Surface Tension (chemicals.interface)¶
This module contains various surface tension estimation routines, dataframes of fit coefficients, fitting model equations, mixing rules, and water-hydrocarbon interfacial tension estimation routines.
For reporting bugs, adding feature requests, or submitting pull requests, please use the GitHub issue tracker.
Pure Component Correlations¶
- chemicals.interface.Brock_Bird(T, Tb, Tc, Pc)[source]¶
Calculates air-liquid surface tension using the [1] emperical method. Old and tested.
- Parameters
- Returns
- sigma
float
Liquid surface tension, N/m
- sigma
Notes
Numerous arrangements of this equation are available. This is DIPPR Procedure 7A: Method for the Surface Tension of Pure, Nonpolar, Nonhydrocarbon Liquids The exact equation is not in the original paper. If Tc is larger than T, 0 is returned as the model would return complex numbers.
References
- 1
Brock, James R., and R. Byron Bird. “Surface Tension and the Principle of Corresponding States.” AIChE Journal 1, no. 2 (June 1, 1955): 174-77. doi:10.1002/aic.690010208
Examples
p-dichloribenzene at 412.15 K, from DIPPR; value differs due to a slight difference in method.
>>> Brock_Bird(412.15, 447.3, 685, 3.952E6) 0.02208448325192495
Chlorobenzene from Poling, as compared with a % error value at 293 K.
>>> Brock_Bird(293.15, 404.75, 633.0, 4530000.0) 0.032985686413713036
- chemicals.interface.Pitzer_sigma(T, Tc, Pc, omega)[source]¶
Calculates air-liquid surface tension using the correlation derived by [1] from the works of [2] and [3]. Based on critical property CSP methods.
- Parameters
- Returns
- sigma
float
Liquid surface tension, N/m
- sigma
Notes
The source of this equation has not been reviewed. Internal units of presure are bar, surface tension of mN/m. If Tc is larger than T, 0 is returned as the model would return complex numbers.
References
- 1
Poling, Bruce E. The Properties of Gases and Liquids. 5th edition. New York: McGraw-Hill Professional, 2000.
- 2
Curl, R. F., and Kenneth Pitzer. “Volumetric and Thermodynamic Properties of Fluids-Enthalpy, Free Energy, and Entropy.” Industrial & Engineering Chemistry 50, no. 2 (February 1, 1958): 265-74. doi:10.1021/ie50578a047
- 3
Pitzer, K. S.: Thermodynamics, 3d ed., New York, McGraw-Hill, 1995, p. 521.
Examples
Chlorobenzene from Poling, as compared with a % error value at 293 K.
>>> Pitzer_sigma(293., 633.0, 4530000.0, 0.249) 0.03458453513446388
- chemicals.interface.Sastri_Rao(T, Tb, Tc, Pc, chemicaltype=None)[source]¶
Calculates air-liquid surface tension using the correlation derived by [1] based on critical property CSP methods and chemical classes.
- Parameters
- Returns
- sigma
float
Liquid surface tension, N/m
- sigma
Notes
The source of this equation has not been reviewed. Internal units of presure are bar, surface tension of mN/m. If Tc is larger than T, 0 is returned as the model would return complex numbers.
References
- 1
Sastri, S. R. S., and K. K. Rao. “A Simple Method to Predict Surface Tension of Organic Liquids.” The Chemical Engineering Journal and the Biochemical Engineering Journal 59, no. 2 (October 1995): 181-86. doi:10.1016/0923-0467(94)02946-6.
Examples
Chlorobenzene from Poling, as compared with a % error value at 293 K.
>>> Sastri_Rao(293.15, 404.75, 633.0, 4530000.0) 0.03234567739694441
- chemicals.interface.Zuo_Stenby(T, Tc, Pc, omega)[source]¶
Calculates air-liquid surface tension using the reference fluids methods of [1].
- Parameters
- Returns
- sigma
float
Liquid surface tension, N/m
- sigma
Notes
Presently untested. Have not personally checked the sources. The reference values for methane and n-octane are from the DIPPR database. If Tc is larger than T, 0 is returned as the model would return complex numbers.
