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< div class = "document" > < h1 > Thermal Conductivity of Mixtures< / h1 >
< p > The determination of the thermal conductivity of gas mixtures is a central aspect of modeling
transport phenomena, particularly in high-temperature and high-pressure processes. Among the
most established approaches is the empirical equation introduced by Wassiljewa, which was
subsequently refined by Mason and Saxena to improve its applicability to multicomponent systems.
This model offers a reliable means of estimating the thermal conductivity of gas mixtures based
on the properties of the pure components and their molar interactions.< / p >
< p > The thermal conductivity of a gas mixture, denoted by < span class = "inline-equation" > < svg xmlns:xlink = "http://www.w3.org/1999/xlink" width = "24.566351pt" height = "15.0336pt" viewBox = "0 0 24.566351 15.0336" xmlns = "http://www.w3.org/2000/svg" version = "1.1" >
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< / span > , can expressed as
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< / g >
< / g >
< / g >
< / g >
< / svg >
< / span > represents the molar fraction of component < span class = "inline-equation" > < svg xmlns:xlink = "http://www.w3.org/1999/xlink" width = "4.995pt" height = "12.96pt" viewBox = "0 0 4.995 12.96" xmlns = "http://www.w3.org/2000/svg" version = "1.1" >
< defs >
< style type = "text/css" > * { stroke-linejoin : round ; stroke-linecap : butt } < / style >
< / defs >
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< g id = "svg-auto_id_3-figure_1" >
< g id = "svg-auto_id_3-patch_1" >
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< path d = "M 0 12 . 96
L 4.995 12.96
L 4.995 0
L 0 0
z
" style="fill: #ffffff"/>
< / g >
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< g id = "svg-auto_id_3-axes_1" >
< g id = "svg-auto_id_3-text_1" >
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<!-- $i$ -->
< g transform = "translate(1.159937 9.304175) scale(0.1 -0.1)" >
< defs >
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< path id = "svg-auto_id_3-DejaVuSans-Oblique-69" d = "M 1172 4863
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L 1747 4863
L 1606 4134
L 1031 4134
L 1172 4863
z
M 909 3500
L 1484 3500
L 800 0
L 225 0
L 909 3500
z
" transform="scale(0.015625)"/>
< / defs >
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< use xlink:href = "#svg-auto_id_3-DejaVuSans-Oblique-69" transform = "translate(0 0.015625)" / >
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< / g >
< / g >
< / g >
< / g >
< / svg >
< / span > within the mixture,
while < span class = "inline-equation" > < svg xmlns:xlink = "http://www.w3.org/1999/xlink" width = "11.643961pt" height = "15.0336pt" viewBox = "0 0 11.643961 15.0336" xmlns = "http://www.w3.org/2000/svg" version = "1.1" >
< defs >
< style type = "text/css" > * { stroke-linejoin : round ; stroke-linecap : butt } < / style >
< / defs >
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< g id = "svg-auto_id_4-figure_1" >
< g id = "svg-auto_id_4-patch_1" >
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< path d = "M 0 15 . 0336
L 11.643961 15.0336
L 11.643961 0
L 0 0
z
" style="fill: #ffffff"/>
< / g >
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< g id = "svg-auto_id_4-axes_1" >
