Techniques to determine and compensate for the force transmission error (FTE), including the magnetic effects of the fluid being measured, in magnetic suspension densimeters are presented. For a two-sinker densimeter, the forces on the balance are expressed for each of the weighings comprising a density determination (i.e., the two sinkers plus balance calibration and tare weights). This yields a system of four equations, which are solved for the fluid density, a balance calibration factor, a coupling factor (related to the FTE), and a quantity related to the balance tare. For a single-sinker densimeter, an in situ weighing of the sinker in vacuum compensates for the FTE of the apparatus itself. A determination of the fluid-specific effect requires measurements with two different sinkers—analogous to the two-sinker analysis, but with the measurements spread out over time. The apparatus part of the FTE is generally less than ±20 ppm. Measurements on propane, helium, neon, nitrogen, argon, toluene, and air are analyzed for the fluid-specific effect; this effect is correlated with the magnetic susceptibility of the fluid together with an apparatus constant. With this analysis, the force transmission “error” becomes an effect that can be accounted for rather than a significant source of uncertainty in density measurements carried out with magnetic suspension densimeters.
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References
Wagner W., Kleinrahm R. (2004). Metrologia 41:S24
H. W. Lösch, Entwicklung und Aufbau von neuen Magnetschwebewaagen zur berührungsfreien Messung vertikaler Kräfte, Fortschr.-Ber. VDI, Reihe 3, No. 138 (VDI-Verlag, Düsseldorf, 1987).
Kuramoto N., Fujii K., Waseda A. (2004). Metrologia 41:S84
R. Kleinrahm and W. Wagner, Entwicklung und Aufbau einer Dichtemeßanlage zur Messung der Siede- und Taudichten reiner fluider Stoffe auf der gesamten Phasengrenzkurve, Fortschr.-Ber. VDI, Reihe 3, No. 92 (VDI-Verlag, Düsseldorf, 1984).
Kleinrahm R., Wagner W. (1986). J. Chem. Thermodyn. 18:739
Lösch H.W., Kleinrahm R., Wagner W. (1994). Chem.-Ing.-Tech. 66:1055
McLinden M.O., Lösch-Will C. (2007). J. Chem. Thermo. 39:507
M. O. McLinden, submitted to J. Chem. Eng. Data.
D. R. Lide, ed., CRC Handbook of Chemistry and Physics, 85th Ed., (CRC Press, Boca Raton, Florida, 2004).
M. O. McLinden, unpublished data, National Institute of Standards and Technology, Boulder, Colorado, U.S.A. (2006).
Davis R.S. (1998). Metrologia 35:49
McLinden M.O. (2006). Meas. Sci. Technol. 17:2597
Beams J.W., Clarke A.M. (1962). Rev. Sci. Instrum. 33:750
K. Brachthäuser, R. Kleinrahm, H. W. Lösch, and W. Wagner, Entwicklung eines neuen Dichtemeßverfahrens und Aufbau einer Hochtemperatur-Hochdruck-Dichtemeßanlage, Fortschr.-Ber. VDI, Reihe 8, No. 371 (VDI-Verlag, Düsseldorf, 1993).
Wagner W., de Reuck K.M. (1987). International Thermodynamic Tables of the Fluid State—9, Oxygen. Blackwell Scientific Publishing, Oxford
Span R., Lemmon E.W., Jacobsen R.T., Wagner W., Yokozeki A. (2000). J. Phys. Chem. Ref. Data 29:1361
J. Klimeck, Weiterentwicklung einer Ein-Senkkörper-Dichtemessanlage und Präzisionsmessungen der thermischen Zustandsgrößen von Kohlendioxid, Argon, Stickstoff und Methan, (Dissertation, Ruhr-Universität Bochum, Germany, 1997).
Richter M., Sommer D., Kleinrahm R. (2007). personal communication, Lehrstuhl für Thermodynamik. Ruhr-Universität Bochum, Germany
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McLinden, M.O., Kleinrahm, R. & Wagner, W. Force Transmission Errors in Magnetic Suspension Densimeters. Int J Thermophys 28, 429–448 (2007). https://doi.org/10.1007/s10765-007-0176-0
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DOI: https://doi.org/10.1007/s10765-007-0176-0