References
- 1
Zuo, You-Xiang, and Erling H. Stenby. “Corresponding-States and Parachor Models for the Calculation of Interfacial Tensions.” The Canadian Journal of Chemical Engineering 75, no. 6 (December 1, 1997): 1130-37. doi:10.1002/cjce.5450750617
Examples
Chlorobenzene
>>> Zuo_Stenby(293., 633.0, 4530000.0, 0.249) 0.03345569011871088
- chemicals.interface.Hakim_Steinberg_Stiel(T, Tc, Pc, omega, StielPolar=0.0)[source]¶
Calculates air-liquid surface tension using the reference fluids methods of [1].
- Parameters
- Returns
- sigma
float
Liquid surface tension, N/m
- sigma
Notes
Original equation for m and Q are used. Internal units are atm and mN/m. If Tc is larger than T, 0 is returned as the model would return complex numbers.
References
- 1
Hakim, D. I., David Steinberg, and L. I. Stiel. “Generalized Relationship for the Surface Tension of Polar Fluids.” Industrial & Engineering Chemistry Fundamentals 10, no. 1 (February 1, 1971): 174-75. doi:10.1021/i160037a032.
Examples
1-butanol, as compared to value in CRC Handbook of 0.02493.
>>> Hakim_Steinberg_Stiel(298.15, 563.0, 4414000.0, 0.59, StielPolar=-0.07872) 0.02190790257519
- chemicals.interface.Miqueu(T, Tc, Vc, omega)[source]¶
Calculates air-liquid surface tension using the methods of [1].
- Parameters
- Returns
- sigma
float
Liquid surface tension, N/m
- sigma
Notes
Uses Avogadro’s constant and the Boltsman constant. Internal units of volume are mL/mol and mN/m. However, either a typo is in the article or author’s work, or my value of k is off by 10; this is corrected nonetheless. Created with 31 normal fluids, none polar or hydrogen bonded. Has an AARD of 3.5%. If Tc is larger than T, 0 is returned as the model would return complex numbers.
References
- 1
Miqueu, C, D Broseta, J Satherley, B Mendiboure, J Lachaise, and A Graciaa. “An Extended Scaled Equation for the Temperature Dependence of the Surface Tension of Pure Compounds Inferred from an Analysis of Experimental Data.” Fluid Phase Equilibria 172, no. 2 (July 5, 2000): 169-82. doi:10.1016/S0378-3812(00)00384-8.
Examples
Bromotrifluoromethane, 2.45 mN/m
>>> Miqueu(300., 340.1, 0.000199, 0.1687) 0.003474100774091376
- chemicals.interface.Aleem(T, MW, Tb, rhol, Hvap_Tb, Cpl)[source]¶
Calculates vapor-liquid surface tension using the correlation derived by [1] based on critical property CSP methods.
- Parameters
- Returns
- sigma
float
Liquid-vapor surface tension [N/m]
- sigma
Notes
Internal units of molecuar weight are kg/mol. This model is dimensionally consistent.
This model does not use the critical temperature. After it predicts a surface tension of 0 at a sufficiently high temperature, it returns negative results. The temperature at which this occurs (the “predicted” critical temperature) can be calculated as follows:
To handle this case, if Tc is larger than T, 0 is returned as the model would return complex numbers.
Because of its dependence on density, it has the potential to model the effect of pressure on surface tension.
Claims AAD of 4.3%. Developed for normal alkanes. Total of 472 data points. Behaves worse for higher alkanes. Behaves very poorly overall.
References
- 1
Aleem, W., N. Mellon, S. Sufian, M. I. A. Mutalib, and D. Subbarao. “A Model for the Estimation of Surface Tension of Pure Hydrocarbon Liquids.” Petroleum Science and Technology 33, no. 23-24 (December 17, 2015): 1908-15. doi:10.1080/10916466.2015.1110593.
Examples
Methane at 90 K
>>> Aleem(T=90, MW=16.04246, Tb=111.6, rhol=458.7, Hvap_Tb=510870., ... Cpl=2465.) 0.01669970230131523
- chemicals.interface.Mersmann_Kind_sigma(T, Tm, Tb, Tc, Pc, n_associated=1)[source]¶
Estimates the surface tension of organic liquid substances according to the method of [1].
