Abstract

The nitrogen sorption isotherm is conventionally used to deduce the specific surface area of porous materials. However, it often exhibits a sharp drop around 0.5 relative pressure. A theory explicitly accounting for intermolecular-scale pressure, instead of classical theories of constant disjoining pressure in condensed liquid, is constructed and used to determine cavitation during desorption. Intermolecular-scale liquid pressure distribution is quantified using a recently developed soil sorptive potential framework, showing compressive liquid nitrogen pressure decaying nonlinearly with increasing distance to the particle surface. A range of cavitation pressure is predicted by classical nucleation theory and the van der Waals equation of state. Cavitation is shown to be triggered when nitrogen’s global minimum liquid pressure falls within the cavitation threshold. It is shown that this criterion is valid for all tested soils. Computed minimum liquid pressure always occurs at 0.5 relative pressure, which is in accordance with experimental isotherm data and further indicates the validity of the cavitation onset criterion.

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Data Availability Statement

All experimental data used in this work are reported in the paper.

Acknowledgments

This research is sponsored by a Tsinghua University grant (SKLHSE-D-03) the and National Natural Science Foundation of China (NSFC51661165015).

References

Atkins, P. W., J. De Paula, and J. Keeler. 2018. Atkins’ physical chemistry. Oxford, UK: Oxford University Press.
Aylmore, L. A. G., I. D. Sills, and J. P. Quirk. 1970. “Surface area of homoionic illite and montmorillonite clay minerals as measured by the sorption of nitrogen and carbon dioxide.” Clays Clay Miner. 18 (2): 91–96. https://doi.org/10.1346/CCMN.1970.0180204.
Baidakov, V. G., V. E. Vinogradov, and P. A. Pavlov. 2016a. “Homogeneous nucleation in liquid nitrogen at negative pressures.” J. Exp. Theor. Phys. 123 (4): 629–637. https://doi.org/10.1134/S1063776116100010.
Baidakov, V. G., V. E. Vinogradov, and P. A. Pavlov. 2016b. “Limiting tensile strength of liquid nitrogen.” Phys. Fluids 28 (5): 051702. https://doi.org/10.1063/1.4951703.
Barrett, E. P., L. G. Joyner, and P. P. Halenda. 1951. “The determination of pore volume and area distributions in porous substances. I: Computations from nitrogen isotherms.” J. Am. Chem. Soc. 73 (1): 373–380. https://doi.org/10.1021/ja01145a126.
Brunauer, S., L. S. Deming, W. E. Deming, and E. Teller. 1940. “On A theory of the van der Waals adsorption of gases.” J. Am. Chem. Soc. 62 (7): 1723–1732. https://doi.org/10.1021/ja01864a025.
Brunauer, S., P. H. Emmett, and E. Teller. 1938. “Adsorption of gases in multimolecular layers.” J. Am. Chem. Soc. 60 (2): 309–319. https://doi.org/10.1021/ja01269a023.
Caupin, F., A. Arvengas, K. Davitt, M. Azouzi Mel, K. I. Shmulovich, C. Ramboz, D. A. Sessoms, and A. D. Stroock. 2012. “Exploring water and other liquids at negative pressure.” J. Phys.: Condens. Matter 24 (28): 284110. https://doi.org/10.1088/0953-8984/24/28/284110.
Chen, P., N. Lu, and C. F. Wei. 2019. “General scanning hysteresis model for soil-water retention curves.” J. Geotech. Geoenviron. Eng. 145 (12): 04019116. https://doi.org/10.1061/(ASCE)GT.1943-5606.0002184.
Cheung, P. S. Y., and J. G. Powles. 1975. “The properties of liquid nitrogen.” Mol. Phys. 30 (3): 921–949. https://doi.org/10.1080/00268977500102461.
Chiou, C. T., D. W. Rutherford, and M. Manes. 2002. “Sorption of nitrogen and ethylene glycol monoethyl ether (EGME) vapors on some soils, clays, and mineral oxides and determination of sample surface areas by use of sorption data.” Environ. Sci. Technol. 27 (8): 1587–1594. https://doi.org/10.1021/es00045a014.
Coasne, B., K. E. Gubbins, and R. J. M. Pellenq. 2005. “Domain theory for capillary condensation hysteresis.” Phys. Rev. B 72 (2): 024304. https://doi.org/10.1103/PhysRevB.72.024304.
Cole, M. W., and W. F. Saam. 1974. “Excitation spectrum and thermodynamic properties of liquid films in cylindrical pores.” Phys. Rev. Lett. 32 (18): 985. https://doi.org/10.1103/PhysRevLett.32.985.
Duan, C., R. Karnik, M. C. Lu, and A. Majumdar. 2012. “Evaporation-induced cavitation in nanofluidic channels.” Proc. Natl. Acad. Sci. U.S.A 109 (10): 3688–3693. https://doi.org/10.1073/pnas.1014075109.
Dular, M., and M. Petkovsek. 2018. “Cavitation erosion in liquid nitrogen.” Wear 400–401 (Apr): 111–118. https://doi.org/10.1016/j.wear.2018.01.003.
Hayward, A. T. J. 1967. “Compressibility equations for liquids: A comparative study.” Br. J. Appl. Phys. 18 (7): 965–977. https://doi.org/10.1088/0508-3443/18/7/312.
Heffelfinger, G. S., F. V. Swol, and K. E. Gubbins. 1998. “Adsorption hysteresis in narrow pores.” J. Chem. Phys. 89 (8): 5202–5205. https://doi.org/10.1063/1.455610.
Heister, K. 2014. “The measurement of the specific surface area of soils by gas and polar liquid adsorption methods—Limitations and potentials.” Geoderma 216 (Mar): 75–87. https://doi.org/10.1016/j.geoderma.2013.10.015.
Herbert, E., S. Balibar, and F. Caupin. 2006. “Cavitation pressure in water.” Phys. Rev. E 74 (4): 041603. https://doi.org/10.1103/PhysRevE.74.041603.
Imre, A. R. 2007. How to generate and measure negative pressure in liquids? Dordrecht, Netherlands: Springer.
Israelachvili, J. 2011. Intermolecular and surface forces. Burlington, MA: Academic Press.
Itterbeek, A. V., and O. Verbeke. 1960. “Density of liquid nitrogen and argon as a function of pressure and temperature.” Physica 26 (11): 931–938. https://doi.org/10.1016/0031-8914(60)90042-2.
Jacobsen, R. T., R. B. Stewart, and M. Jahangiri. 1986. “Thermodynamic properties of nitrogen from the freezing line to 2000-K at pressures to 1000-MPa.” J. Phys. Chem. Ref. Data 15 (2): 735–909. https://doi.org/10.1063/1.555754.
Khorshidi, M., N. Lu, I. D. Akin, and W. J. Likos. 2017. “Intrinsic relationship between specific surface area and soil water retention.” J. Geotech. Geoenviron. Eng. 143 (1): 04016078. https://doi.org/10.1061/(ASCE)GT.1943-5606.0001572.
Kuila, U., and M. Prasad. 2012. “Specific surface area and pore-size distribution in clays and shales.” Geophys. Prospect. 61 (2): 341–362. https://doi.org/10.1111/1365-2478.12028.
Lee, J. G., and R. W. Flumerfelt. 1996. “A refined approach to bubble nucleation and polymer foaming process: Dissolved gas and cluster size effects.” J. Colloid Interface Sci. 184 (2): 335–348. https://doi.org/10.1006/jcis.1996.0628.
Levine, I. N. 2009. Physical chemistry. 6th ed. Boston: McGraw-Hill.
Lu, N., M. T. Anderson, W. J. Likos, and G. W. Mustoe. 2008. “A discrete element model for kaolinite aggregate formation during sedimentation.” Int. J. Numer. Anal. Methods Geomech. 32 (8): 965–980. https://doi.org/10.1002/nag.656.
Lu, N., and C. Zhang. 2019. “Soil sorptive potential: Concept, theory, and verification.” J. Geotech. Geoenviron. Eng. 145 (4): 04019006. https://doi.org/10.1061/(ASCE)GT.1943-5606.0002025.
Or, D., and M. Tuller. 2002. “Cavitation during desaturation of porous media under tension.” Water Resour. Res. 38 (5): 19-1–19-14. https://doi.org/10.1029/2001WR000282.
Philip, J. R. 1977. “Unitary approach to capillary condensation and adsorption.” J. Chem. Phys. 66 (11): 5069–5075. https://doi.org/10.1063/1.433814.
Rasmussen, C. J., A. Vishnyakov, M. Thommes, B. M. Smarsly, F. Kleitz, and A. V. Neimark. 2010. “Cavitation in metastable liquid nitrogen confined to nanoscale pores.” Langmuir 26 (12): 10147–10157. https://doi.org/10.1021/la100268q.
Ravikovitch, P. I., B. W. Bogan, and A. V. Neimark. 2005. “Nitrogen and carbon dioxide adsorption by soils.” Environ. Sci. Technol. 39 (13): 4990–4995. https://doi.org/10.1021/es048307b.
Ravikovitch, P. I., and A. V. Neimark. 2002. “Experimental confirmation of different mechanisms of evaporation from ink-bottle type pores: Equilibrium, pore blocking, and cavitation.” Langmuir 18 (25): 9830–9837. https://doi.org/10.1021/la026140z.
Salles, F., J. M. Douillard, R. Denoyel, O. Bildstein, M. Jullien, I. Beurroies, and H. Van Damme. 2009. “Hydration sequence of swelling clays: Evolutions of specific surface area and hydration energy.” J. Colloid Interface Sci. 333 (2): 510–522. https://doi.org/10.1016/j.jcis.2009.02.018.
Sing, K. 2001. “The use of nitrogen adsorption for the characterisation of porous materials.” Colloids Surf., A 187 (Aug): 3–9. https://doi.org/10.1016/S0927-7757(01)00612-4.
Span, R., E. W. Lemmon, R. T. Jacobsen, and W. Wagner. 1998. “A reference quality equation of state for nitrogen.” Int. J. Thermophys. 19 (4): 1121–1132. https://doi.org/10.1023/A:1022689625833.
Span, R., E. W. Lemmon, R. T. Jacobsen, W. Wagner, and A. Yokozeki. 2000. “A reference equation of state for the thermodynamic properties of nitrogen for temperatures from 63.151 to 1000 K and pressures to 2200 MPa.” J. Phys. Chem. Ref. Data 29 (6): 1361–1433. https://doi.org/10.1063/1.1349047.
Thommes, M. 2010. “Physical adsorption characterization of nanoporous materials.” Chem. Ing. Tech. 82 (7): 1059–1073. https://doi.org/10.1002/cite.201000064.
Thommes, M., and K. A. Cychosz. 2014. “Physical adsorption characterization of nanoporous materials: Progress and challenges.” Adsorpt.-J. Int. Adsorpt. Soc. 20 (2–3): 233–250. https://doi.org/10.1007/s10450-014-9606-z.
Thommes, M., K. Kaneko, A. V. Neimark, J. P. Olivier, F. Rodriguez-Reinoso, J. Rouquerol, and K. S. W. Sing. 2015. “Physisorption of gases, with special reference to the evaluation of surface area and pore size distribution (IUPAC Technical Report).” Pure Appl. Chem. 87 (9–10): 1051–1069. https://doi.org/10.1515/pac-2014-1117.
Thommes, M., R. Kohn, and M. Froba. 2000. “Sorption and pore condensation behavior of nitrogen, argon, and krypton in mesoporous MCM-48 silica materials.” J. Phys. Chem. B 104 (33): 7932–7943. https://doi.org/10.1021/jp994133m.
Thommes, M., B. Smarsly, M. Groenewolt, P. I. Ravikovitch, and A. V. Neimark. 2006. “Adsorption hysteresis of nitrogen and argon in pore networks and characterization of novel micro- and mesoporous silicas.” Langmuir 22 (2): 756–764. https://doi.org/10.1021/la051686h.
Tuller, M., and D. Or. 2005. “Water films and scaling of soil characteristic curves at low water contents.” Water Resour. Res. 41 (9). https://doi.org/10.1029/2005WR004142.
Wagner, W., and R. Kleinrahm. 2004. “Densimeters for very accurate density measurements of fluids over large ranges of temperature, pressure, and density.” Metrologia 41 (2): S24–S39. https://doi.org/10.1088/0026-1394/41/2/S03.
Yamamuro, J. A., F. M. Wood, and P. V. Lade. 2008. “Effect of depositional method on the undrained response of silty sand.” Can. Geotech. J. 45 (11): 1538–1555. https://doi.org/10.1139/T08-080.
Yukselen-Aksoy, Y., and A. Kaya. 2010. “Predicting soil swelling behaviour from specific surface area.” Proc. Inst. Civ. Eng. Geotech. Eng. 163 (4): 229–238. https://doi.org/10.1680/geng.2010.163.4.229.
Zhang, C., and N. Lu. 2019. “Augmented Brunauer–Emmett–Teller equation for water adsorption on soils.” Vadose Zone J. 18 (1): 1–12. https://doi.org/10.2136/vzj2019.01.0011.
Zhang, C., and N. Lu. 2020. “Soil sorptive potential: Its determination and predicting soil water density.” J. Geotech. Geoenviron. Eng. 146 (1): 04019118. https://doi.org/10.1061/(ASCE)GT.1943-5606.0002188.
Zheng, Q., D. J. Durben, G. H. Wolf, and C. A. Angell. 1991. “Liquids at large negative pressures—Water at the homogeneous nucleation limit.” Science 254 (5033): 829–832. https://doi.org/10.1126/science.254.5033.829.

