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Estimation of Thermal Conductivities for Binary and Ternary Liquid Mixtures Using Excess Thermal Conductivity Model

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Abstract

The objective of this work is the estimation of thermal conductivities for binary and ternary liquid mixtures using an excess thermal conductivity model. Firstly, calculation methods for thermal conductivities of ideal solutions are discussed using four models, including mole fraction average, One intuitively similar to Eyring’s model for kinematic viscosity and mass fraction average. Next, the Wilson-ThermConduct model was applied as the excess thermal conductivity model. The binary parameters in the model were determined from non-aqueous and aqueous binary thermal conductivity data. The prediction of the thermal conductivities for the ternary systems was done using the binary parameters of the binary constituent systems. The model presented in this work gave a 0.66% average absolute relative deviation of overall datasets. The evaluated results were compared with those using the mass fraction average (ideal) model, the Vredeveld’s power-law model, and Rowley’s local composition model with NRTL parameters determined from VLE data.

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Abbreviations

AAD:

Average absolute deviation (W·m−1·K−1)

AARD:

Average absolute relative deviation (%)

F obj :

Objective function

G :

Gibbs free energy

G ij :

Binary parameter of the NRTL model

k :

Eyring’s empirical constant

M :

Molecular weight

NC:

Number of components

NDP:

Number of data points

PR:

Peng–Robinson

PT:

Patel–Teja

R :

Gas constant = 8.314 (J·mol−1·K−1)

T :

Temperature (K)

TC:

Thermal conductivity

w :

Liquid mass fraction

x :

Liquid mole fraction

λ:

Thermal conductivity (W·m−1·K−1)

Λij, Λji :

Parameter in the Wilson-ThermConduct model

Δ1 :

Absolute deviation between experimental and calculated thermal conductivities (W·m−1·K−1) defined as λexptl.− λcalcd.

Δ2 :

Relative deviation between experimental and calculated thermal conductivities defined as (λexptl.− λcalcd.)/λexptl.

E:

Excess property

1, 2, i, j :

Components 1, 2, i, and j

calcd.:

Calculated

exptl.:

Experimental

max.:

Maximum

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Authors and Affiliations

  1. Department of Materials and Applied Chemistry, Nihon University, 1-8-14 Kanda Surugadai, Chiyoda-ku, Tokyo, 101-8308, Japan

    Hiroyuki Matsuda, Katsumi Tochigi & Kiyofumi Kurihara

  2. Department of Applied Chemistry, Chuo University, 1-13-27 Kasuga, Bunkyo-ku, Tokyo, 112-8551, Japan

    Toshitaka Funazukuri

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  1. Hiroyuki Matsuda
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  2. Katsumi Tochigi
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  3. Kiyofumi Kurihara
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  4. Toshitaka Funazukuri
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Contributions

HM and KT contributed to conceptualization, formal analysis, investigation, methodology, software, and writing—original draft preparation; KT contributed to data curation; HM and KK contributed to funding acquisition and resources; HM contributed to project administration; KT and TF contributed to supervision; TF contributed to validation; KT contributed to visualization; KK and TF contributed to writing—review and editing.

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Correspondence to Hiroyuki Matsuda.

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Matsuda, H., Tochigi, K., Kurihara, K. et al. Estimation of Thermal Conductivities for Binary and Ternary Liquid Mixtures Using Excess Thermal Conductivity Model. J Solution Chem 52, 105–133 (2023). https://doi.org/10.1007/s10953-022-01220-9

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