- Parameters
- Returns
- sigma
float
Liquid-vapor surface tension [N/m]
- sigma
Notes
In the equation, all quantities must be in SI units. k is the boltzman constant. If Tc is larger than T, 0 is returned as the model would return complex numbers.
References
- 1
Mersmann, Alfons, and Matthias Kind. “Prediction of Mechanical and Thermal Properties of Pure Liquids, of Critical Data, and of Vapor Pressure.” Industrial & Engineering Chemistry Research, January 31, 2017. https://doi.org/10.1021/acs.iecr.6b04323.
Examples
MTBE at STP (the actual value is 0.0181):
>>> Mersmann_Kind_sigma(298.15, 164.15, 328.25, 497.1, 3430000.0) 0.016744311449290426
- chemicals.interface.sigma_Gharagheizi_1(T, Tc, MW, omega)[source]¶
Calculates air-liquid surface tension using the equation 4 derived in [1] by gene expression programming.
- Parameters
- Returns
- sigma
float
Liquid surface tension, N/m
- sigma
Notes
This equation may fail before the critical point. In this case it returns 0.0 If Tc is larger than T, 0 is returned as the model would return complex numbers.
References
- 1(1,2)
Gharagheizi, Farhad, Ali Eslamimanesh, Mehdi Sattari, Amir H. Mohammadi, and Dominique Richon. “Development of Corresponding States Model for Estimation of the Surface Tension of Chemical Compounds.” AIChE Journal 59, no. 2 (2013): 613-21. https://doi.org/10.1002/aic.13824.
Examples
Methane at 93 K, point from [1]’s supporting material:
>>> sigma_Gharagheizi_1(T=95, Tc=190.564, MW=16.04, omega=0.012) 0.0110389739
- chemicals.interface.sigma_Gharagheizi_2(T, Tb, Tc, Pc, Vc)[source]¶
Calculates air-liquid surface tension using the equation 6 derived in [1] by gene expression programming.
- Parameters
- Returns
- sigma
float
Liquid surface tension, N/m
- sigma
Notes
This expression gives does converge to 0 at the critical point. If Tc is larger than T, 0 is returned as the model would return complex numbers.
References
- 1(1,2)
Gharagheizi, Farhad, Ali Eslamimanesh, Mehdi Sattari, Amir H. Mohammadi, and Dominique Richon. “Development of Corresponding States Model for Estimation of the Surface Tension of Chemical Compounds.” AIChE Journal 59, no. 2 (2013): 613-21. https://doi.org/10.1002/aic.13824.
Examples
Methane at 93 K, point from [1]’s supporting material:
>>> sigma_Gharagheizi_2(T=95, Tb=111.66, Tc=190.564, Pc=45.99e5, Vc=0.0986e-3) 0.01674894057
Mixing Rules¶
- chemicals.interface.Winterfeld_Scriven_Davis(xs, sigmas, rhoms)[source]¶
Calculates surface tension of a liquid mixture according to mixing rules in [1] and also in [2].
- Parameters
- xsarray_like
Mole fractions of all components, [-]
- sigmasarray_like
Surface tensions of all components, [N/m]
- rhomsarray_like
Molar densities of all components, [mol/m^3]
- Returns
- sigma
float
Air-liquid surface tension of mixture, [N/m]
- sigma
Notes
DIPPR Procedure 7C: Method for the Surface Tension of Nonaqueous Liquid Mixtures
Becomes less accurate as liquid-liquid critical solution temperature is approached. DIPPR Evaluation: 3-4% AARD, from 107 nonaqueous binary systems, 1284 points. Internally, densities are converted to kmol/m^3. The Amgat function is used to obtain liquid mixture density in this equation.
Raises a ZeroDivisionError if either molar volume are zero, and a ValueError if a surface tensions of a pure component is negative.
References
- 1
Winterfeld, P. H., L. E. Scriven, and H. T. Davis. “An Approximate Theory of Interfacial Tensions of Multicomponent Systems: Applications to Binary Liquid-Vapor Tensions.” AIChE Journal 24, no. 6 (November 1, 1978): 1010-14. doi:10.1002/aic.690240610.
- 2
Danner, Ronald P, and Design Institute for Physical Property Data. Manual for Predicting Chemical Process Design Data. New York, N.Y, 1982.
