Simple Direct Relationship between Scaled Viscosity and a Dimensionless Calorimetric Parameter for Saturated Liquids

Abstract

The relationship between the transport property and thermodynamic property was explored in this paper. More specifically, a dimensionless calorimetric parameter (DCP) was employed in order to predict the viscosity of different fluids for the first time. It was found that a strong linear correlation between the macroscopically scaled viscosity and the DCP of different fluids in saturated liquid states takes place. Additionally, the values of linearly correlated slopes K for each fluid were found to be in a narrow range (0.411 ± 0.034). Based on this, a quasi-universal viscosity prediction model was proposed. Fourteen fluids representing different molecular structures were selected, and the reliability of the theoretical framework was verified through comparison with experimental data. The results indicated that the correlation approach was very satisfactory with a maximum average absolute deviation (AAD) of 4.40%. Furthermore, by correlating the slopes with the fluid-specific parameters, a generalized function with no adjusting parameters was finally established. Compared with experimental data, the AADs were all located within 7.23%, except those for R125 and R143a. This work provides a convenient calculation method for the estimation of the transport property (viscosity) of different fluids only from the respective thermodynamic properties.

Linking Thermal Conductivity and Self-Diffusion Coefficient with a Simple Dimensionless Calorimetric Parameter for Saturated Liquids

“…Therefore, with the knowledge of the precise calorimetric properties of the working medium and the fluid-specific coefficients, the thermal conductivity and self-diffusion coefficient could be relatively conveniently evaluated. It should be noted that consistent with the universal RES and DCP-η relation, 29 the above linear models also failed to describe liquid systems containing hydrogen bonds (water, methanol, ethanol, etc.). The transport properties of associating fluids, on the other hand, might be obtained from the modified thermal conductivity through reference thermal conductivity as proposed by Hopp and Gross, 19,20 or an improved linking model is required.…”

“…To link the thermal conductivity λ and self-diffusion coefficient D with the thermodynamic properties, more specifically, calorimetric parameters which can be obtained accurately, DCP-based correlation models were conceived based on the following concept. The DCP was proposed as where w is the speed of sound, c p is the isobaric heat capacity, c v is the isochoric heat capacity, R = R m / M is the individual gas constant in J·kg –1 ·K –1 , R m = 8.3144598 J·mol –1 ·K –1 is the universal gas constant, M is the molar mass, and T is the temperature in K. According to the classic thermodynamic relation, the DCP can be expressed in a Helmholtz free energy-based equation as where δ = ρ/ρ c is the reduced density, Φ r is the dimensionless residual free energy, and . This equation shows that the DCP only depends on the residual part of the Helmholtz free energy, which means it is affected solely by the molecular interactions and thus more likely to show similar behavior according to the success applications of the corresponding state principal.…”

“…We modified and proposed an applicable form of the Stokes–Einstein equation for the estimation and verification of the dimensionless self-diffusion coefficient ln­( D *) with a correlation coefficient of 0.984 wherein the macroscopically scaled viscosity η̃ was calculated as …”

“…Inspired by this fascinating link, a new dimensionless calorimetric parameter (DCP) containing only the residual term extracted from the Helmholtz free energy relation was proposed in our previous work . The quasi-universal relation between the DCP and viscosity was successfully developed for different nonassociation systems ( ), which provided an easily accessible way for property estimation.…”

“…To link the thermal conductivity λ and self-diffusion coefficient D with the thermodynamic properties, more specifically, calorimetric parameters which can be obtained accurately, DCP-based correlation models were conceived based on the following concept. The DCP was proposed as29…”