Shuai Lu, Dandan Li, Bin Lan, Chuanlin Fan, Fan Xu, Ji Xu, Bidan Zhao, Zheng Zou, Hongzhong Li, Junwu Wang, Qingshan Zhu
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{"title":"扩大多室流化床中多分散颗粒平均停留时间比的可控范围:粗粒度 CFD-DEM 研究","authors":"Shuai Lu, Dandan Li, Bin Lan, Chuanlin Fan, Fan Xu, Ji Xu, Bidan Zhao, Zheng Zou, Hongzhong Li, Junwu Wang, Qingshan Zhu","doi":"10.1021/acs.iecr.4c02112","DOIUrl":null,"url":null,"abstract":"The residence time of polydisperse particles is crucial for their simultaneous conversion in a fluidized bed. This study focuses on regulating the residence time of polydisperse particles to expand their controllable range by optimizing the reactor design and operation step-by-step. The mean residence time (MRT) ratio of coarse and fine particles (<i></i><span style=\"color: inherit;\"></span><span data-mathml='<math xmlns=\"http://www.w3.org/1998/Math/MathML\" display=\"inline\"><msubsup><mrow><mi>t</mi></mrow><mrow><mi>p</mi></mrow><mrow><mi>c</mi></mrow></msubsup><mo>/</mo><msubsup><mrow><mi>t</mi></mrow><mrow><mi>p</mi></mrow><mrow><mi>f</mi></mrow></msubsup></math>' role=\"presentation\" style=\"position: relative;\" tabindex=\"0\"><nobr aria-hidden=\"true\"><span style=\"width: 2.564em; display: inline-block;\"><span style=\"display: inline-block; position: relative; width: 2.103em; height: 0px; font-size: 122%;\"><span style=\"position: absolute; clip: rect(1.078em, 1002.1em, 2.769em, -999.997em); top: -2.2em; left: 0em;\"><span><span><span style=\"display: inline-block; position: relative; width: 0.771em; height: 0px;\"><span style=\"position: absolute; clip: rect(3.23em, 1000.31em, 4.152em, -999.997em); top: -3.993em; left: 0em;\"><span><span style=\"font-family: MathJax_Math-italic;\">t</span></span><span style=\"display: inline-block; width: 0px; height: 3.998em;\"></span></span><span style=\"position: absolute; clip: rect(3.537em, 1000.36em, 4.152em, -999.997em); top: -4.352em; left: 0.361em;\"><span><span style=\"font-size: 70.7%; font-family: MathJax_Math-italic;\">c</span></span><span style=\"display: inline-block; width: 0px; height: 3.998em;\"></span></span><span style=\"position: absolute; clip: rect(3.537em, 1000.41em, 4.306em, -999.997em); top: -3.737em; left: 0.361em;\"><span><span style=\"font-size: 70.7%; font-family: MathJax_Math-italic;\">p</span></span><span style=\"display: inline-block; width: 0px; height: 3.998em;\"></span></span></span></span><span style=\"font-family: MathJax_Main;\">/</span><span><span style=\"display: inline-block; position: relative; width: 0.822em; height: 0px;\"><span style=\"position: absolute; clip: rect(3.23em, 1000.31em, 4.152em, -999.997em); top: -3.993em; left: 0em;\"><span><span style=\"font-family: MathJax_Math-italic;\">t</span></span><span style=\"display: inline-block; width: 0px; height: 3.998em;\"></span></span><span style=\"position: absolute; clip: rect(3.332em, 1000.46em, 4.306em, -999.997em); top: -4.506em; left: 0.361em;\"><span><span style=\"font-size: 70.7%; font-family: MathJax_Math-italic;\">f<span style=\"display: inline-block; overflow: hidden; height: 1px; width: 0.054em;\"></span></span></span><span style=\"display: inline-block; width: 0px; height: 3.998em;\"></span></span><span style=\"position: absolute; clip: rect(3.537em, 1000.41em, 4.306em, -999.997em); top: -3.84em; left: 0.361em;\"><span><span style=\"font-size: 70.7%; font-family: MathJax_Math-italic;\">p</span></span><span style=\"display: inline-block; width: 0px; height: 3.998em;\"></span></span></span></span></span><span style=\"display: inline-block; width: 0px; height: 2.205em;\"></span></span></span><span style=\"display: inline-block; overflow: hidden; vertical-align: -0.559em; border-left: 0px solid; width: 0px; height: 1.816em;\"></span></span></nobr><span role=\"presentation\"><math display=\"inline\" xmlns=\"http://www.w3.org/1998/Math/MathML\"><msubsup><mrow><mi>t</mi></mrow><mrow><mi>p</mi></mrow><mrow><mi>c</mi></mrow></msubsup><mo>/</mo><msubsup><mrow><mi>t</mi></mrow><mrow><mi>p</mi></mrow><mrow><mi>f</mi></mrow></msubsup></math></span></span><script type=\"math/mml\"><math display=\"inline\"><msubsup><mrow><mi>t</mi></mrow><mrow><mi>p</mi></mrow><mrow><mi>c</mi></mrow></msubsup><mo>/</mo><msubsup><mrow><mi>t</mi></mrow><mrow><mi>p</mi></mrow><mrow><mi>f</mi></mrow></msubsup></math></script>) increased significantly with increasing elutriation pipe width of the multiple-chamber fluidized bed, thus enabling the MRT ratio to exceed <i></i><span style=\"color: inherit;\"></span><span data-mathml='<math xmlns=\"http://www.w3.org/1998/Math/MathML\" display=\"inline\"><msup><mrow><mrow><mo stretchy=\"false\">(</mo></mrow><mrow><mrow><msubsup><mrow><mi>d</mi></mrow><mrow><mi>p</mi></mrow><mrow><mi>c</mi></mrow></msubsup></mrow><mrow><mo>/</mo></mrow><mrow><msubsup><mrow><mi>d</mi></mrow><mrow><mi>p</mi></mrow><mrow><mi>f</mi></mrow></msubsup></mrow></mrow><mrow><mo stretchy=\"false\">)</mo></mrow></mrow><mrow><mn>2</mn></mrow></msup></math>' role=\"presentation\" style=\"position: relative;\" tabindex=\"0\"><nobr aria-hidden=\"true\"><span style=\"width: 4.511em; display: inline-block;\"><span style=\"display: inline-block; position: relative; width: 3.691em; height: 0px; font-size: 122%;\"><span style=\"position: absolute; clip: rect(0.925em, 1003.69em, 2.769em, -999.997em); top: -2.2em; left: 0em;\"><span><span><span style=\"display: inline-block; position: relative; width: 3.691em; height: 0px;\"><span style=\"position: absolute; clip: rect(2.923em, 1003.18em, 4.562em, -999.997em); top: -3.993em; left: 0em;\"><span><span><span style=\"font-family: MathJax_Main;\">(</span></span><span><span><span><span style=\"display: inline-block; position: relative; width: 0.976em; height: 0px;\"><span style=\"position: absolute; clip: rect(3.128em, 1000.51em, 4.152em, -999.997em); top: -3.993em; left: 0em;\"><span><span style=\"font-family: MathJax_Math-italic;\">d<span style=\"display: inline-block; overflow: hidden; height: 1px; width: 0.003em;\"></span></span></span><span style=\"display: inline-block; width: 0px; height: 3.998em;\"></span></span><span style=\"position: absolute; clip: rect(3.537em, 1000.36em, 4.152em, -999.997em); top: -4.403em; left: 0.566em;\"><span><span style=\"font-size: 70.7%; font-family: MathJax_Math-italic;\">c</span></span><span style=\"display: inline-block; width: 0px; height: 3.998em;\"></span></span><span style=\"position: absolute; clip: rect(3.537em, 1000.41em, 4.306em, -999.997em); top: -3.737em; left: 0.515em;\"><span><span style=\"font-size: 70.7%; font-family: MathJax_Math-italic;\">p</span></span><span style=\"display: inline-block; width: 0px; height: 3.998em;\"></span></span></span></span></span><span><span style=\"font-family: MathJax_Main;\">/</span></span><span><span><span style=\"display: inline-block; position: relative; width: 1.027em; height: 0px;\"><span style=\"position: absolute; clip: rect(3.128em, 1000.51em, 4.152em, -999.997em); top: -3.993em; left: 0em;\"><span><span style=\"font-family: MathJax_Math-italic;\">d<span style=\"display: inline-block; overflow: hidden; height: 1px; width: 0.003em;\"></span></span></span><span style=\"display: inline-block; width: 0px; height: 3.998em;\"></span></span><span style=\"position: absolute; clip: rect(3.332em, 1000.46em, 4.306em, -999.997em); top: -4.403em; left: 0.566em;\"><span><span style=\"font-size: 70.7%; font-family: MathJax_Math-italic;\">f<span style=\"display: inline-block; overflow: hidden; height: 1px; width: 0.054em;\"></span></span></span><span style=\"display: inline-block; width: 0px; height: 3.998em;\"></span></span><span style=\"position: absolute; clip: rect(3.537em, 1000.41em, 4.306em, -999.997em); top: -3.737em; left: 0.515em;\"><span><span style=\"font-size: 70.7%; font-family: MathJax_Math-italic;\">p</span></span><span style=\"display: inline-block; width: 0px; height: 3.998em;\"></span></span></span></span></span></span><span><span style=\"font-family: MathJax_Main;\">)</span></span></span><span style=\"display: inline-block; width: 0px; height: 3.998em;\"></span></span><span style=\"position: absolute; top: -4.659em; left: 3.281em;\"><span><span style=\"font-size: 70.7%; font-family: MathJax_Main;\">2</span></span><span style=\"display: inline-block; width: 0px; height: 3.998em;\"></span></span></span></span></span><span style=\"display: inline-block; width: 0px; height: 2.205em;\"></span></span></span><span style=\"display: inline-block; overflow: hidden; vertical-align: -0.559em; border-left: 0px solid; width: 0px; height: 1.941em;\"></span></span></nobr><span role=\"presentation\"><math display=\"inline\" xmlns=\"http://www.w3.org/1998/Math/MathML\"><msup><mrow><mrow><mo stretchy=\"false\">(</mo></mrow><mrow><mrow><msubsup><mrow><mi>d</mi></mrow><mrow><mi>p</mi></mrow><mrow><mi>c</mi></mrow></msubsup></mrow><mrow><mo>/</mo></mrow><mrow><msubsup><mrow><mi>d</mi></mrow><mrow><mi>p</mi></mrow><mrow><mi>f</mi></mrow></msubsup></mrow></mrow><mrow><mo stretchy=\"false\">)</mo></mrow></mrow><mrow><mn>2</mn></mrow></msup></math></span></span><script type=\"math/mml\"><math display=\"inline\"><msup><mrow><mrow><mo stretchy=\"false\">(</mo></mrow><mrow><mrow><msubsup><mrow><mi>d</mi></mrow><mrow><mi>p</mi></mrow><mrow><mi>c</mi></mrow></msubsup></mrow><mrow><mo>/</mo></mrow><mrow><msubsup><mrow><mi>d</mi></mrow><mrow><mi>p</mi></mrow><mrow><mi>f</mi></mrow></msubsup></mrow></mrow><mrow><mo stretchy=\"false\">)</mo></mrow></mrow><mrow><mn>2</mn></mrow></msup></math></script>; however, the MRT ratio of medium and fine particles (<i></i><span style=\"color: inherit;\"></span><span data-mathml='<math xmlns=\"http://www.w3.org/1998/Math/MathML\" display=\"inline\"><msubsup><mrow><mi>t</mi></mrow><mrow><mi>p</mi></mrow><mrow><mi>m</mi></mrow></msubsup><mo>/</mo><msubsup><mrow><mi>t</mi></mrow><mrow><mi>p</mi></mrow><mrow><mi>f</mi></mrow></msubsup></math>' role=\"presentation\" style=\"position: relative;\" tabindex=\"0\"><nobr aria-hidden=\"true\"><span style=\"width: 2.974em; display: inline-block;\"><span style=\"display: inline-block; position: relative; width: 2.41em; height: 0px; font-size: 122%;\"><span style=\"position: absolute; clip: rect(1.078em, 1002.41em, 2.769em, -999.997em); top: -2.2em; left: 0em;\"><span><span><span style=\"display: inline-block; position: relative; width: 1.078em; height: 0px;\"><span style=\"position: absolute; clip: rect(3.23em, 1000.31em, 4.152em, -999.997em); top: -3.993em; left: 0em;\"><span><span style=\"font-family: MathJax_Math-italic;\">t</span></span><span style=\"display: inline-block; width: 0px; height: 3.998em;\"></span></span><span style=\"position: absolute; clip: rect(3.537em, 1000.72em, 4.152em, -999.997em); top: -4.352em; left: 0.361em;\"><span><span style=\"font-size: 70.7%; font-family: MathJax_Math-italic;\">m</span></span><span style=\"display: inline-block; width: 0px; height: 3.998em;\"></span></span><span style=\"position: absolute; clip: rect(3.537em, 1000.41em, 4.306em, -999.997em); top: -3.737em; left: 0.361em;\"><span><span style=\"font-size: 70.7%; font-family: MathJax_Math-italic;\">p</span></span><span style=\"display: inline-block; width: 0px; height: 3.998em;\"></span></span></span></span><span style=\"font-family: MathJax_Main;\">/</span><span><span style=\"display: inline-block; position: relative; width: 0.822em; height: 0px;\"><span style=\"position: absolute; clip: rect(3.23em, 1000.31em, 4.152em, -999.997em); top: -3.993em; left: 0em;\"><span><span style=\"font-family: MathJax_Math-italic;\">t</span></span><span style=\"display: inline-block; width: 0px; height: 3.998em;\"></span></span><span style=\"position: absolute; clip: rect(3.332em, 1000.46em, 4.306em, -999.997em); top: -4.506em; left: 0.361em;\"><span><span style=\"font-size: 70.7%; font-family: MathJax_Math-italic;\">f<span style=\"display: inline-block; overflow: hidden; height: 1px; width: 0.054em;\"></span></span></span><span style=\"display: inline-block; width: 0px; height: 3.998em;\"></span></span><span style=\"position: absolute; clip: rect(3.537em, 1000.41em, 4.306em, -999.997em); top: -3.84em; left: 0.361em;\"><span><span style=\"font-size: 70.7%; font-family: MathJax_Math-italic;\">p</span></span><span style=\"display: inline-block; width: 0px; height: 3.998em;\"></span></span></span></span></span><span style=\"display: inline-block; width: 0px; height: 2.205em;\"></span></span></span><span style=\"display: inline-block; overflow: hidden; vertical-align: -0.559em; border-left: 0px solid; width: 0px; height: 1.816em;\"></span></span></nobr><span role=\"presentation\"><math display=\"inline\" xmlns=\"http://www.w3.org/1998/Math/MathML\"><msubsup><mrow><mi>t</mi></mrow><mrow><mi>p</mi></mrow><mrow><mi>m</mi></mrow></msubsup><mo>/</mo><msubsup><mrow><mi>t</mi></mrow><mrow><mi>p</mi></mrow><mrow><mi>f</mi></mrow></msubsup></math></span></span><script type=\"math/mml\"><math display=\"inline\"><msubsup><mrow><mi>t</mi></mrow><mrow><mi>p</mi></mrow><mrow><mi>m</mi></mrow></msubsup><mo>/</mo><msubsup><mrow><mi>t</mi></mrow><mrow><mi>p</mi></mrow><mrow><mi>f</mi></mrow></msubsup></math></script>) is only slightly exceeded <i></i><span style=\"color: inherit;\"></span><span data-mathml='<math xmlns=\"http://www.w3.org/1998/Math/MathML\" display=\"inline\"><msubsup><mrow><mi>d</mi></mrow><mrow><mi>p</mi></mrow><mrow><mi>m</mi></mrow></msubsup><mo>/</mo><msubsup><mrow><mi>d</mi></mrow><mrow><mi>p</mi></mrow><mrow><mi>f</mi></mrow></msubsup></math>' role=\"presentation\" style=\"position: relative;\" tabindex=\"0\"><nobr aria-hidden=\"true\"><span style=\"width: 3.435em; display: inline-block;\"><span style=\"display: inline-block; position: relative; width: 2.82em; height: 0px; font-size: 122%;\"><span style=\"position: absolute; clip: rect(1.13em, 1002.82em, 2.769em, -999.997em); top: -2.2em; left: 0em;\"><span><span><span style=\"display: inline-block; position: relative; width: 1.283em; height: 0px;\"><span style=\"position: absolute; clip: rect(3.128em, 1000.51em, 4.152em, -999.997em); top: -3.993em; left: 0em;\"><span><span style=\"font-family: MathJax_Math-italic;\">d<span style=\"display: inline-block; overflow: hidden; height: 1px; width: 0.003em;\"></span></span></span><span style=\"display: inline-block; width: 0px; height: 3.998em;\"></span></span><span style=\"position: absolute; clip: rect(3.537em, 1000.72em, 4.152em, -999.997em); top: -4.403em; left: 0.566em;\"><span><span style=\"font-size: 70.7%; font-family: MathJax_Math-italic;\">m</span></span><span style=\"display: inline-block; width: 0px; height: 3.998em;\"></span></span><span style=\"position: absolute; clip: rect(3.537em, 1000.41em, 4.306em, -999.997em); top: -3.737em; left: 0.515em;\"><span><span style=\"font-size: 70.7%; font-family: MathJax_Math-italic;\">p</span></span><span style=\"display: inline-block; width: 0px; height: 3.998em;\"></span></span></span></span><span style=\"font-family: MathJax_Main;\">/</span><span><span style=\"display: inline-block; position: relative; width: 1.027em; height: 0px;\"><span style=\"position: absolute; clip: rect(3.128em, 1000.51em, 4.152em, -999.997em); top: -3.993em; left: 0em;\"><span><span style=\"font-family: MathJax_Math-italic;\">d<span style=\"display: inline-block; overflow: hidden; height: 1px; width: 0.003em;\"></span></span></span><span style=\"display: inline-block; width: 0px; height: 3.998em;\"></span></span><span style=\"position: absolute; clip: rect(3.332em, 1000.46em, 4.306em, -999.997em); top: -4.403em; left: 0.566em;\"><span><span style=\"font-size: 70.7%; font-family: MathJax_Math-italic;\">f<span style=\"display: inline-block; overflow: hidden; height: 1px; width: 0.054em;\"></span></span></span><span style=\"display: inline-block; width: 0px; height: 3.998em;\"></span></span><span style=\"position: absolute; clip: rect(3.537em, 1000.41em, 4.306em, -999.997em); top: -3.737em; left: 0.515em;\"><span><span style=\"font-size: 70.7%; font-family: MathJax_Math-italic;\">p</span></span><span style=\"display: inline-block; width: 0px; height: 3.998em;\"></span></span></span></span></span><span style=\"display: inline-block; width: 0px; height: 2.205em;\"></span></span></span><span style=\"display: inline-block; overflow: hidden; vertical-align: -0.559em; border-left: 0px solid; width: 0px; height: 1.691em;\"></span></span></nobr><span role=\"presentation\"><math