Examples
>>> Winterfeld_Scriven_Davis([0.1606, 0.8394], [0.01547, 0.02877], ... [8610., 15530.]) 0.02496738845043982
- chemicals.interface.Weinaug_Katz(parachors, Vml, Vmg, xs, ys)[source]¶
Calculates surface tension of a liquid mixture according to mixing rules in [1] and also in [2]. This is based on the Parachor concept. This is called the Macleod-Sugden model in some places.
- Parameters
- parachors
list
[float
] Parachors of each component, [N^0.25*m^2.75/mol]
- Vml
float
Liquid mixture molar volume, [m^3/mol]
- Vmg
float
Gas mixture molar volume; this can be set to zero at low pressures, [m^3/mol]
- xs
list
[float
] Mole fractions of all components in liquid phase, [-]
- ys
list
[float
] Mole fractions of all components in gas phase, [-]
- parachors
- Returns
- sigma
float
Air-liquid surface tension of mixture, [N/m]
- sigma
Notes
This expression is efficient and does not require pure component surface tensions. Its accuracy is dubious.
References
- 1
Weinaug, Charles F., and Donald L. Katz. “Surface Tensions of Methane-Propane Mixtures.” Industrial & Engineering Chemistry 35, no. 2 (February 1, 1943): 239-246. https://doi.org/10.1021/ie50398a028.
- 2
Pedersen, Karen Schou, Aage Fredenslund, and Per Thomassen. Properties of Oils and Natural Gases. Vol. 5. Gulf Pub Co, 1989.
Examples
>>> Weinaug_Katz([5.1e-5, 7.2e-5], Vml=0.000125, Vmg=0.02011, xs=[.4, .6], ys=[.6, .4]) 0.06547479150776776
Neglect the vapor phase density by setting Vmg to a high value:
>>> Weinaug_Katz([5.1e-5, 7.2e-5], Vml=0.000125, Vmg=1e100, xs=[.4, .6], ys=[.6, .4]) 0.06701752894095361
- chemicals.interface.Diguilio_Teja(T, xs, sigmas_Tb, Tbs, Tcs)[source]¶
Calculates surface tension of a liquid mixture according to mixing rules in [1].
- Parameters
- T
float
Temperature of fluid [K]
- xsarray_like
Mole fractions of all components
- sigmas_Tbarray_like
Surface tensions of all components at the boiling point, [N/m]
- Tbsarray_like
Boiling temperatures of all components, [K]
- Tcsarray_like
Critical temperatures of all components, [K]
- T
- Returns
- sigma
float
Air-liquid surface tension of mixture, [N/m]
- sigma
Notes
Simple model, however it has 0 citations. Gives similar results to the Winterfeld_Scriven_Davis model.
Raises a ValueError if temperature is greater than the mixture’s critical temperature or if the given temperature is negative, or if the mixture’s boiling temperature is higher than its critical temperature.
[1] claims a 4.63 percent average absolute error on 21 binary and 4 ternary non-aqueous systems. [1] also considered Van der Waals mixing rules for Tc, but found it provided a higher error of 5.58%
References
- 1(1,2,3)
Diguilio, Ralph, and Amyn S. Teja. “Correlation and Prediction of the Surface Tensions of Mixtures.” The Chemical Engineering Journal 38, no. 3 (July 1988): 205-8. doi:10.1016/0300-9467(88)80079-0.
Examples
>>> Diguilio_Teja(T=298.15, xs=[0.1606, 0.8394], ... sigmas_Tb=[0.01424, 0.02530], Tbs=[309.21, 312.95], Tcs=[469.7, 508.0]) 0.025716823875045505
Correlations for Specific Substances¶
- chemicals.interface.sigma_IAPWS(T)[source]¶
Calculate the surface tension of pure water as a function of . temperature. Assumes the 2011 IAPWS [1] formulation.
Notes
This function is valid from the triple temperature to the critical temperature. No effects for pressure are included in the formulation. Test values are from IAPWS 2010 book.
The equation is valid from the triple point to the critical point, 647.096 K; but [1] also recommends its use down to -25°C.
If a value larger than the critical temperature is input, 0.0 is returned.
