Validity of the Kelvin equation and the equation-of-state-with-capillary-pressure model for the phase behavior of a pure component under nanoconfinement

Wang, Yingnan; Shardt, Nadia; Lu, Chang; Li, Huazhou; Elliott, Janet A.W.; Jin, Zhehui

doi:10.1016/j.ces.2020.115839

Cited by 23 publications

(18 citation statements)

References 81 publications

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“…By regressing measured θ with the [O] for PCMs using available data in the literature (see supporting information for details), θ is estimated using θ = −188°(±16°) [O] + 86.0°(±1.8°). For desorption, θ = 0°is assumed which is consistent with previous studies where water already wetted PCM surfaces (Wang et al, 2020;Wongkoblap et al, 2011). As will be shown below, this approach can account for hysteresis in water retention for both slit and cylindrical pores and the wider hysteresis loops for water retention in more hydrophobic PCMs when a slit pore geometry is assumed (Thommes et al, 2013;Velasco, Guillet-Nicolas, et al, 2016).…”

Section: Gwc Bsupporting

confidence: 72%

“…The constant C depends on the assumed pore geometry and if water is adsorbing or desorbing. For a slit pore geometry, C = 2 for both adsorption and desorption (Wang et al, 2020), while for a cylindrical pore, C = 2 for adsorption (without the term cos θ in Equation ) and C = 4 for desorption (Wang et al, 2020; Wongkoblap et al, 2011). To use Equation for specified ψ , t b and θ between water and biochar surface must be known.…”

Section: Methodsmentioning

confidence: 99%

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Models for Predicting Water Retention in Pyrogenic Carbon (Biochar) and Biochar‐Amended Soil at Low Water Contents

Nakhli

Imhoff

2020

Water Resources Research

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The dry end of the soil water retention curve (WRC) plays an important role in various hydrologic, solute transport, plant, and microbial processes. Despite increasing application of biochar as a soil amendment, knowledge about water retention in biochars and biochar-amended soils under dry conditions is lacking. Mechanistic models are presented to predict the WRC for biochars and biochar-amended soils at matric potential (ψ) <~−1 MPa. For biochars, the amount of water retained is linked to biochar surficial oxygen content and pore volume and surface area distributions. The WRC for soils at dry conditions is predicted using specific surface area. The WRC model for biochar-amended soils is the sum of the contributions of models for biochar and soil. The model's utility was examined for three natural soils and a uniform sand, a wood-based biochar, and 10 different combinations of these soils and biochar. The accuracy of the model for biochars was further tested for six other pyrogenic carbonaceous materials (PCMs). The models agreed well with experimental data: for the biochar and PCMs, soils, and biochar-amended soils, the root mean square error normalized to the range of water content was almost always <10%. The line of best fit for predicted versus measured gravimetric water content at permanent wilting point had slope of 0.935 ± 0.013 and a coefficient of determination of 0.997. The applicability of these models for different biochars, soils, and their mixtures is discussed.

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Section: Gwc Bsupporting

confidence: 72%

Section: Methodsmentioning

confidence: 99%

Models for Predicting Water Retention in Pyrogenic Carbon (Biochar) and Biochar‐Amended Soil at Low Water Contents

Nakhli

Imhoff

2020

Water Resources Research

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“…Recent studies show that the accuracy of the Kelvin equation declines in nanopores smaller than 8 . Wang et al 8 investigated the precision of computed phase-change pressures by the Kelvin equation and equation-of-state-with-capillary-pressure (EOS-P cap ) in extended confined pores. Quantitatively, the study demonstrated that overestimation and underestimation issues were noticed with the Kelvin equation and EOS-P cap when predicting condensation and evaporation pressures of propane in pores below 8 , comparing with the density function theory (DFT) predicted outcomes.…”

Section: Introductionmentioning

confidence: 99%

Revisiting Kelvin equation and Peng–Robinson equation of state for accurate modeling of hydrocarbon phase behavior in nano capillaries

Al-Kindi

Babadagli

2021

Sci Rep

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The thermodynamics of fluids in confined (capillary) media is different from the bulk conditions due to the effects of the surface tension, wettability, and pore radius as described by the classical Kelvin equation. This study provides experimental data showing the deviation of propane vapour pressures in capillary media from the bulk conditions. Comparisons were also made with the vapour pressures calculated by the Peng–Robinson equation-of-state (PR-EOS). While the propane vapour pressures measured using synthetic capillary medium models (Hele–Shaw cells and microfluidic chips) were comparable with those measured at bulk conditions, the measured vapour pressures in the rock samples (sandstone, limestone, tight sandstone, and shale) were 15% (on average) less than those modelled by PR-EOS.

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“…Finally, some limitations and expectations are discussed, and the conclusions are made. Besides, some basic assumptions are adopted in this study: The fluids are nonpolar, and intermolecular interactions are described with the classical 12-6 LJ potential model; Our work focuses on the ST at the thermodynamic equilibrium state; The fluids are supported to completely wet the pores, and this assumption is common in most of the studies about the thermodynamic equilibrium …”

Section: Introductionmentioning

confidence: 99%

“…The fluids are supported to completely wet the pores, and this assumption is common in most of the studies about the thermodynamic equilibrium …”

Section: Introductionmentioning

confidence: 99%

Nanoconfinement Effect on Surface Tension: Perspectives from Molecular Potential Theory

Feng

Bakhshian

et al. 2020

Langmuir

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Liquid–vapor surface tension (ST) in nanopores attracts great attention in many industries because of the prosperity of nanoscience and nanotechnology. Here, considering the important emerging new physical phenomena induced by nanoconfinement effects, including curvature-dependent and shift-critical temperature (T c)-dependent effects, the anomalous variation of ST in nanopores is captured from the molecular potential perspective. Furthermore, a simple analytical model is proposed to determine the ST in nanopores by correlating these two effects with an easily accessible parameter, that is, normalized pore dimension, which is the ratio of the pore radius to Lennard-Jones size parameter. The model is validated to be reliable for determining the STs of different substances both in the bulk phase as well as nanopores through comparison with the experimental results and molecular simulations. Our results show that the reduction of ST induced by the nanoconfinement effects is visible when the pore diameter is within tens of nanometers, and the reduction is more sensitive as the pore size decreases. In detail, the curvature-dependent effect is remarkable in the pores with diameters ranging from a few nanometers to tens of nanometers. Moreover, a simply generalized formula is obtained to determine the curvature-dependent effect and the Tolman length for different substances. The shift-T c-dependent effect is not only related to the pore dimension but also depends on the temperature. As the pore size decreases, the critical temperature of confined fluids diverges significantly from the bulk values. While at high temperatures, the range of pore size impacted by the shift-Tc-dependent effect is enlarged. Additionally, the nanoconfined STs of different substances are calculated and compared. Overall, the new model captures the underlying physics behind the variation of STs in nanopores and can determine the nanoconfined STs reasonably. Moreover, the simple formulation of the model is beneficial to the practical applications in many chemical engineering processes, such as chemical separation, nucleation phenomenon, and capillary condensation.

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Validity of the Kelvin equation and the equation-of-state-with-capillary-pressure model for the phase behavior of a pure component under nanoconfinement

Cited by 23 publications

References 81 publications

Models for Predicting Water Retention in Pyrogenic Carbon (Biochar) and Biochar‐Amended Soil at Low Water Contents

Models for Predicting Water Retention in Pyrogenic Carbon (Biochar) and Biochar‐Amended Soil at Low Water Contents

Revisiting Kelvin equation and Peng–Robinson equation of state for accurate modeling of hydrocarbon phase behavior in nano capillaries

Nanoconfinement Effect on Surface Tension: Perspectives from Molecular Potential Theory

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