.969 963.66 77.313 963.66 77.616 964.77 81.072 965.82 85.025 965.82 85.350 966.34 87.222 967.50 92.249 968.63 96.322 969.67 101.25 Tnom = 343.15 K 933.52 11.787 933.52 11.821 933.51 11.868 934.80 12.140 936.10 12.535 937.38 13.056 937.38 12.965 938.55 13.350 938.55 13.439 939.22 13.736 939.24 13.733 940.69 14.254 940.69 14.266 942.02 14.726 942.02 14.711 943.21 15.139

η(Tnom,p)/mPa·s 68.34 68.52 68.04 71.81 71.74 74.97 75.27 78.60 82.42 82.74 84.55 89.42 93.33 98.10

η /(mPa· s) = exp(4.16307 + 0.02444(T /K))

11.60 11.63 11.68 11.94 12.33 12.84 12.75 13.13 13.22 13.51 13.51 14.02 14.03 14.48 14.47 14.88

(15)

at 343.15 K η /(mPa· s) = exp(2.4116 + 0.01720(T /K))

(16)

The standard deviation of our measurements from the above equations is ± 0.5 % and ± 0.7 % (at the 95 % confidence level), respectively. As already stated in the introduction of this work, four more investigators have reported measurements of the viscosity of DIDP at high pressures. In Figures 6 and 7, the deviations of these investigators from the values calculated by eqs 6 and 7 are shown. The measurements of Peleties and Trusler,8 and Al Motari et al.,10 were both performed in an absolute manner with uncertainties of ± 2 % and ± 2.5 % (at 95 % confidence level), respectively. Both these sets show deviations that are well within the mutual uncertainties of the instruments. Harris and Bair,6 and Paredes et al.11 performed also viscosity measurements in a relative way, with uncertainties of ± 2 % and ± 4 % (at 95 % confidence level), respectively. Both these sets also show deviations that are well within the mutual uncertainties of the instruments.

a Standard uncertainties u are u(p) = 0.1 %, u(T) = 0.02 K, and u(ρ) = 0.2 %,11 and the combined expanded uncertainty Uc is Uc(η) = 1.5 % (level of confidence = 0.95).

Figure 6. Percentage deviations of the measurements of the viscosity of DIDP as a function of pressure at 303.15 K, from the values obtained by eq 15: ○, this work; ―, Peleties and Trusler;8 - - -, Al Motari et al.;10 ···, Harris and Bair;6 -·-·, Paredes et al.11 F



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Figure 7. Percentage deviations of the measurements of the viscosity of DIDP as a function of pressure at 343.15 K, from the values obtained by eq 16: ○, this work; ―, Peleties and Trusler;8 - - -, Al Motari et al.;10 ···, Harris and Bair;6 -·-·, Paredes et al.11

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(6) Harris, K. R.; Bair, S. Temperature and pressure dependence of the viscosity of diisodecyl phthalate at temperatures between (0 and 100) °C and at pressures to 1 GPa. J. Chem. Eng. Data 2007, 52, 272− 278. (7) Fröba, A. P.; Leipertz, A. Viscosity of diisodecyl phthalate by surface light scattering (SLS). J. Chem. Eng. Data 2007, 52, 1803− 1810. (8) Peleties, F.; Trusler, J. P. M. Viscosity of liquid diisodecyl phthalate at temperatures between (274 and 373) K and at pressures up to 140 MPa. J. Chem. Eng. Data 2011, 56, 2236−2241. (9) Caetano, F. J. P.; Fareleira, J. M. N. A.; Froba, A. P.; Harris, K. R.; Leipertz, A.; Oliveira, C. M. B. P.; Trusler, J. P. M.; Wakeham, W. A. An industrial reference fluid for moderately high viscosity. J. Chem. Eng. Data 2008, 53, 2003−2011. (10) Al Motari, M. M.; Kandil, M. E.; Marsh, K. N.; Goodwin, A. R. H. Density and viscosity of diisodecyl phthalate C6H4(COOC10H21)2, with nominal viscosity at T = 298 K and p = 0.1 MPa of 87 mPa·s, at temperatures from (298.15 to 423.15) K and pressures up to 70 MPa. J. Chem. Eng. Data 2007, 52 (4), 1233−1239. (11) Paredes, X.; Fandino, O.; Comunas, M. J. P.; Pensado, A. S.; Fernandez, J. Study of the effects of pressure on the viscosity and density of diisodecyl phthalate. J. Chem. Thermodynamics 2009, 41, 1007−1015. (12) Retsina, T.; Richardson, S. M.; Wakeham, W. A. The theory of a vibrating-rod viscometer. Appl. Sci. Res. 1987, 43, 325−346. (13) Retsina, T.; Richardson, S. M.; Wakeham, W. A. The theory of a vibrating-rod densimeter. Appl. Sci. Res. 1986, 43, 127−158. (14) Papadaki, M. An Absolute Technique for the Measurement of the Viscosity of Liquids: Aristotle University: Thessaloniki, Greece, 1991. (15) Assael, M. J.; Papadaki, M.; Dix, M.; Richardson, S. M.; Wakeham, W. A. An absolute vibrating-wire viscometer for liquids at high pressures. Int. J. Thermophys. 1991, 12, 231−244. (16) Assael, M. J.; Avelino, H. M. T.; Dalaouti, N. K.; Fareleira, J. M. N. A. H.; Harris, K. R. Reference correlation for the viscosity of liquid toluene from 213 to 373 K at pressures to 250 MPa. Int. J. Thermophys. 2001, 22, 789−799. (17) Santos, F. J. V.; Nieto de Castro, C. A.; Dymond, J. H.; Dalaouti, N. K.; Assael, M. J.; Nagashima, A. Standard reference data for the viscosity of toluene. J. Phys. Chem. Ref. Data 2006, 35, 1−8. (18) Caudwell, D. R.; Trusler, J. P. M.; Vesovic, V.; Wakeham, W. A. Viscosity and density of five hydrocarnon liquids at pressures up to 200 MPa and temperatures up to 473 K. J. Chem. Eng. Data 2009, 54, 359−366. (19) Et-Tahir, A.; Boned, C.; Lagourette, B.; Xans, P. Determination of the viscosity of various hydrocarbons and mixtures of hydrocarbons