References
Examples
>>> sigma_IAPWS(300.) 0.0716859625271 >>> sigma_IAPWS(450.) 0.0428914991565 >>> sigma_IAPWS(600.) 0.0083756108728
Petroleum Correlations¶
- chemicals.interface.API10A32(T, Tc, K_W)[source]¶
Calculates the interfacial tension between a liquid petroleum fraction and air, using the oil’s pseudocritical temperature and Watson K Characterization factor.
- Parameters
- Returns
- sigma
float
Air-liquid surface tension, [N/m]
- sigma
Notes
[1] cautions that this should not be applied to coal liquids, and that it will give higher errors at pressures above 500 psi. [1] claims this has an average error of 10.7%.
This function converges to zero at Tc. If Tc is larger than T, 0 is returned as the model would return complex numbers.
References
- 1(1,2,3)
API Technical Data Book: General Properties & Characterization. American Petroleum Institute, 7E, 2005.
Examples
Sample problem in Comments on Procedure 10A3.2.1 of [1];
>>> from fluids.core import F2K, R2K >>> API10A32(T=F2K(60), Tc=R2K(1334), K_W=12.4) 29.577333312096968
Oil-Water Interfacial Tension Correlations¶
- chemicals.interface.Meybodi_Daryasafar_Karimi(rho_water, rho_oil, T, Tc)[source]¶
Calculates the interfacial tension between water and a hydrocabon liquid according to the correlation of [1].
- Parameters
- Returns
- sigma
float
Hydrocarbon-water surface tension [N/m]
- sigma
Notes
Internal units of the equation are g/mL and mN/m.
References
- 1
Kalantari Meybodi, Mahdi, Amin Daryasafar, and Masoud Karimi. “Determination of Hydrocarbon-Water Interfacial Tension Using a New Empirical Correlation.” Fluid Phase Equilibria 415 (May 15, 2016): 42-50. doi:10.1016/j.fluid.2016.01.037.
Examples
>>> Meybodi_Daryasafar_Karimi(980, 760, 580, 914) 0.02893598143089256
Fit Correlations¶
- chemicals.interface.REFPROP_sigma(T, Tc, sigma0, n0, sigma1=0.0, n1=0.0, sigma2=0.0, n2=0.0)[source]¶
Calculates air-liquid surface tension using the REFPROP_sigma [1] regression-based method. Relatively recent, and most accurate.
- Parameters
- T
float
Temperature of fluid [K]
- Tc
float
Critical temperature of fluid [K]
- sigma0
float
First emperical coefficient of a fluid
- n0
float
First emperical exponent of a fluid
- sigma1
float
,optional
Second emperical coefficient of a fluid.
- n1
float
,optional
Second emperical exponent of a fluid.
- sigma2
float
,optional
Third emperical coefficient of a fluid.
- n2
float
,optional
Third emperical exponent of a fluid.
- T
- Returns
- sigma
float
Liquid surface tension, [N/m]
- sigma
Notes
Function as implemented in [1]. No example necessary; results match literature values perfectly. Form of function returns imaginary results when T > Tc; 0 is returned if this is the case.
When fitting parameters to this function, it is easy to end up with a fit that returns negative surface tension near but not quite at the critical point.
References
- 1(1,2)
Diky, Vladimir, Robert D. Chirico, Chris D. Muzny, Andrei F. Kazakov, Kenneth Kroenlein, Joseph W. Magee, Ilmutdin Abdulagatov, and Michael Frenkel. “ThermoData Engine (TDE): Software Implementation of the Dynamic Data Evaluation Concept.” Journal of Chemical Information and Modeling 53, no. 12 (2013): 3418-30. doi:10.1021/ci4005699.
Examples
Parameters for water at 298.15 K
>>> REFPROP_sigma(298.15, 647.096, -0.1306, 2.471, 0.2151, 1.233) 0.07205503890847453
- chemicals.interface.Somayajulu(T, Tc, A, B, C)[source]¶
Calculates air-liquid surface tension using the [1] emperical (parameter-regressed) method. Well regressed, no recent data.
