logo
calendar31 Avgust 2026
view5
Main language:English

Maxwell–Wagner Observability Analysis in Two-Frequency Capacitive Measurement of Water Content and Density in Hydrocarbon Emulsions

Field of Science:Multidisciplinary
pdf

A-3_9fa0a9d5.pdf

PDF

International Scientific Journal Science and Innovation

International Scientific Journal Science and Innovation

Publish Articlesee more

ARTICLE ANNOTATION

quote
Capacitive transducers are widely used for in-line control of fuels and other hydrocarbon media, but a single-frequency reading of effective permittivity cannot separate the water content of an emulsion from the density of the hydrocarbon phase because both quantities shift the same scalar output. This study formulates the separation task as a parameter-observability problem and shows that Maxwell–Wagner interfacial polarization provides the physical mechanism required to resolve it. A Maxwell–Garnett mixture model with complex phase permittivities was combined with the Clausius–Mossotti relation linking hydrocarbon density to permittivity, and the Jacobian of the two-frequency measurement map was analysed over a five-decade band. The determinant of the Jacobian vanishes identically when the two probing frequencies coincide, demonstrating that a second frequency is a necessary condition for observability rather than merely an accuracy refinement. Numerical analysis places the practical optimum at a low frequency below 0.05 of the relaxation frequency and a high frequency above ten times it; beyond this separation, the gain saturates within 1%. With a channel resolution of 1·10⁻⁴ in relative permittivity, the propagated standard uncertainties are 0.033% for water volume fraction and 1.07 kg/m³ for density; Monte Carlo inversion reproduced these values and revealed negligible bias. The scheme was tolerant to salinity: a 50% error in the assumed water conductivity displaced the density estimate by only 0.11 kg/m³.

AUTHORS

D.Eshmuradov

"MUHAMMAD AL-XORAZMIY NOMIDAGI TOSHKENT AXBOROT TEXNOLOGIYALARI UNIVERSITETI" DAVLAT MUASSASASI

O.Ismailov

"MUHAMMAD AL-XORAZMIY NOMIDAGI TOSHKENT AXBOROT TEXNOLOGIYALARI UNIVERSITETI" DAVLAT MUASSASASI

N.Nizomov

"MUHAMMAD AL-XORAZMIY NOMIDAGI TOSHKENT AXBOROT TEXNOLOGIYALARI UNIVERSITETI" DAVLAT MUASSASASI

Tags

# Maxwell–Wagner polarization# capacitive transducer# water content# observability# measurement uncertainty

SIMILAR ARTICLES

OTHER ARTICLES IN THIS JOURNAL

Rate Article

0
0 ratings
5
4
3
2
1

References

Adohi, B. J. P., Vanga Bouanga, C., Fatyeyeva, K., & Tabellout, M. (2009). Application of the Maxwell–Wagner–Hanai effective medium theory to the analysis of the interfacial polarization relaxations in conducting composite films. Journal of Physics D: Applied Physics, 42(1), 015302. https://doi.org/10.1088/0022-3727/42/1/015302

Asami, K. (2002). Characterization of heterogeneous systems by dielectric spectroscopy. Progress in Polymer Science, 27(8), 1617–1659. https://doi.org/10.1016/S0079-6700(02)00015-1

Böttcher, C. J. F. (1973). Theory of electric polarization (2nd ed., Vol. 1). Elsevier.

Hanai, T. (1960). Theory of the dielectric dispersion due to the interfacial polarization and its application to emulsions. Kolloid-Zeitschrift, 171(1), 23–31. https://doi.org/10.1007/BF01520320

Joint Committee for Guides in Metrology. (2008). Evaluation of measurement data—Guide to the expression of uncertainty in measurement (JCGM 100:2008). https://doi.org/10.59161/JCGM100-2008E

Jumamuratov, B. A., Abduqayumov, A. A., & Eshmuradov, D. E. (2024). Kompozit materiallarning radioshofonligini nazorat qiluvchi vositaning metrologik ta’minoti [Metrological support for a means of controlling the radio transparency of composite materials]. Milliy Standart, (3), 1–5.

Kaatze, U. (1989). Complex permittivity of water as a function of frequency and temperature. Journal of Chemical & Engineering Data, 34(4), 371–374. https://doi.org/10.1021/je00058a001

Kalman, R. E. (1963). Mathematical description of linear dynamical systems. Journal of the Society for Industrial and Applied Mathematics, Series A: Control, 1(2), 152–192. https://doi.org/10.1137/0301010

Maxwell, J. C. (1873). A treatise on electricity and magnetism (Vol. 1). Clarendon Press.

Qian, J., Yan, S., Li, Z., Yu, L., Wang, X., Zhang, Z., Sun, J., & Han, X. (2022). Modification of the Maxwell–Wagner heterogeneous dielectric model for heterogeneous polymers and emulsions. Polymers, 14(13), 2743. https://doi.org/10.3390/polym14132743

Samet, M., Kallel, A., & Serghei, A. (2022). Maxwell–Wagner–Sillars interfacial polarization in dielectric spectra of composite materials: Scaling laws and applications. Journal of Composite Materials, 56(20), 3197–3217. https://doi.org/10.1177/00219983221090629

Sharipov, G. N., Turayeva, N. M., & Eshmuradov, D. E. (2022). Voprosy povysheniya metrologicheskoy nadezhnosti sredstv izmereniy [Issues in improving the metrological reliability of measuring instruments]. In Proceedings of the International Conference “State and Trends in the Development of Standardization and Technical Regulation in the World” (pp. 178–184). Tashkent State Technical University.

Sihvola, A. (1999). Electromagnetic mixing formulas and applications. Institution of Electrical Engineers.

Sillars, R. W. (1937). The properties of a dielectric containing semiconducting particles of various shapes. Journal of the Institution of Electrical Engineers, 80(484), 378–394. https://doi.org/10.1049/jiee-1.1937.0058

Wagner, K. W. (1914). Erklärung der dielektrischen Nachwirkungsvorgänge auf Grund Maxwellscher Vorstellungen. Archiv für Elektrotechnik, 2(9), 371–387. https://doi.org/10.1007/BF01657322