< g id = "svg-auto_id_4-text_1" >
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<!-- $\lambda_i$ -->
< g transform = "translate(1.86753 10.351343) scale(0.1 -0.1)" >
< defs >
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< path id = "svg-auto_id_4-DejaVuSans-Oblique-3bb" d = "M 2350 4316
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L 3125 0
L 2516 0
L 2038 2588
L 328 0
L -281 0
L 1903 3356
L 1794 3975
Q 1725 4369 1391 4369
L 1091 4369
L 1184 4863
L 1550 4856
Q 2253 4847 2350 4316
z
" transform="scale(0.015625)"/>
2025-05-19 09:44:13 +00:00
< path id = "svg-auto_id_4-DejaVuSans-Oblique-69" d = "M 1172 4863
2025-04-13 22:21:44 +00:00
L 1747 4863
L 1606 4134
L 1031 4134
L 1172 4863
z
M 909 3500
L 1484 3500
L 800 0
L 225 0
L 909 3500
z
" transform="scale(0.015625)"/>
< / defs >
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< use xlink:href = "#svg-auto_id_4-DejaVuSans-Oblique-3bb" transform = "translate(0 0.015625)" / >
< use xlink:href = "#svg-auto_id_4-DejaVuSans-Oblique-69" transform = "translate(59.179688 -16.390625) scale(0.7)" / >
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< / g >
< / g >
< / g >
< / g >
< / svg >
< / span > denotes the thermal conductivity of the pure substance < span class = "inline-equation" > < svg xmlns:xlink = "http://www.w3.org/1999/xlink" width = "4.995pt" height = "12.96pt" viewBox = "0 0 4.995 12.96" xmlns = "http://www.w3.org/2000/svg" version = "1.1" >
< defs >
< style type = "text/css" > * { stroke-linejoin : round ; stroke-linecap : butt } < / style >
< / defs >
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< g id = "svg-auto_id_5-figure_1" >
< g id = "svg-auto_id_5-patch_1" >
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< path d = "M 0 12 . 96
L 4.995 12.96
L 4.995 0
L 0 0
z
" style="fill: #ffffff"/>
< / g >
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< g id = "svg-auto_id_5-axes_1" >
< g id = "svg-auto_id_5-text_1" >
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<!-- $i$ -->
< g transform = "translate(1.159937 9.304175) scale(0.1 -0.1)" >
< defs >
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< path id = "svg-auto_id_5-DejaVuSans-Oblique-69" d = "M 1172 4863
2025-04-13 22:21:44 +00:00
L 1747 4863
L 1606 4134
L 1031 4134
L 1172 4863
z
M 909 3500
L 1484 3500
L 800 0
L 225 0
L 909 3500
z
" transform="scale(0.015625)"/>
< / defs >
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< use xlink:href = "#svg-auto_id_5-DejaVuSans-Oblique-69" transform = "translate(0 0.015625)" / >
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< / g >
< / g >
< / g >
< / g >
< / svg >
< / span > . The denominator
contains the interaction parameter < span class = "inline-equation" > < svg xmlns:xlink = "http://www.w3.org/1999/xlink" width = "15.951782pt" height = "15.8112pt" viewBox = "0 0 15.951782 15.8112" xmlns = "http://www.w3.org/2000/svg" version = "1.1" >
< defs >
< style type = "text/css" > * { stroke-linejoin : round ; stroke-linecap : butt } < / style >
< / defs >
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< g id = "svg-auto_id_6-figure_1" >
< g id = "svg-auto_id_6-patch_1" >
2025-04-13 22:21:44 +00:00
< path d = "M 0 15 . 8112
L 15.951782 15.8112
L 15.951782 0
L 0 0
z
" style="fill: #ffffff"/>
< / g >
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< g id = "svg-auto_id_6-axes_1" >
