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# It should be noted that there are other methods

It should be noted that there are other methods, such as artificial intelligence, like Artificial Neural Networks/ANN (such as PSO-ANN, ICA-ANN), Least Square Support Vector Machine/LSSVM, etc. [10], [11], [12], [13], [14], [15], [16], [17], [18], or molecular simulations, for modeling the fluid's viscosity. The later models are out of the scope of the present study.
In this study, we have examined the capability of CPA ƒ-theory model in modeling viscosity of alcohols. It must be said that the performance of the mentioned model, indicates better results compared to PR ƒ-theory and SRK ƒ-theory models for systems with alcohols. Also, following assumptions have been used in this study:

Friction theory
Quiñones-Cisneros et al. in 2000 introduced the friction theory (f-theory) for modeling the viscosity by using the basic principles of classical mechanics and thermodynamics [5]. The basic difference between f-theory and other methods used for modeling the viscosity is that the mechanical properties of the viscosity is more important than its transport properties in increasing the viscosity of diluted gas [5]. In f-theory, the viscosity depends to the pressure which is a main variable. Friction theory can estimate the viscosity from low to very high pressures by using EOS with high accuracy [5]. Consistent performance of pressure–viscosity takes place, as the EOS for good performance of pressure-temperature has been optimized [5]. In f-theory the total viscosity (η) is divided in two terms of diluted gases viscosity (ηο) and residual Friction (ηƒ) [5],
The dilute gas viscosity (ηο) is defined as the viscosity zero density limit and to the kinetic theory of gases [19] and is related to Chapman–Enskog theory [5], [19], [20]. Based on Chapman–Enskog theory and empirical L-a-Hydroxyglutaric acid disodium salt for the reduced collision integral, Chung et al. [21] did an empirical dilute gas viscosity model incorporating structural effects in order to apply the model to polar, and hydrogen bonding fluids over wide ranges of temperature [7], [19], [20], [21].
And reduced collision integral (Ω⁎) corresponds to:
With
The dilute gas viscosity is obtained from Eq. (2) and its unit is micro-poise [μP]. T is temperature with unit of [K] and v critical volume with unit of [cm3/mol]. Molecular weight is Mw and Tc is critical temperature. The best performance of this model is at a time that the real critical volume of fluid vc be used. And Fc is defined as below [22], [23]:
ω is the acentric factor, μr is the dimensionless dipole moment, and χ is the correction factor for effects of hydrogen bonding associating substances, such as alcohols [6]:
μ is the dipole moment with unit of Debye. Also Chung et al. [21] offered correction factor for coverage the hydrogen bonding effects of alcohol, as the following empirical expression [6]:
N is the number of OH groups in the alcohol and M is the molecular weight.
Next term is residual friction (η) which creates a connection between the van der Waals attraction and repulsive pressure terms and Amontons–Coulomb friction law [5]. The residual friction term shows by the quadratic model as following [5]:
Ka, K and K respectively are linear attractive friction coefficient and linear repulsive friction coefficient and quadratic repulsive friction coefficient. P and P are van der Waals repulsive and attraction pressures. Attraction and repulsive pressures are created through simple cubic equations of state such as SRK-EOS [8] and PR-EOS [9]. The capability of f-theory was shown by Quiñones-Cisneros et al. [5] in 2000 with detailed modeling of the viscosity of n-alkanes and its mixtures for low to very high pressures in the wide ranges of temperature near the triple point with the conditions of light supercritical gas [5].
Quiñones-Cisneros et al. solved the temperature dependences of different friction coefficients based on the following parametric laws [5], [6]: