Measurement of bulk density using the Archimedes method with an inductive spring balance
DOI:
https://doi.org/10.24425/mms.2025.155808Abstract
The article presents a new version of the hydrostatic method for determining bulk density. A spring balance was designed and constructed for measuring the bulk density of porous samples using the liquid displacement method (Archimedes’ principle). In the innovative spring balance, a weight-to-frequency converter based on an LC oscillator was used, in which the sensor consists of springs that simultaneously serve as the source of inductance in the oscillator’s resonant circuit. Changes in inductance caused by the variation in the spring length under the load of the weighed object result in a change in oscillation frequency. The spring balance design is characterized by great simplicity, and the converter has a high sensitivity at the level of 10-5. In this work, the bulk density of reference samples, both porous and non-porous, was investigated. The results of bulk density measurements for aluminium block and porous sandstone were compared with values obtained from professional pycnometers, namely, the helium AccuPyc 1340 and the quasi-liquid (powder) GeoPyc 1360 (Micromeritics Instrument Corporation, United States). The results confirm the full suitability of the spring balance for the intended purpose.References
[1] Park, S., Kang, M., Oinam, Y., Amoozegar, A., & Pyo, S. (2022). Measurement of skeletal density and porosity of construction materials using a new proposed vacuum pycnometer. Measurement, 196, 111209. https://doi.org/10.1016/j.measurement.2022.111209
[2] Zhao, C., Zhou, W., Hu, Q., Xu, H., & Zhang, C. (2021). Porosity measurement of granular rock samples by modified bulk density analyses with particle envelopment. Marine and Petroleum Geology, 133, 105273. https://doi.org/10.1016/j.marpetgeo.2021.105273
[3] Nurkowski, J., & Nowakowski, A. (2023). Inductive sensor for measuring linear displacement and velocity - Version with stationary magnetic core. Measurement, 222, 113675. https://doi.org/10.1016/j.measurement.2023.113675
[4] Nurkowski, J., & Nowakowski, A. (2022). Thermally compensated inductive deformation sensor - Mathematical background and practical implementation. Measurement, 197, 111282. https://doi.org/10.1016/j.measurement.2022.111282
[5] Nowakowski, A., & Nurkowski, J. (2023). About some problems related to determination of the e.g. the Biot coefficient for rocks. Archives of Mining Sciences. https://doi.org/10.24425/ams.2021.136697
[6] Strzałkowski, P. (2018). Requirements and Test Methods for Selected Natural Stone Products (in Polish). Górnictwo Odkrywkowe, 59, 34-40.
[7] Serway, R., Jewett, J. (2008). Physics for Scientists and Engineers with Modern Physics. Seventh Edition. Thomson Higher Education.
[8] Agrawal, S. (2021). Simplified Measurement of Density of Irregular Shaped Composites Material Using Archimedes Principle by Mixing Two Fluids Having Different Densities. International Research Journal of Engineering and Technology, 8, 1005-1009. https://doi.org/10.1107/S002188986800542X
[9] Washburn, E. W. (1921). Note on a method of determining the distribution of pore sizes in a porous material. Proceedings of the National Academy of Sciences, 7(4), 115-116. https://doi.org/10.1073/pnas.7.4.115
[10] Godyń, K., & Dutka, B. (2021). Sorption and Micro-Scale strength properties of coals susceptible to outburst caused by changes in degree of coalification. Materials, 14(19), 5807. https://doi.org/10.3390/ma14195807
[11] Ledwaba, T., Mbuyisa, B., Blakey-Milner, B., Steenkamp, C., & Du Plessis, A. (2023). X-ray computed tomography vs Archimedes method: a head-to-head comparison. MATEC Web of Conferences, 388, 08002. https://doi.org/10.1051/matecconf/202338808002
[12] Mohazzab, P. (2017). Archimedes’ principle revisited. Journal of Applied Mathematics and Physics, 05(04), 836-843. https://doi.org/10.4236/jamp.2017.54073
[13] Bruce, D., Paradise, P., Saxena, A., Temes, S., Clark, R., Noe, C., Benedict, M., Broderick, T., & Bhate, D. (2022). A critical assessment of the Archimedes density method for thin-wall specimens in laser powder bed fusion: Measurement capability, process sensitivity and property correlation. Journal of Manufacturing Processes, 79, 185-192. https://doi.org/10.1016/j.jmapro.2022.04.059
[14] Sizov, A., Mihiretie, B., Ma, Y., Gustafsson, S. E., & Gustavsson, M. (2023). Thermal conductivity vs depth profiling using the hot disk technique - Analysis of anisotropic, inhomogeneous structures. Review of Scientific Instruments, 94(7). https://doi.org/10.1063/5.0145902
[15] Ramos, C. C., Preizal, J., Hu, X., Caucheteur, C., Woyessa, G., Bang, O., Rocha, A. M., & Oliveira, R. (2025). High resolution liquid level sensor based on Archimedes’ law of buoyancy using polymer optical fiber Bragg gratings. Measurement, 252, 117368. https://doi.org/10.1016/j.measurement.2025.117368
[16] Horowitz, P., Hill, W. (2015). Oscillators and Timers. The Art of Electronics, 425-470. Cambridge University Press.
[17] Pawłowski, J. (1980). Wzmacniacze i generatory (Amplifiers and Generators). Wydawnictwa Komunikacji i Łączności. Warszawa.
[18] Kou, H., Gao, Y., Shao, J., Dou, K., & Wang, N. (2022). Temperature-porosity-dependent elastic modulus model for metallic materials. Reviews on Advanced Materials Science, 61(1), 769-777. https://doi.org/10.1515/rams-2022-0270
[19] Li, W., Kou, H., Zhang, X., Ma, J., Li, Y., Geng, P., Wu, X., Chen, L., & Fang, D. (2019). Temperature-dependent elastic modulus model for metallic bulk materials. Mechanics of Materials, 139, 103194. https://doi.org/10.1016/j.mechmat.2019.103194
[20] European Committee for Standardization. (2008). Natural Stone Test Methods Determination of Real Density and Apparent Density, and of Total and Open Porosity. EN-1936.
[21] International Organization for Standardization. (2018). Ceramic Tiles. Part 3: Determination of Water Absorption, Apparent Porosity, Apparent Relative Density and Bulk Density. EN ISO 10545-3.
[22] Franklin, J.A., Vogler, U.V., Szlavin, J., Edmond, J.M. & Bieniawski, Z.T. (2007). Suggested Methods for Determining Water Content, Porosity, Density, Absorption and Related Properties and Swelling and Slake-Durability (pp. 143-151). [Ulusay, R., Hudson, J.A. (Eds.) The Complete ISRM Suggested Methods for Rock Characterisation, Testing and Monitoring 1974-2006, ISRM Turkish National Group, Ankara]
[23] Moradi, A., Pramanik, S., Ataollahi, F., Kamarul, T., & Pingguan-Murphy, B. (2014). Archimedes revisited: computer assisted micro-volumetric modification of the liquid displacement method for porosity measurement of highly porous light materials. Analytical Methods, 6(12), 4396-4401. https://doi.org/10.1039/c4ay00666f