display=\"inline\" xmlns=\"http://www.w3.org/1998/Math/MathML\"><msubsup><mrow><mi>d</mi></mrow><mrow><mi>p</mi></mrow><mrow><mi>m</mi></mrow></msubsup><mo>/</mo><msubsup><mrow><mi>d</mi></mrow><mrow><mi>p</mi></mrow><mrow><mi>f</mi></mrow></msubsup></math></span></span><script type=\"math/mml\"><math display=\"inline\"><msubsup><mrow><mi>d</mi></mrow><mrow><mi>p</mi></mrow><mrow><mi>m</mi></mrow></msubsup><mo>/</mo><msubsup><mrow><mi>d</mi></mrow><mrow><mi>p</mi></mrow><mrow><mi>f</mi></mrow></msubsup></math></script>. Moreover, by further optimizing the elutriation pipe gas velocity, the latter can be adjusted to be exceed <i></i><span style=\"color: inherit;\"></span><span data-mathml='<math xmlns=\"http://www.w3.org/1998/Math/MathML\" display=\"inline\"><msup><mrow><mrow><mo stretchy=\"false\">(</mo></mrow><mrow><mrow><msubsup><mrow><mi>d</mi></mrow><mrow><mi>p</mi></mrow><mrow><mi>m</mi></mrow></msubsup></mrow><mrow><mo>/</mo></mrow><mrow><msubsup><mrow><mi>d</mi></mrow><mrow><mi>p</mi></mrow><mrow><mi>f</mi></mrow></msubsup></mrow></mrow><mrow><mo stretchy=\"false\">)</mo></mrow></mrow><mrow><mn>1.5</mn></mrow></msup></math>' role=\"presentation\" style=\"position: relative;\" tabindex=\"0\"><nobr aria-hidden=\"true\"><span style=\"width: 5.587em; display: inline-block;\"><span style=\"display: inline-block; position: relative; width: 4.562em; height: 0px; font-size: 122%;\"><span style=\"position: absolute; clip: rect(0.925em, 1004.56em, 2.769em, -999.997em); top: -2.2em; left: 0em;\"><span><span><span style=\"display: inline-block; position: relative; width: 4.562em; height: 0px;\"><span style=\"position: absolute; clip: rect(2.923em, 1003.49em, 4.562em, -999.997em); top: -3.993em; left: 0em;\"><span><span><span style=\"font-family: MathJax_Main;\">(</span></span><span><span><span><span style=\"display: inline-block; position: relative; width: 1.283em; height: 0px;\"><span style=\"position: absolute; clip: rect(3.128em, 1000.51em, 4.152em, -999.997em); top: -3.993em; left: 0em;\"><span><span style=\"font-family: MathJax_Math-italic;\">d<span style=\"display: inline-block; overflow: hidden; height: 1px; width: 0.003em;\"></span></span></span><span style=\"display: inline-block; width: 0px; height: 3.998em;\"></span></span><span style=\"position: absolute; clip: rect(3.537em, 1000.72em, 4.152em, -999.997em); top: -4.403em; left: 0.566em;\"><span><span style=\"font-size: 70.7%; font-family: MathJax_Math-italic;\">m</span></span><span style=\"display: inline-block; width: 0px; height: 3.998em;\"></span></span><span style=\"position: absolute; clip: rect(3.537em, 1000.41em, 4.306em, -999.997em); top: -3.737em; left: 0.515em;\"><span><span style=\"font-size: 70.7%; font-family: MathJax_Math-italic;\">p</span></span><span style=\"display: inline-block; width: 0px; height: 3.998em;\"></span></span></span></span></span><span><span style=\"font-family: MathJax_Main;\">/</span></span><span><span><span style=\"display: inline-block; position: relative; width: 1.027em; height: 0px;\"><span style=\"position: absolute; clip: rect(3.128em, 1000.51em, 4.152em, -999.997em); top: -3.993em; left: 0em;\"><span><span style=\"font-family: MathJax_Math-italic;\">d<span style=\"display: inline-block; overflow: hidden; height: 1px; width: 0.003em;\"></span></span></span><span style=\"display: inline-block; width: 0px; height: 3.998em;\"></span></span><span style=\"position: absolute; clip: rect(3.332em, 1000.46em, 4.306em, -999.997em); top: -4.403em; left: 0.566em;\"><span><span style=\"font-size: 70.7%; font-family: MathJax_Math-italic;\">f<span style=\"display: inline-block; overflow: hidden; height: 1px; width: 0.054em;\"></span></span></span><span style=\"display: inline-block; width: 0px; height: 3.998em;\"></span></span><span style=\"position: absolute; clip: rect(3.537em, 1000.41em, 4.306em, -999.997em); top: -3.737em; left: 0.515em;\"><span><span style=\"font-size: 70.7%; font-family: MathJax_Math-italic;\">p</span></span><span style=\"display: inline-block; width: 0px; height: 3.998em;\"></span></span></span></span></span></span><span><span style=\"font-family: MathJax_Main;\">)</span></span></span><span style=\"display: inline-block; width: 0px; height: 3.998em;\"></span></span><span style=\"position: absolute; top: -4.659em; left: 3.589em;\"><span><span style=\"font-size: 70.7%; font-family: MathJax_Main;\">1.5</span></span><span style=\"display: inline-block; width: 0px; height: 3.998em;\"></span></span></span></span></span><span style=\"display: inline-block; width: 0px; height: 2.205em;\"></span></span></span><span style=\"display: inline-block; overflow: hidden; vertical-align: -0.559em; border-left: 0px solid; width: 0px; height: 1.941em;\"></span></span></nobr><span role=\"presentation\"><math display=\"inline\" xmlns=\"http://www.w3.org/1998/Math/MathML\"><msup><mrow><mrow><mo stretchy=\"false\">(</mo></mrow><mrow><mrow><msubsup><mrow><mi>d</mi></mrow><mrow><mi>p</mi></mrow><mrow><mi>m</mi></mrow></msubsup></mrow><mrow><mo>/</mo></mrow><mrow><msubsup><mrow><mi>d</mi></mrow><mrow><mi>p</mi></mrow><mrow><mi>f</mi></mrow></msubsup></mrow></mrow><mrow><mo stretchy=\"false\">)</mo></mrow></mrow><mrow><mn>1.5</mn></mrow></msup></math></span></span><script type=\"math/mml\"><math display=\"inline\"><msup><mrow><mrow><mo stretchy=\"false\">(</mo></mrow><mrow><mrow><msubsup><mrow><mi>d</mi></mrow><mrow><mi>p</mi></mrow><mrow><mi>m</mi></mrow></msubsup></mrow><mrow><mo>/</mo></mrow><mrow><msubsup><mrow><mi>d</mi></mrow><mrow><mi>p</mi></mrow><mrow><mi>f</mi></mrow></msubsup></mrow></mrow><mrow><mo