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Go to Journal of Engineering Mechanics
Journal of Engineering Mechanics
Volume 147Issue 11November 2021

History

Received: Jan 14, 2021
Accepted: Jul 22, 2021
Published online: Sep 10, 2021
Published in print: Nov 1, 2021
Discussion open until: Feb 10, 2022

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Graudate Research Assistant, State Key Laboratory of Hydro-Science and Engineering, Dept. of Hydraulic Engineering, Tsinghua Univ., Beijing 100084, China. ORCID: https://orcid.org/0000-0001-9422-0570. Email: [email protected]
Professor, State Key Laboratory of Hydro-Science and Engineering, Dept. of Hydraulic Engineering, Tsinghua Univ., Beijing 100084, China. ORCID: https://orcid.org/0000-0001-8522-9864. Email: [email protected]
Professor, Ministry of Education Key Laboratory of Building Safety and Energy Efficiency, College of Civil Engineering, Hunan Univ., Changsha 410012, China. ORCID: https://orcid.org/0000-0002-6675-3940. Email: [email protected]
Shengmin Luo, A.M.ASCE [email protected]
Postdoctoral Fellow, Dept. of Civil and Environmental Engineering, Colorado School of Mines, Golden, CO 80401. Email: [email protected]
Professor, Dept. of Civil and Environmental Engineering, Colorado School of Mines, Golden, CO 80401 (corresponding author). ORCID: https://orcid.org/0000-0003-1753-129X. Email: [email protected]

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