- Parameters
- Returns
- sigma
float
Liquid surface tension, N/m
- sigma
Notes
Presently untested, but matches expected values. Internal units are mN/m. Form of function returns imaginary results when T > Tc; 0.0 is returned if this is the case. Function is claimed valid from the triple to the critical point. Results can be evaluated beneath the triple point.
This function can be accidentally fit to return negative values of surface tension.
References
- 1
Somayajulu, G. R. “A Generalized Equation for Surface Tension from the Triple Point to the Critical Point.” International Journal of Thermophysics 9, no. 4 (July 1988): 559-66. doi:10.1007/BF00503154.
Examples
Water at 300 K
>>> Somayajulu(300, 647.126, 232.713514, -140.18645, -4.890098) 0.07166386387996758
- chemicals.interface.Jasper(T, a, b)[source]¶
Calculates surface tension of a fluid given two parameters, a linear fit in Celcius from [1] with data reprinted in [2].
- Parameters
- Returns
- sigma
float
Surface tension [N/m]
- sigma
Notes
Internal units are mN/m, and degrees Celcius. This function has been checked against several references.
As this is a linear model, negative values of surface tension will eventually arise. 0 is returned in these cases.
References
- 1
Jasper, Joseph J. “The Surface Tension of Pure Liquid Compounds.” Journal of Physical and Chemical Reference Data 1, no. 4 (October 1, 1972): 841-1010. doi:10.1063/1.3253106.
- 2
Speight, James. Lange’s Handbook of Chemistry. 16 edition. McGraw-Hill Professional, 2005.
Examples
>>> Jasper(298.15, 24, 0.0773) 0.0220675
- chemicals.interface.PPDS14(T, Tc, a0, a1, a2)[source]¶
Calculates air-liquid surface tension using the [1] emperical (parameter-regressed) method, called the PPDS 14 equation for surface tension.
- Parameters
- Returns
- sigma
float
Liquid surface tension, [N/m]
- sigma
Notes
If Tc is larger than T, 0 is returned as the model would return complex numbers.
If this model is fit with a0 and a2 as positive values, it is guaranteed to predict only positive values of sigma right up to the critical point. However, a2 is often fit to be a negative value.
References
- 1(1,2)
“ThermoData Engine (TDE103b V10.1) User`s Guide.” https://trc.nist.gov/TDE/Help/TDE103b/Eqns-Pure-SurfaceTension/PPDS14.htm.
- 2
Frenkel, Michael, Robert D. Chirico, Vladimir Diky, Xinjian Yan, Qian Dong, and Chris Muzny. “ThermoData Engine (TDE): Software Implementation of the Dynamic Data Evaluation Concept.” Journal of Chemical Information and Modeling 45, no. 4 (July 1, 2005): 816-38. https://doi.org/10.1021/ci050067b.
Examples
Benzene at 280 K from [1]
>>> PPDS14(T=280, Tc=562.05, a0=0.0786269, a1=1.28646, a2=-0.112304) 0.030559764256249854
- chemicals.interface.Watson_sigma(T, Tc, a1, a2, a3=0.0, a4=0.0, a5=0.0)[source]¶
Calculates air-liquid surface tension using the Watson [1] emperical (parameter-regressed) method developed by NIST.
- Parameters
- Returns
- sigma
float
Liquid surface tension, [N/m]
- sigma
Notes
This expression is also used for enthalpy of vaporization in [1]. The coefficients from NIST TDE for enthalpy of vaporization are kJ/mol.
This model is coded to return 0 values at Tr >= 1. It is otherwise not possible to evaluate this expression at Tr = 1, as log(0) is undefined (although the limit shows the expression converges to 0).
This equation does not have any term forcing it to become near-zero at the critical point, but it cannot be fit so as to produce negative values.
References
- 1(1,2,3)
“ThermoData Engine (TDE103b V10.1) User`s Guide.” https://trc.nist.gov/TDE/Help/TDE103b/Eqns-Pure-SurfaceTension/HVPExpansion-SurfaceTension.htm
Examples
Isooctane at 350 K from [1]:
>>> Watson_sigma(T=350.0, Tc=543.836, a1=-3.02417, a2=1.21792, a3=-5.26877e-9, a4=5.62659e-9, a5=-2.27553e-9) 0.0138340926605649
- chemicals.interface.ISTExpansion(T, Tc, a1, a2, a3=0.0, a4=0.0, a5=0.0)[source]¶
Calculates air-liquid surface tension using the IST expansion [1] emperical (parameter-regressed) method developed by NIST.