stretchy=\"false\">)</mo></mrow></mrow><mrow><mn>1.5</mn></mrow></msup></math></script>. Finally, <i></i><span style=\"color: inherit;\"></span><span data-mathml='<math xmlns=\"http://www.w3.org/1998/Math/MathML\" display=\"inline\"><msubsup><mrow><mi>t</mi></mrow><mrow><mi>p</mi></mrow><mrow><mi>c</mi></mrow></msubsup><mo>/</mo><msubsup><mrow><mi>t</mi></mrow><mrow><mi>p</mi></mrow><mrow><mi>f</mi></mrow></msubsup></math>' role=\"presentation\" style=\"position: relative;\" tabindex=\"0\"><nobr aria-hidden=\"true\"><span style=\"width: 2.564em; display: inline-block;\"><span style=\"display: inline-block; position: relative; width: 2.103em; height: 0px; font-size: 122%;\"><span style=\"position: absolute; clip: rect(1.078em, 1002.1em, 2.769em, -999.997em); top: -2.2em; left: 0em;\"><span><span><span style=\"display: inline-block; position: relative; width: 0.771em; height: 0px;\"><span style=\"position: absolute; clip: rect(3.23em, 1000.31em, 4.152em, -999.997em); top: -3.993em; left: 0em;\"><span><span style=\"font-family: MathJax_Math-italic;\">t</span></span><span style=\"display: inline-block; width: 0px; height: 3.998em;\"></span></span><span style=\"position: absolute; clip: rect(3.537em, 1000.36em, 4.152em, -999.997em); top: -4.352em; left: 0.361em;\"><span><span style=\"font-size: 70.7%; font-family: MathJax_Math-italic;\">c</span></span><span style=\"display: inline-block; width: 0px; height: 3.998em;\"></span></span><span style=\"position: absolute; clip: rect(3.537em, 1000.41em, 4.306em, -999.997em); top: -3.737em; left: 0.361em;\"><span><span style=\"font-size: 70.7%; font-family: MathJax_Math-italic;\">p</span></span><span style=\"display: inline-block; width: 0px; height: 3.998em;\"></span></span></span></span><span style=\"font-family: MathJax_Main;\">/</span><span><span style=\"display: inline-block; position: relative; width: 0.822em; height: 0px;\"><span style=\"position: absolute; clip: rect(3.23em, 1000.31em, 4.152em, -999.997em); top: -3.993em; left: 0em;\"><span><span style=\"font-family: MathJax_Math-italic;\">t</span></span><span style=\"display: inline-block; width: 0px; height: 3.998em;\"></span></span><span style=\"position: absolute; clip: rect(3.332em, 1000.46em, 4.306em, -999.997em); top: -4.506em; left: 0.361em;\"><span><span style=\"font-size: 70.7%; font-family: MathJax_Math-italic;\">f<span style=\"display: inline-block; overflow: hidden; height: 1px; width: 0.054em;\"></span></span></span><span style=\"display: inline-block; width: 0px; height: 3.998em;\"></span></span><span style=\"position: absolute; clip: rect(3.537em, 1000.41em, 4.306em, -999.997em); top: -3.84em; left: 0.361em;\"><span><span style=\"font-size: 70.7%; font-family: MathJax_Math-italic;\">p</span></span><span style=\"display: inline-block; width: 0px; height: 3.998em;\"></span></span></span></span></span><span style=\"display: inline-block; width: 0px; height: 2.205em;\"></span></span></span><span style=\"display: inline-block; overflow: hidden; vertical-align: -0.559em; border-left: 0px solid; width: 0px; height: 1.816em;\"></span></span></nobr><span role=\"presentation\"><math display=\"inline\" xmlns=\"http://www.w3.org/1998/Math/MathML\"><msubsup><mrow><mi>t</mi></mrow><mrow><mi>p</mi></mrow><mrow><mi>c</mi></mrow></msubsup><mo>/</mo><msubsup><mrow><mi>t</mi></mrow><mrow><mi>p</mi></mrow><mrow><mi>f</mi></mrow></msubsup></math></span></span><script type=\"math/mml\"><math display=\"inline\"><msubsup><mrow><mi>t</mi></mrow><mrow><mi>p</mi></mrow><mrow><mi>c</mi></mrow></msubsup><mo>/</mo><msubsup><mrow><mi>t</mi></mrow><mrow><mi>p</mi></mrow><mrow><mi>f</mi></mrow></msubsup></math></script> and <i></i><span style=\"color: inherit;\"></span><span data-mathml='<math xmlns=\"http://www.w3.org/1998/Math/MathML\" display=\"inline\"><msubsup><mrow><mi>t</mi></mrow><mrow><mi>p</mi></mrow><mrow><mi>m</mi></mrow></msubsup><mo>/</mo><msubsup><mrow><mi>t</mi></mrow><mrow><mi>p</mi></mrow><mrow><mi>f</mi></mrow></msubsup></math>' role=\"presentation\" style=\"position: relative;\" tabindex=\"0\"><nobr aria-hidden=\"true\"><span style=\"width: 2.974em; display: inline-block;\"><span style=\"display: inline-block; position: relative; width: 2.41em; height: 0px; font-size: 122%;\"><span style=\"position: absolute; clip: rect(1.078em, 1002.41em, 2.769em, -999.997em); top: -2.2em; left: 0em;\"><span><span><span style=\"display: inline-block; position: relative; width: 1.078em; height: 0px;\"><span style=\"position: absolute; clip: rect(3.23em, 1000.31em, 4.152em, -999.997em); top: -3.993em; left: 0em;\"><span><span style=\"font-family: MathJax_Math-italic;\">t</span></span><span style=\"display: inline-block; width: 0px; height: 3.998em;\"></span></span><span style=\"position: absolute; clip: rect(3.537em, 1000.72em, 4.152em, -999.997em); top: -4.352em; left: 0.361em;\"><span><span style=\"font-size: 70.7%; font-family: MathJax_Math-italic;\">m</span></span><span style=\"display: inline-block; width: 0px; height: 3.998em;\"></span></span><span style=\"position: absolute; clip: rect(3.537em, 1000.41em, 4.306em, -999.997em); top: -3.737em; left: 0.361em;\"><span><span style=\"font-size: 70.7%; font-family: MathJax_Math-italic;\">p</span></span><span style=\"display: inline-block; width: 0px; height: 3.998em;\"></span></span></span></span><span style=\"font-family: MathJax_Main;\">/</span><span><span style=\"display: inline-block; position: relative; width: 0.822em; height: 0px;\"><span style=\"position: absolute; clip: rect(3.23em, 1000.31em, 