CONCLUSIONS In this paper, the design and operation of a new vibrating-wire viscometer for the measurement of high-viscosity liquids (50 to 125) mPa·s, and up to 18 MPa were described. The viscosity of liquid diisodecyl phthalate (DIDP) was measured at temperatures between (293 and 363) K and pressures between (0.1 and 18) MPa with an absolute uncertainty of ± 1.5 %.

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AUTHOR INFORMATION

Corresponding Author

*Tel.: +30 2310 996163. Fax: +30 2310 996170. E-mail: [email protected]. Funding

S.M. gratefully acknowledges the partial financial support of the Research Committee of the Aristotle University of Thessaloniki. Notes

The authors declare no competing financial interest.

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ACKNOWLEDGMENTS The design and construction of the new viscometer was not an easy job. The authors are indebted to Mr. T. Tsilipiras for his mechanical expertise. In the operation of the viscometer, the help of Dr. S. Polymatidou, and Dr. E. Karagiannidis was invaluable! We also would like to thank Prof. P.D. Jiannakoudaki, for valuable discussions during this work.

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REFERENCES

(1) Kunzel, W.; Van Wijk, H. F.; Marsh, K. N., Viscosity In Recommended Reference Materials for the Realization of Physicochemical Properties, (IUPAC) Blackwells Scientific Publ.; Oxford, UK, 1987; pp 45−72. (2) Dymond, J. H.; Oye, H. A. Viscosity of selected liquid n-alkanes. J. Phys. Chem. Ref. Data 1994, 23, 41−53. (3) Viscosity of Water. Technical Report, ISO/TR 3666; International Organization for Standardization: Geneva, Switzerland, 1988. (4) Bauer, H. In Physikalisch-Technische Bundensanstalt (PTB); Braunschweig: Germany, private communication, 2003. (5) Caetano, F. J. P.; Fareleira, J. M. N. A.; Oliveira, C. M. B. P.; Wakeham, W. A. New measurements of the viscosity of diisodecyl phthalate using a vibrating wire technique. J. Chem. Eng. Data 2005, 50, 1875−1878. G



Article

versus temperature and pressure. Int. J. Thermophys. 1995, 16, 1309− 1334. (20) Harris, K. R. Temperature and pressure dependence of the viscosities of 2-ethylhexyl benzoate, bis(2-ethyhexyl) phthalate. 2, 6, 10, 15, 19, 23-Hexamethyltetracosane (squalane), and diisodecyl phthalate. J. Chem. Eng. Data 2009, 54, 2729−2738. (21) Caetano, F. J. P.; Fareleira, J. M. N. A.; Oliveira, C. M. B. P.; Wakeham, W. A. Viscosity of di-isodecylphthalate: A potential standard of moderate viscosity. Int. J. Thermophys. 2004, 25, 1311− 1322. (22) Correia da Mata, J. L.; Caetano, F. J. P.; Oliveira, C. M. B. P.; Fareleira, J. M. N. A. Viscosity measurements of diisodecyl phthalate using a vibrating wire instrument operated in free decay mode: Comparison with results obtained with the forced mode of operation. J. Chem. Eng. Data 2009, 54, 2562−2568.

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A Novel Vibrating-Wire Viscometer for High-Viscosity Liquids at

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