< g id = "svg-auto_id_6-text_1" >
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<!-- $\Phi_{ij}$ -->
< g transform = "translate(2.075289 10.084656) scale(0.1 -0.1)" >
< defs >
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< path id = "svg-auto_id_6-DejaVuSans-3a6" d = "M 2206 3644
2025-04-13 22:21:44 +00:00
Q 1738 3578 1431 3306
Q 1025 2947 1025 2328
Q 1025 1713 1431 1353
Q 1738 1081 2206 1016
L 2206 3644
z
M 2838 1016
Q 3306 1081 3613 1353
Q 4013 1713 4013 2328
Q 4013 2947 3613 3306
Q 3306 3578 2838 3644
L 2838 1016
z
M 2206 494
Q 1444 563 950 981
Q 359 1481 359 2328
Q 359 3175 950 3678
Q 1441 4100 2206 4169
L 2206 4666
L 2838 4666
L 2838 4169
Q 3600 4097 4091 3678
Q 4678 3175 4678 2328
Q 4678 1484 4091 981
Q 3600 563 2838 491
L 2838 0
L 2206 0
L 2206 494
z
" transform="scale(0.015625)"/>
2025-05-19 09:44:13 +00:00
< path id = "svg-auto_id_6-DejaVuSans-Oblique-69" d = "M 1172 4863
2025-04-13 22:21:44 +00:00
L 1747 4863
L 1606 4134
L 1031 4134
L 1172 4863
z
M 909 3500
L 1484 3500
L 800 0
L 225 0
L 909 3500
z
" transform="scale(0.015625)"/>
2025-05-19 09:44:13 +00:00
< path id = "svg-auto_id_6-DejaVuSans-Oblique-6a" d = "M 928 3500
2025-04-13 22:21:44 +00:00
L 1503 3500
L 813 -63
L 809 -78
Q 694 -675 544 -897
Q 403 -1106 132 -1218
Q -138 -1331 -506 -1331
L -722 -1331
L -628 -844
L -481 -844
Q -144 -844 -1 -703
Q 141 -563 238 -63
L 928 3500
z
M 1197 4863
L 1772 4863
L 1631 4134
L 1056 4134
L 1197 4863
z
" transform="scale(0.015625)"/>
< / defs >
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< use xlink:href = "#svg-auto_id_6-DejaVuSans-3a6" transform = "translate(0 0.09375)" / >
< use xlink:href = "#svg-auto_id_6-DejaVuSans-Oblique-69" transform = "translate(79.667969 -16.3125) scale(0.7)" / >
< use xlink:href = "#svg-auto_id_6-DejaVuSans-Oblique-6a" transform = "translate(99.116211 -16.3125) scale(0.7)" / >
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< / g >
< / g >
< / g >
< / g >
< / svg >
< / span > , which describes the influence of component
< span class = "inline-equation" > < svg xmlns:xlink = "http://www.w3.org/1999/xlink" width = "6.399pt" height = "15.552pt" viewBox = "0 0 6.399 15.552" xmlns = "http://www.w3.org/2000/svg" version = "1.1" >
< defs >
< style type = "text/css" > * { stroke-linejoin : round ; stroke-linecap : butt } < / style >
< / defs >
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< g id = "svg-auto_id_7-figure_1" >
< g id = "svg-auto_id_7-patch_1" >
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< path d = "M 0 15 . 552
L 6.399 15.552
L 6.399 0
L 0 0
z
" style="fill: #ffffff"/>
< / g >
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< g id = "svg-auto_id_7-axes_1" >
< g id = "svg-auto_id_7-text_1" >
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<!-- $j$ -->
< g transform = "translate(1.879487 10.60376) scale(0.1 -0.1)" >
< defs >
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< path id = "svg-auto_id_7-DejaVuSans-Oblique-6a" d = "M 928 3500
2025-04-13 22:21:44 +00:00
L 1503 3500
L 813 -63
L 809 -78
Q 694 -675 544 -897
Q 403 -1106 132 -1218
Q -138 -1331 -506 -1331
L -722 -1331
L -628 -844
L -481 -844
Q -144 -844 -1 -703
Q 141 -563 238 -63
L 928 3500
z
M 1197 4863
L 1772 4863
L 1631 4134
L 1056 4134
L 1197 4863
z
" transform="scale(0.015625)"/>
< / defs >