4.152em, -999.997em); top: -3.993em; left: 0em;\"><span><span style=\"font-family: MathJax_Math-italic;\">t</span></span><span style=\"display: inline-block; width: 0px; height: 3.998em;\"></span></span><span style=\"position: absolute; clip: rect(3.332em, 1000.46em, 4.306em, -999.997em); top: -4.506em; left: 0.361em;\"><span><span style=\"font-size: 70.7%; font-family: MathJax_Math-italic;\">f<span style=\"display: inline-block; overflow: hidden; height: 1px; width: 0.054em;\"></span></span></span><span style=\"display: inline-block; width: 0px; height: 3.998em;\"></span></span><span style=\"position: absolute; clip: rect(3.537em, 1000.41em, 4.306em, -999.997em); top: -3.84em; left: 0.361em;\"><span><span style=\"font-size: 70.7%; font-family: MathJax_Math-italic;\">p</span></span><span style=\"display: inline-block; width: 0px; height: 3.998em;\"></span></span></span></span></span><span style=\"display: inline-block; width: 0px; height: 2.205em;\"></span></span></span><span style=\"display: inline-block; overflow: hidden; vertical-align: -0.559em; border-left: 0px solid; width: 0px; height: 1.816em;\"></span></span></nobr><span role=\"presentation\"><math display=\"inline\" xmlns=\"http://www.w3.org/1998/Math/MathML\"><msubsup><mrow><mi>t</mi></mrow><mrow><mi>p</mi></mrow><mrow><mi>m</mi></mrow></msubsup><mo>/</mo><msubsup><mrow><mi>t</mi></mrow><mrow><mi>p</mi></mrow><mrow><mi>f</mi></mrow></msubsup></math></span></span><script type=\"math/mml\"><math display=\"inline\"><msubsup><mrow><mi>t</mi></mrow><mrow><mi>p</mi></mrow><mrow><mi>m</mi></mrow></msubsup><mo>/</mo><msubsup><mrow><mi>t</mi></mrow><mrow><mi>p</mi></mrow><mrow><mi>f</mi></mrow></msubsup></math></script> can be simultaneously adjusted to exceed <i></i><span style=\"color: inherit;\"></span><span data-mathml='<math xmlns=\"http://www.w3.org/1998/Math/MathML\" display=\"inline\"><msup><mrow><mrow><mo stretchy=\"false\">(</mo></mrow><mrow><mrow><msub><mrow><mi>d</mi></mrow><mrow><mi>p</mi></mrow></msub></mrow><mrow><mo>/</mo></mrow><mrow><msubsup><mrow><mi>d</mi></mrow><mrow><mi>p</mi></mrow><mrow><mi>f</mi></mrow></msubsup></mrow></mrow><mrow><mo stretchy=\"false\">)</mo></mrow></mrow><mrow><mn>2</mn></mrow></msup></math>' role=\"presentation\" style=\"position: relative;\" tabindex=\"0\"><nobr aria-hidden=\"true\"><span style=\"width: 4.511em; display: inline-block;\"><span style=\"display: inline-block; position: relative; width: 3.691em; height: 0px; font-size: 122%;\"><span style=\"position: absolute; clip: rect(0.925em, 1003.69em, 2.769em, -999.997em); top: -2.2em; left: 0em;\"><span><span><span style=\"display: inline-block; position: relative; width: 3.691em; height: 0px;\"><span style=\"position: absolute; clip: rect(2.923em, 1003.18em, 4.562em, -999.997em); top: -3.993em; left: 0em;\"><span><span><span style=\"font-family: MathJax_Main;\">(</span></span><span><span><span><span style=\"display: inline-block; position: relative; width: 0.976em; height: 0px;\"><span style=\"position: absolute; clip: rect(3.128em, 1000.51em, 4.152em, -999.997em); top: -3.993em; left: 0em;\"><span><span style=\"font-family: MathJax_Math-italic;\">d<span style=\"display: inline-block; overflow: hidden; height: 1px; width: 0.003em;\"></span></span></span><span style=\"display: inline-block; width: 0px; height: 3.998em;\"></span></span><span style=\"position: absolute; top: -3.84em; left: 0.515em;\"><span><span style=\"font-size: 70.7%; font-family: MathJax_Math-italic;\">p</span></span><span style=\"display: inline-block; width: 0px; height: 3.998em;\"></span></span></span></span></span><span><span style=\"font-family: MathJax_Main;\">/</span></span><span><span><span style=\"display: inline-block; position: relative; width: 1.027em; height: 0px;\"><span style=\"position: absolute; clip: rect(3.128em, 1000.51em, 4.152em, -999.997em); top: -3.993em; left: 0em;\"><span><span style=\"font-family: MathJax_Math-italic;\">d<span style=\"display: inline-block; overflow: hidden; height: 1px; width: 0.003em;\"></span></span></span><span style=\"display: inline-block; width: 0px; height: 3.998em;\"></span></span><span style=\"position: absolute; clip: rect(3.332em, 1000.46em, 4.306em, -999.997em); top: -4.403em; left: 0.566em;\"><span><span style=\"font-size: 70.7%; font-family: MathJax_Math-italic;\">f<span style=\"display: inline-block; overflow: hidden; height: 1px; width: 0.054em;\"></span></span></span><span style=\"display: inline-block; width: 0px; height: 3.998em;\"></span></span><span style=\"position: absolute; clip: rect(3.537em, 1000.41em, 4.306em, -999.997em); top: -3.737em; left: 0.515em;\"><span><span style=\"font-size: 70.7%; font-family: MathJax_Math-italic;\">p</span></span><span style=\"display: inline-block; width: 0px; height: 3.998em;\"></span></span></span></span></span></span><span><span style=\"font-family: MathJax_Main;\">)</span></span></span><span style=\"display: inline-block; width: 0px; height: 3.998em;\"></span></span><span style=\"position: absolute; top: -4.659em; left: 3.281em;\"><span><span style=\"font-size: 70.7%; font-family: MathJax_Main;\">2</span></span><span style=\"display: inline-block; width: 0px; height: 3.998em;\"></span></span></span></span></span><span style=\"display: inline-block; width: 0px; height: 2.205em;\"></span></span></span><span style=\"display: inline-block; overflow: hidden; vertical-align: -0.559em; border-left: 0px solid; width: 0px; height: 1.941em;\"></span></span></nobr><span role=\"presentation\"><math