- Parameters
- Returns
- sigma
float
Liquid surface tension, [N/m]
- sigma
Notes
This equation hsa a term term forcing it to become zero at the critical point, but it can easily be fit so as to produce negative values at any reduced temperature.
References
- 1(1,2)
“ThermoData Engine (TDE103b V10.1) User`s Guide.” https://trc.nist.gov/TDE/Help/TDE103b/Eqns-Pure-SurfaceTension/ISTExpansion-SurfaceTension.htm
Examples
Diethyl phthalate at 400 K from [1]:
>>> ISTExpansion(T=400.0, Tc=776.0, a1=0.037545, a2=0.0363288) 0.02672100905515996
Fit Coefficients¶
All of these coefficients are lazy-loaded, so they must be accessed as an attribute of this module.
- chemicals.interface.sigma_data_Mulero_Cachadina¶
Data from [5] with
REFPROP_sigma
coefficients.
- chemicals.interface.sigma_data_Jasper_Lange¶
Data as shown in [4] but originally in [3] with
Jasper
coefficients.
- chemicals.interface.sigma_data_Somayajulu¶
Data from [1] with
Somayajulu
coefficients.
- chemicals.interface.sigma_data_Somayajulu2¶
Data from [2] with
Somayajulu
coefficients. These should be preferred over the original coefficients.
- chemicals.interface.sigma_data_VDI_PPDS_11¶
Data from [6] with
chemicals.dippr.EQ106
coefficients.
- 1
Somayajulu, G. R. “A Generalized Equation for Surface Tension from the Triple Point to the Critical Point.” International Journal of Thermophysics 9, no. 4 (July 1988): 559-66. doi:10.1007/BF00503154.
- 2
Mulero, A., M. I. Parra, and I. Cachadina. “The Somayajulu Correlation for the Surface Tension Revisited.” Fluid Phase Equilibria 339 (February 15, 2013): 81-88. doi:10.1016/j.fluid.2012.11.038.
- 3
Jasper, Joseph J. “The Surface Tension of Pure Liquid Compounds.” Journal of Physical and Chemical Reference Data 1, no. 4 (October 1, 1972): 841-1010. doi:10.1063/1.3253106.
- 4
Speight, James. Lange’s Handbook of Chemistry. 16 edition. McGraw-Hill Professional, 2005.
- 5
Mulero, A., I. Cachadiña, and M. I. Parra. “Recommended Correlations for the Surface Tension of Common Fluids.” Journal of Physical and Chemical Reference Data 41, no. 4 (December 1, 2012): 043105. doi:10.1063/1.4768782.
- 6
Gesellschaft, V. D. I., ed. VDI Heat Atlas. 2nd edition. Berlin; New York:: Springer, 2010.
The structure of each dataframe is shown below:
In [1]: import chemicals
In [2]: chemicals.interface.sigma_data_Mulero_Cachadina
Out[2]:
Fluid ... Tmax
CAS ...
60-29-7 Diethyl ether ... 453.15
64-17-5 Ethanol ... 513.15
67-56-1 Methanol ... 508.15
67-64-1 Acetone ... 353.15
71-43-2 Benzene ... 553.15
... ... ... ...
7783-54-2 Nitrogen trifluoride ... 206.36
7789-20-0 D2O ... 642.02
10024-97-2 Nitrous oxide ... 293.15
22410-44-2 RE245cb2 (Methyl-pentafluoroethyl ether) ... 353.41
29118-24-9 R1234ze(E) (trans-1,3,3,3-tetrafluoropropene) ... 373.14
[115 rows x 10 columns]
In [3]: chemicals.interface.sigma_data_Jasper_Lange
Out[3]:
Name a b Tmin Tmax
CAS
55-21-0 Benzamide 47.26 0.0705 402.15 563.15
55-63-0 Glycerol tris(nitrate) 55.74 0.2504 286.15 433.15
56-23-5 Carbon tetrachloride 29.49 0.1224 250.15 349.85
57-06-7 Allyl isothiocyanate 36.76 0.1074 193.15 425.15
60-29-7 Diethyl ether 18.92 0.0908 157.15 307.75
... ... ... ... ... ...
13952-84-6 sec-Butylamine 23.75 0.1057 169.15 336.15
14901-07-6 -Ionone 35.36 0.0950 401.15 401.15
18854-56-3 1,2-Dipropoxyethane 25.03 0.0972 NaN NaN
19550-30-2 2,3-Dimethyl-1-butanol 26.22 0.0992 259.15 391.15
40626-78-6 2-Methylhexane 21.22 0.0966 155.15 363.15
[522 rows x 5 columns]
In [4]: chemicals.interface.sigma_data_Somayajulu
Out[4]:
Chemical Tt Tc A B C
CAS
60-29-7 Ethyl ether 157.00 466.74 61.0417 -6.7908 0.14046
64-17-5 Ethanol 159.00 513.92 111.4452 -146.0229 89.57030
64-19-7 Acetic acid 290.00 592.70 91.9020 -91.7035 77.50720
67-56-1 Methanol 175.59 512.64 122.6257 -199.4044 153.37440
71-23-8 Propanaol 147.00 536.78 107.1238 -133.8128 84.43570
... ... ... ... ... ... ...
10035-10-6 Hydrogen bromide 187.15 363.20 74.0521 20.1043 -30.25710
10102-43-9 Nitric oxide 112.15 180.00 58.6304 97.8722 -33.67390
13465-07-1 Hydrogen disulfide 185.15 572.00 130.1176 -40.6216 4.77160
17778-80-2 Oxygen 54.35 154.58 38.2261 5.6316 -7.74050
19287-45-7 Diborane 104.15 289.80 38.0417 29.7743 -24.26050
[64 rows x 6 columns]
In [5]: chemicals.interface.sigma_data_Somayajulu2
Out[5]:
Chemical Tt Tc A B C
CAS
60-29-7 Ethyl ether 157.00 466.74 61.0417 -6.7908 0.14046
64-17-5 Ethanol 159.00 513.92 111.4452 -146.0229 89.57030
64-19-7 Acetic acid 290.00 592.70 91.9020 -91.7035 77.50720
67-56-1 Methanol 175.59 512.64 122.6257 -199.4044 153.37440
71-23-8 Propanaol 147.00 536.78 107.1238 -133.8128 84.43570
... ... ... ... ... ... ...
10035-10-6 Hydrogen bromide 187.15 363.20 74.0521 20.1043 -30.25710
10102-43-9 Nitric oxide 112.15 180.00 58.6304 97.8722 -33.67390
13465-07-1 Hydrogen disulfide 185.15 572.00 150.6970 -102.9100 56.72580
17778-80-2 Oxygen 54.35 154.58 38.2261 5.6316 -7.74050
19287-45-7 Diborane 104.15 289.80 38.0417 29.7743 -24.26050
[64 rows x 6 columns]
In [6]: chemicals.interface.sigma_data_VDI_PPDS_11
Out[6]:
Chemical Tm Tc ... C D E
CAS ...
50-00-0 Formaldehyde 181.15 408.05 ... 0.00000 0.00000 0.00000
56-23-5 Carbon tetrachloride 250.25 556.35 ... 0.00000 0.00000 0.00000
56-81-5 Glycerol 291.45 850.05 ... 0.00000 0.00000 0.00000
60-29-7 Diethyl ether 156.75 466.63 ... 0.00000 0.00000 0.00000
62-53-3 Aniline 267.15 699.05 ... 0.00000 0.00000 0.00000
... ... ... ... ... ... ... ...
10097-32-2 Bromine 265.85 584.15 ... 0.00000 0.00000 0.00000
10102-43-9 Nitric oxide 112.15 180.15 ... 0.00000 0.00000 0.00000
10102-44-0 Nitrogen dioxide 261.85 431.15 ... 0.00000 0.00000 0.00000
10544-72-6 Dinitrogentetroxide 261.85 431.10 ... 0.00000 0.00000 0.00000
132259-10-0 Air 63.05 132.53 ... 0.06889 0.17918 -0.14564
[272 rows x 8 columns]