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< use xlink:href = "#svg-auto_id_7-DejaVuSans-Oblique-6a" transform = "translate(0 0.015625)" / >
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< / g >
< / g >
< / g >
< / g >
< / svg >
< / span > on the transport properties of component < span class = "inline-equation" > < svg xmlns:xlink = "http://www.w3.org/1999/xlink" width = "4.995pt" height = "12.96pt" viewBox = "0 0 4.995 12.96" xmlns = "http://www.w3.org/2000/svg" version = "1.1" >
< defs >
< style type = "text/css" > * { stroke-linejoin : round ; stroke-linecap : butt } < / style >
< / defs >
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< g id = "svg-auto_id_8-figure_1" >
< g id = "svg-auto_id_8-patch_1" >
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< path d = "M 0 12 . 96
L 4.995 12.96
L 4.995 0
L 0 0
z
" style="fill: #ffffff"/>
< / g >
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< g id = "svg-auto_id_8-axes_1" >
< g id = "svg-auto_id_8-text_1" >
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<!-- $i$ -->
< g transform = "translate(1.159937 9.304175) scale(0.1 -0.1)" >
< defs >
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< path id = "svg-auto_id_8-DejaVuSans-Oblique-69" d = "M 1172 4863
2025-04-13 22:21:44 +00:00
L 1747 4863
L 1606 4134
L 1031 4134
L 1172 4863
z
M 909 3500
L 1484 3500
L 800 0
L 225 0
L 909 3500
z
" transform="scale(0.015625)"/>
< / defs >
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< use xlink:href = "#svg-auto_id_8-DejaVuSans-Oblique-69" transform = "translate(0 0.015625)" / >
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< / g >
< / g >
< / g >
< / g >
< / svg >
< / span > .< / p >
< p > The interaction parameter < span class = "inline-equation" > < svg xmlns:xlink = "http://www.w3.org/1999/xlink" width = "15.951782pt" height = "15.8112pt" viewBox = "0 0 15.951782 15.8112" xmlns = "http://www.w3.org/2000/svg" version = "1.1" >
< defs >
< style type = "text/css" > * { stroke-linejoin : round ; stroke-linecap : butt } < / style >
< / defs >
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< g id = "svg-auto_id_9-figure_1" >
< g id = "svg-auto_id_9-patch_1" >
2025-04-13 22:21:44 +00:00
< path d = "M 0 15 . 8112
L 15.951782 15.8112
L 15.951782 0
L 0 0
z
" style="fill: #ffffff"/>
< / g >
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< g id = "svg-auto_id_9-axes_1" >
< g id = "svg-auto_id_9-text_1" >
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<!-- $\Phi_{ij}$ -->
< g transform = "translate(2.075289 10.084656) scale(0.1 -0.1)" >
< defs >
2025-05-19 09:44:13 +00:00
< path id = "svg-auto_id_9-DejaVuSans-3a6" d = "M 2206 3644
2025-04-13 22:21:44 +00:00
Q 1738 3578 1431 3306
Q 1025 2947 1025 2328
Q 1025 1713 1431 1353
Q 1738 1081 2206 1016
L 2206 3644
z
M 2838 1016
Q 3306 1081 3613 1353
Q 4013 1713 4013 2328
Q 4013 2947 3613 3306
Q 3306 3578 2838 3644
L 2838 1016
z
M 2206 494
Q 1444 563 950 981
Q 359 1481 359 2328
Q 359 3175 950 3678
Q 1441 4100 2206 4169
L 2206 4666
L 2838 4666
L 2838 4169
Q 3600 4097 4091 3678
Q 4678 3175 4678 2328
Q 4678 1484 4091 981
Q 3600 563 2838 491
L 2838 0
L 2206 0
L 2206 494
z
" transform="scale(0.015625)"/>
2025-05-19 09:44:13 +00:00
< path id = "svg-auto_id_9-DejaVuSans-Oblique-69" d = "M 1172 4863
2025-04-13 22:21:44 +00:00
L 1747 4863
L 1606 4134
L 1031 4134
L 1172 4863
z
M 909 3500
L 1484 3500
L 800 0
L 225 0
L 909 3500
