# Gradient Theory simulations of pure fluid interfaces using a generalized expression for influence parameters and a Helmholtz energy equation of state for fundamentally consistent two-phase calculations

## Abstract

The fidelity of Gradient Theory simulations depends on the accuracy of saturation properties and influence parameters, and require equations of state (EoS) which exhibit a fundamentally consistent behavior in the two-phase regime. Widely applied multi-parameter EoS, however, are generally invalid inside this region. Hence, they may not be fully suitable for application in concert with Gradient Theory despite their ability to accurately predict saturation properties. The commonly assumed temperature-dependence of pure component influence parameters usually restricts their validity to subcritical temperature regimes. This may distort predictions for general multi-component interfaces where temperatures often exceed the critical temperature of vapor phase components. Then, the calculation of influence parameters is not well defined. In this paper, one of the first studies is presented in which Gradient Theory is combined with a next-generation Helmholtz energy EoS which facilitates fundamentally consistent calculations over the entire two-phase regime. Illustrated on pentafluoroethane as an example, reference simulations using this method are performed. They demonstrate the significance of such high-accuracy and fundamentally consistent calculations for the computation of interfacial properties. These reference simulations are compared to corresponding results from cubic PR EoS, widely-applied in combination with Gradient Theory, and mBWR EoS. The analysis reveals that neither ofmore »

- Authors:

- Sandia National Lab. (SNL-CA), Livermore, CA (United States)

- Publication Date:

- Research Org.:
- Sandia National Lab. (SNL-CA), Livermore, CA (United States)

- Sponsoring Org.:
- USDOE Office of Secretary of Energy (S)

- OSTI Identifier:
- 1235923

- Alternate Identifier(s):
- OSTI ID: 1244591

- Report Number(s):
- SAND-2015-20792J

Journal ID: ISSN 0021-9797; PII: S0021979714010388

- Grant/Contract Number:
- AC04-94AL85000; AC04-94-AL85000

- Resource Type:
- Journal Article: Accepted Manuscript

- Journal Name:
- Journal of Colloid and Interface Science

- Additional Journal Information:
- Journal Volume: 445; Journal Issue: C; Journal ID: ISSN 0021-9797

- Country of Publication:
- United States

- Language:
- English

- Subject:
- 75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND SUPERFLUIDITY; Gradient Theory; interfacial tension; influence parameter; equation of state; pure fluid; metastability

### Citation Formats

```
Dahms, Rainer N.
```*Gradient Theory simulations of pure fluid interfaces using a generalized expression for influence parameters and a Helmholtz energy equation of state for fundamentally consistent two-phase calculations*. United States: N. p., 2014.
Web. doi:10.1016/j.jcis.2014.12.069.

```
Dahms, Rainer N.
```*Gradient Theory simulations of pure fluid interfaces using a generalized expression for influence parameters and a Helmholtz energy equation of state for fundamentally consistent two-phase calculations*. United States. doi:10.1016/j.jcis.2014.12.069.

```
Dahms, Rainer N. Wed .
"Gradient Theory simulations of pure fluid interfaces using a generalized expression for influence parameters and a Helmholtz energy equation of state for fundamentally consistent two-phase calculations". United States.
doi:10.1016/j.jcis.2014.12.069. https://www.osti.gov/servlets/purl/1235923.
```

```
@article{osti_1235923,
```

title = {Gradient Theory simulations of pure fluid interfaces using a generalized expression for influence parameters and a Helmholtz energy equation of state for fundamentally consistent two-phase calculations},

author = {Dahms, Rainer N.},

abstractNote = {The fidelity of Gradient Theory simulations depends on the accuracy of saturation properties and influence parameters, and require equations of state (EoS) which exhibit a fundamentally consistent behavior in the two-phase regime. Widely applied multi-parameter EoS, however, are generally invalid inside this region. Hence, they may not be fully suitable for application in concert with Gradient Theory despite their ability to accurately predict saturation properties. The commonly assumed temperature-dependence of pure component influence parameters usually restricts their validity to subcritical temperature regimes. This may distort predictions for general multi-component interfaces where temperatures often exceed the critical temperature of vapor phase components. Then, the calculation of influence parameters is not well defined. In this paper, one of the first studies is presented in which Gradient Theory is combined with a next-generation Helmholtz energy EoS which facilitates fundamentally consistent calculations over the entire two-phase regime. Illustrated on pentafluoroethane as an example, reference simulations using this method are performed. They demonstrate the significance of such high-accuracy and fundamentally consistent calculations for the computation of interfacial properties. These reference simulations are compared to corresponding results from cubic PR EoS, widely-applied in combination with Gradient Theory, and mBWR EoS. The analysis reveals that neither of those two methods succeeds to consistently capture the qualitative distribution of obtained key thermodynamic properties in Gradient Theory. Furthermore, a generalized expression of the pure component influence parameter is presented. This development is informed by its fundamental definition based on the direct correlation function of the homogeneous fluid and by presented high-fidelity simulations of interfacial density profiles. As a result, the new model preserves the accuracy of previous temperature-dependent expressions, remains well-defined at supercritical temperatures, and is fully suitable for calculations of general multi-component two-phase interfaces.},

doi = {10.1016/j.jcis.2014.12.069},

journal = {Journal of Colloid and Interface Science},

number = C,

volume = 445,

place = {United States},

year = {Wed Dec 31 00:00:00 EST 2014},

month = {Wed Dec 31 00:00:00 EST 2014}

}

*Citation information provided by*

Web of Science

Web of Science