z
" transform="scale(0.015625)"/>
2025-05-19 09:44:13 +00:00
< path id = "svg-auto_id_9-DejaVuSans-Oblique-6a" d = "M 928 3500
2025-04-13 22:21:44 +00:00
L 1503 3500
L 813 -63
L 809 -78
Q 694 -675 544 -897
Q 403 -1106 132 -1218
Q -138 -1331 -506 -1331
L -722 -1331
L -628 -844
L -481 -844
Q -144 -844 -1 -703
Q 141 -563 238 -63
L 928 3500
z
M 1197 4863
L 1772 4863
L 1631 4134
L 1056 4134
L 1197 4863
z
" transform="scale(0.015625)"/>
< / defs >
2025-05-19 09:44:13 +00:00
< use xlink:href = "#svg-auto_id_9-DejaVuSans-3a6" transform = "translate(0 0.09375)" / >
< use xlink:href = "#svg-auto_id_9-DejaVuSans-Oblique-69" transform = "translate(79.667969 -16.3125) scale(0.7)" / >
< use xlink:href = "#svg-auto_id_9-DejaVuSans-Oblique-6a" transform = "translate(99.116211 -16.3125) scale(0.7)" / >
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< / g >
< / g >
< / g >
< / g >
< / svg >
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< / span > is given by the relation shown in equation < a href = "#pyld-ref-eq:interaction-parameter" > 2< / a > .< / p > < div class = "equation-container" id = "pyld-ref-eq:interaction-parameter" > < div class = "equation" > < svg xmlns:xlink = "http://www.w3.org/1999/xlink" width = "221.766721pt" height = "26.13pt" viewBox = "0 0 221.766721 26.13" xmlns = "http://www.w3.org/2000/svg" version = "1.1" >
2025-04-13 22:21:44 +00:00
< defs >
< style type = "text/css" > * { stroke-linejoin : round ; stroke-linecap : butt } < / style >
< / defs >
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< g id = "svg-eq:interaction-parameter-figure_1" >
< g id = "svg-eq:interaction-parameter-patch_1" >
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< path d = "M 0 26 . 13
L 221.766721 26.13
L 221.766721 0
L 0 0
z
" style="fill: #ffffff"/>
< / g >
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< g id = "svg-eq:interaction-parameter-axes_1" >
< g id = "svg-eq:interaction-parameter-text_1" >
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<!-- $\Phi_{ij} = \frac{1}{\sqrt{8}} \left(1 + \frac{M_i}{M_j} \right)^{ - 1/2} \left[ 1 + \left( \frac{\lambda_i}{\lambda_j} \right)^{1/2} \left( \frac{M_j}{M_i} \right)^{1/4} \right]^2$ -->
< g transform = "translate(21.255444 15.69565) scale(0.1 -0.1)" >
< defs >
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< path id = "svg-eq:interaction-parameter-DejaVuSans-3a6" d = "M 2206 3644
2025-04-13 22:21:44 +00:00
Q 1738 3578 1431 3306
Q 1025 2947 1025 2328
Q 1025 1713 1431 1353
Q 1738 1081 2206 1016
L 2206 3644
z
M 2838 1016
Q 3306 1081 3613 1353
Q 4013 1713 4013 2328
Q 4013 2947 3613 3306
Q 3306 3578 2838 3644
L 2838 1016
z
M 2206 494
Q 1444 563 950 981
Q 359 1481 359 2328
Q 359 3175 950 3678
Q 1441 4100 2206 4169
L 2206 4666
L 2838 4666
L 2838 4169
Q 3600 4097 4091 3678
Q 4678 3175 4678 2328
Q 4678 1484 4091 981
Q 3600 563 2838 491
L 2838 0
L 2206 0
L 2206 494
z
" transform="scale(0.015625)"/>
2025-05-19 09:44:13 +00:00
< path id = "svg-eq:interaction-parameter-DejaVuSans-Oblique-69" d = "M 1172 4863
2025-04-13 22:21:44 +00:00
L 1747 4863
L 1606 4134
L 1031 4134
L 1172 4863
z
M 909 3500
L 1484 3500
L 800 0
L 225 0
L 909 3500
z
" transform="scale(0.015625)"/>
2025-05-19 09:44:13 +00:00
< path id = "svg-eq:interaction-parameter-DejaVuSans-Oblique-6a" d = "M 928 3500
2025-04-13 22:21:44 +00:00
L 1503 3500
L 813 -63
L 809 -78
Q 694 -675 544 -897
Q 403 -1106 132 -1218
Q -138 -1331 -506 -1331
L -722 -1331
L -628 -844
L -481 -844
Q -144 -844 -1 -703
Q 141 -563 238 -63
L 928 3500
z
M 1197 4863
L 1772 4863
L 1631 4134
L 1056 4134
L 1197 4863
z
" transform="scale(0.015625)"/>
2025-05-19 09:44:13 +00:00
< path id = "svg-eq:interaction-parameter-DejaVuSans-3d" d = "M 678 2906
2025-04-13 22:21:44 +00:00
L 4684 2906
L 4684 2381
L 678 2381
L 678 2906
z
M 678 1631
L 4684 1631
L 4684 1100
L 678 1100
L 678 1631
z
" transform="scale(0.015625)"/>
2025-05-19 09:44:13 +00:00
< path id = "svg-eq:interaction-parameter-DejaVuSans-31" d = "M 794 531
2025-04-13 22:21:44 +00:00
L 1825 531
L 1825 4091
L 703 3866
L 703 4441
L 1819 4666
L 2450 4666
L 2450 531
L 3481 531
L 3481 0
L 794 0
L 794 531
z
" transform="scale(0.015625)"/>
2025-05-19 09:44:13 +00:00
< path id = "svg-eq:interaction-parameter-STIXSizeOneSym-Regular-221a" d = "M 6970 9933
2025-04-13 22:21:44 +00:00
L 3373 -1888
L 3104 -1888
L 1626 2918
Q 1555 3149 1465 3251
Q 1376 3354 1229 3354
Q 1011 3354 794 3181
L 717 3309
L 1766 4115
L 1926 4115
L 3379 -602
L 3405 -602
L 6605 9933
L 6970 9933
z
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Molar masses and thermal conductivity of the pure substances are listed in table < a href = "#pyld-ref-table:gas-probs" > 1< / a > .
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The structure of this expression illustrates the nonlinear dependence of the interaction term on
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both the molar mass ratio and the square root of the conductivity ratio of the involved species.< / p > < div id = "pyld-ref-table:gas-probs" >
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< table id = "T_gas_probs" >
< caption > Table 1: Properties of some gases< / caption >
< thead >
< tr >
< th id = "T_gas_probs_level0_col0" class = "col_heading level0 col0" > Gas< / th >
< th id = "T_gas_probs_level0_col1" class = "col_heading level0 col1" > Molar mass in g/mol< / th >
< th id = "T_gas_probs_level0_col2" class = "col_heading level0 col2" > Thermal conductivity in W/m/K< / th >
< / tr >
< / thead >
< tbody >
< tr >
< td id = "T_gas_probs_row0_col0" class = "data row0 col0" > H2< / td >
< td id = "T_gas_probs_row0_col1" class = "data row0 col1" > 2.016< / td >
< td id = "T_gas_probs_row0_col2" class = "data row0 col2" > 0.1805< / td >
< / tr >
< tr >
< td id = "T_gas_probs_row1_col0" class = "data row1 col0" > O2< / td >
< td id = "T_gas_probs_row1_col1" class = "data row1 col1" > 32.00< / td >
< td id = "T_gas_probs_row1_col2" class = "data row1 col2" > 0.0263< / td >
< / tr >
< tr >
< td id = "T_gas_probs_row2_col0" class = "data row2 col0" > N2< / td >
< td id = "T_gas_probs_row2_col1" class = "data row2 col1" > 28.02< / td >
< td id = "T_gas_probs_row2_col2" class = "data row2 col2" > 0.0258< / td >
< / tr >
< tr >
< td id = "T_gas_probs_row3_col0" class = "data row3 col0" > CO2< / td >
< td id = "T_gas_probs_row3_col1" class = "data row3 col1" > 44.01< / td >
< td id = "T_gas_probs_row3_col2" class = "data row3 col2" > 0.0166< / td >
< / tr >
< tr >
< td id = "T_gas_probs_row4_col0" class = "data row4 col0" > CH4< / td >
< td id = "T_gas_probs_row4_col1" class = "data row4 col1" > 16.04< / td >
< td id = "T_gas_probs_row4_col2" class = "data row4 col2" > 0.0341< / td >
< / tr >
< tr >
< td id = "T_gas_probs_row5_col0" class = "data row5 col0" > Ar< / td >
< td id = "T_gas_probs_row5_col1" class = "data row5 col1" > 39.95< / td >
< td id = "T_gas_probs_row5_col2" class = "data row5 col2" > 0.0177< / td >
< / tr >
< tr >
< td id = "T_gas_probs_row6_col0" class = "data row6 col0" > He< / td >
< td id = "T_gas_probs_row6_col1" class = "data row6 col1" > 4.0026< / td >
< td id = "T_gas_probs_row6_col2" class = "data row6 col2" > 0.1513< / td >
< / tr >
< / tbody >
< / table >
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< / div > < p > This formulation acknowledges that the transport properties of a gas mixture are not a simple
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linear combination of the individual conductivities. Rather, they are governed by intermolecular
interactions, which affect the energy exchange and diffusion behavior of each component. These
interactions are particularly significant at elevated pressures or in cases where the gas components
exhibit widely differing molecular masses or transport properties.< / p >
< p > The equation proposed by Wassiljewa and refined by Mason and Saxena assumes that binary interactions
dominate the behavior of the mixture, while higher-order (three-body or more) interactions are
neglected. It also presumes that the gases approximate ideal behavior, although in practical
applications, moderate deviations from ideality are tolerated without significant loss of accuracy.
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In figure < a href = "#pyld-ref-fig:mixture" > 1< / a > the resulting thermal conductivity of an H2/CO2-mixture is shown.< / p > < div id = "pyld-ref-fig:mixture" class = "figure" > < svg xmlns:xlink = "http://www.w3.org/1999/xlink" width = "460.8pt" height = "345.6pt" viewBox = "0 0 460.8 345.6" xmlns = "http://www.w3.org/2000/svg" version = "1.1" >
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< / span > is essential
for the prediction of heat transfer in systems such as membrane modules, chemical reactors, and
combustion chambers. In the context of membrane-based gas separation, for instance, the thermal
conductivity of the gas mixture influences the local temperature distribution, which in turn affects
both the permeation behavior and the structural stability of the membrane.< / p >
< p > It is important to note that the calculated mixture conductivity reflects only the gas phase
behavior. In porous systems such as carbon membranes, additional effects must be considered.
These include the solid-phase thermal conduction through the membrane matrix, radiative transport
in pore channels at high temperatures, and transport in the Knudsen regime for narrow pores.
To account for these complexities, models based on effective medium theory, such as those of
Maxwell-Eucken or Bruggeman, are frequently employed. These models combine the conductivities of
individual phases (gas and solid) with geometrical factors that reflect the morphology of the
porous structure.< / p >
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< hr >
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< p > Expanded by more or less sensible AI jabbering; based on: < a href = "https://doi.org/10.14279/depositonce-7390" > doi:10.14279/depositonce-7390< / a > < / p >
< / div >
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