display=\"inline\" xmlns=\"http://www.w3.org/1998/Math/MathML\"><msup><mrow><mrow><mo stretchy=\"false\">(</mo></mrow><mrow><mrow><msub><mrow><mi>d</mi></mrow><mrow><mi>p</mi></mrow></msub></mrow><mrow><mo>/</mo></mrow><mrow><msubsup><mrow><mi>d</mi></mrow><mrow><mi>p</mi></mrow><mrow><mi>f</mi></mrow></msubsup></mrow></mrow><mrow><mo stretchy=\"false\">)</mo></mrow></mrow><mrow><mn>2</mn></mrow></msup></math></span></span><script type=\"math/mml\"><math display=\"inline\"><msup><mrow><mrow><mo stretchy=\"false\">(</mo></mrow><mrow><mrow><msub><mrow><mi>d</mi></mrow><mrow><mi>p</mi></mrow></msub></mrow><mrow><mo>/</mo></mrow><mrow><msubsup><mrow><mi>d</mi></mrow><mrow><mi>p</mi></mrow><mrow><mi>f</mi></mrow></msubsup></mrow></mrow><mrow><mo stretchy=\"false\">)</mo></mrow></mrow><mrow><mn>2</mn></mrow></msup></math></script> by increasing the number of elutriation pipes. Therefore, present study enables the controllable range of the MRT ratio of polydisperse particles covering from <i></i><span style=\"color: inherit;\"></span><span data-mathml='<math xmlns=\"http://www.w3.org/1998/Math/MathML\" display=\"inline\"><msup><mrow><mrow><mrow><msub><mrow><mi>d</mi></mrow><mrow><mi>p</mi></mrow></msub></mrow><mrow><mo>/</mo></mrow><mrow><msubsup><mrow><mi>d</mi></mrow><mrow><mi>p</mi></mrow><mrow><mi>f</mi></mrow></msubsup></mrow></mrow></mrow><mrow><mn>2</mn></mrow></msup></math>' role=\"presentation\" style=\"position: relative;\" tabindex=\"0\"><nobr aria-hidden=\"true\"><span style=\"width: 3.589em; display: inline-block;\"><span style=\"display: inline-block; position: relative; width: 2.923em; height: 0px; font-size: 122%;\"><span style=\"position: absolute; clip: rect(0.925em, 1002.92em, 2.769em, -999.997em); top: -2.2em; left: 0em;\"><span><span><span style=\"display: inline-block; position: relative; width: 2.923em; height: 0px;\"><span style=\"position: absolute; clip: rect(2.923em, 1002.51em, 4.562em, -999.997em); top: -3.993em; left: 0em;\"><span><span><span><span><span style=\"display: inline-block; position: relative; width: 0.976em; height: 0px;\"><span style=\"position: absolute; clip: rect(3.128em, 1000.51em, 4.152em, -999.997em); top: -3.993em; left: 0em;\"><span><span style=\"font-family: MathJax_Math-italic;\">d<span style=\"display: inline-block; overflow: hidden; height: 1px; width: 0.003em;\"></span></span></span><span style=\"display: inline-block; width: 0px; height: 3.998em;\"></span></span><span style=\"position: absolute; top: -3.84em; left: 0.515em;\"><span><span style=\"font-size: 70.7%; font-family: MathJax_Math-italic;\">p</span></span><span style=\"display: inline-block; width: 0px; height: 3.998em;\"></span></span></span></span></span><span><span style=\"font-family: MathJax_Main;\">/</span></span><span><span><span style=\"display: inline-block; position: relative; width: 1.027em; height: 0px;\"><span style=\"position: absolute; clip: rect(3.128em, 1000.51em, 4.152em, -999.997em); top: -3.993em; left: 0em;\"><span><span style=\"font-family: MathJax_Math-italic;\">d<span style=\"display: inline-block; overflow: hidden; height: 1px; width: 0.003em;\"></span></span></span><span style=\"display: inline-block; width: 0px; height: 3.998em;\"></span></span><span style=\"position: absolute; clip: rect(3.332em, 1000.46em, 4.306em, -999.997em); top: -4.403em; left: 0.566em;\"><span><span style=\"font-size: 70.7%; font-family: MathJax_Math-italic;\">f<span style=\"display: inline-block; overflow: hidden; height: 1px; width: 0.054em;\"></span></span></span><span style=\"display: inline-block; width: 0px; height: 3.998em;\"></span></span><span style=\"position: absolute; clip: rect(3.537em, 1000.41em, 4.306em, -999.997em); top: -3.737em; left: 0.515em;\"><span><span style=\"font-size: 70.7%; font-family: MathJax_Math-italic;\">p</span></span><span style=\"display: inline-block; width: 0px; height: 3.998em;\"></span></span></span></span></span></span></span><span style=\"display: inline-block; width: 0px; height: 3.998em;\"></span></span><span style=\"position: absolute; top: -4.659em; left: 2.513em;\"><span><span style=\"font-size: 70.7%; font-family: MathJax_Main;\">2</span></span><span style=\"display: inline-block; width: 0px; height: 3.998em;\"></span></span></span></span></span><span style=\"display: inline-block; width: 0px; height: 2.205em;\"></span></span></span><span style=\"display: inline-block; overflow: hidden; vertical-align: -0.559em; border-left: 0px solid; width: 0px; height: 1.941em;\"></span></span></nobr><span role=\"presentation\"><math display=\"inline\" xmlns=\"http://www.w3.org/1998/Math/MathML\"><msup><mrow><mrow><mrow><msub><mrow><mi>d</mi></mrow><mrow><mi>p</mi></mrow></msub></mrow><mrow><mo>/</mo></mrow><mrow><msubsup><mrow><mi>d</mi></mrow><mrow><mi>p</mi></mrow><mrow><mi>f</mi></mrow></msubsup></mrow></mrow></mrow><mrow><mn>2</mn></mrow></msup></math></span></span><script type=\"math/mml\"><math display=\"inline\"><msup><mrow><mrow><mrow><msub><mrow><mi>d</mi></mrow><mrow><mi>p</mi></mrow></msub></mrow><mrow><mo>/</mo></mrow><mrow><msubsup><mrow><mi>d</mi></mrow><mrow><mi>p</mi></mrow><mrow><mi>f</mi></mrow></msubsup></mrow></mrow></mrow><mrow><mn>2</mn></mrow></msup></math></script> to <i></i><span style=\"color: inherit;\"></span><span data-mathml='<math xmlns=\"http://www.w3.org/1998/Math/MathML\" display=\"inline\"><msup><mrow><mrow><mo stretchy=\"false\">(</mo></mrow><mrow><mrow><msub><mrow><mi>d</mi></mrow><mrow><mi>p</mi></mrow></msub></mrow><mrow><mo>/</mo></mrow><mrow><msubsup><mrow><mi>d</mi></mrow><mrow><mi>p</mi></mrow><mrow><mi>f</mi></mrow></msubsup></mrow></mrow><mrow><mo stretchy=\"false\">)</mo></mrow></mrow><mrow><mn>2</mn></mrow></msup></math>' role=\"presentation\" style=\"position: relative;\" tabindex=\"0\"><nobr aria-hidden=\"true\"><span style=\"width: 4.511em; display: inline-block;\"><span style=\"display: inline-block; position: relative; width: 3.691em; height: 0px; font-size: 122%;\"><span style=\"position: absolute; clip: rect(0.925em, 1003.69em, 2.769em, -999.997em); top: -2.2em; left: 0em;\"><span><span><span style=\"display: inline-block; position: relative; width: 3.691em; height: 0px;\"><span style=\"position: absolute; clip: rect(2.923em, 1003.18em, 4.562em, -999.997em); top: -3.993em; left: 0em;\"><span><span><span style=\"font-family: MathJax_Main;\">(</span></span><span><span><span><span style=\"display: inline-block; position: relative; width: 0.976em; height: 0px;\"><span style=\"position: absolute; clip: rect(3.128em, 1000.51em, 4.152em, -999.997em); top: -3.993em; left: 0em;\"><span><span style=\"font-family: MathJax_Math-italic;\">d<span style=\"display: inline-block; overflow: hidden; height: 1px; width: 0.003em;\"></span></span></span><span style=\"display: inline-block; width: 0px; height: 3.998em;\"></span></span><span style=\"position: absolute; top: -3.84em; left: 0.515em;\"><span><span style=\"font-size: 70.7%; font-family: MathJax_Math-italic;\">p</span></span><span style=\"display: inline-block; width: 0px; height: 3.998em;\"></span></span></span></span></span><span><span style=\"font-family: MathJax_Main;\">/</span></span><span><span><span style=\"display: inline-block; position: relative; width: 1.027em; height: 0px;\"><span style=\"position: absolute; clip: rect(3.128em, 1000.51em, 4.152em, -999.997em); top: -3.993em; left: 0em;\"><span><span style=\"font-family: MathJax_Math-italic;\">d<span style=\"display: inline-block; overflow: hidden; height: 1px; width: 0.003em;\"></span></span></span><span style=\"display: inline-block; width: 0px; height: 3.998em;\"></span></span><span style=\"position: absolute; clip: rect(3.332em, 1000.46em, 4.306em, -999.997em); top: -4.403em; left: 0.566em;\"><span><span style=\"font-size: 70.7%; font-family: MathJax_Math-italic;\">f<span style=\"display: inline-block; overflow: hidden; height: 1px; width: 0.054em;\"></span></span></span><span style=\"display: inline-block; width: 0px; height: 3.998em;\"></span></span><span style=\"position: absolute; clip: rect(3.537em, 1000.41em, 4.306em, -999.997em); top: -3.737em; left: 0.515em;\"><span><span style=\"font-size: 70.7%; font-family: MathJax_Math-italic;\">p</span></span><span style=\"display: inline-block; width: 0px; height: 3.998em;\"></span></span></span></span></span></span><span><span style=\"font-family: MathJax_Main;\">)</span></span></span><span style=\"display: inline-block; width: 0px; height: 3.998em;\"></span></span><span style=\"position: absolute; top: -4.659em; left: 3.281em;\"><span><span style=\"font-size: 70.7%; font-family: MathJax_Main;\">2</span></span><span style=\"display: inline-block; width: 0px; height: 3.998em;\"></span></span></span></span></span><span style=\"display: inline-block; width: 0px; height: 2.205em;\"></span></span></span><span style=\"display: inline-block; overflow: hidden; vertical-align: -0.559em; border-left: 0px solid; width: 0px; height: 1.941em;\"></span></span></nobr><span role=\"presentation\"><math display=\"inline\" xmlns=\"http://www.w3.org/1998/Math/MathML\"><msup><mrow><mrow><mo stretchy=\"false\">(</mo></mrow><mrow><mrow><msub><mrow><mi>d</mi></mrow><mrow><mi>p</mi></mrow></msub></mrow><mrow><mo>/</mo></mrow><mrow><msubsup><mrow><mi>d</mi></mrow><mrow><mi>p</mi></mrow><mrow><mi>f</mi></mrow></msubsup></mrow></mrow><mrow><mo stretchy=\"false\">)</mo></mrow></mrow><mrow><mn>2</mn></mrow></msup></math></span></span><script type=\"math/mml\"><math display=\"inline\"><msup><mrow><mrow><mo stretchy=\"false\">(</mo></mrow><mrow><mrow><msub><mrow><mi>d</mi></mrow><mrow><mi>p</mi></mrow></msub></mrow><mrow><mo>/</mo></mrow><mrow><msubsup><mrow><mi>d</mi></mrow><mrow><mi>p</mi></mrow><mrow><mi>f</mi></mrow></msubsup></mrow></mrow><mrow><mo stretchy=\"false\">)</mo></mrow></mrow><mrow><mn>2</mn></mrow></msup></math></script> that meets the required reaction time ratio of different particle sizes, which is of great interest for realizing the synchronous conversion of polydisperse particles.","PeriodicalId":39,"journal":{"name":"Industrial & Engineering Chemistry Research","volume":null,"pages":null},"PeriodicalIF":3.8000,"publicationDate":"2024-09-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"Expanding the Controllable Range of the Mean Residence Time Ratio of Polydisperse Particles in Multiple-Chamber Fluidized Beds: A Coarse-Grained CFD-DEM Study\",\"authors\":\"Shuai Lu, Dandan Li, Bin Lan, Chuanlin Fan, Fan Xu, Ji Xu, Bidan Zhao, Zheng Zou, Hongzhong Li, Junwu Wang, Qingshan Zhu\",\"doi\":\"10.1021/acs.iecr.4c02112\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"The residence time of polydisperse particles is crucial for their simultaneous conversion in a fluidized bed. This study focuses on regulating the residence time of polydisperse particles to expand their controllable range by optimizing the reactor design and operation step-by-step. The mean residence time (MRT) ratio of coarse and fine particles (<i></i><span style=\\\"color: inherit;\\\"></span><span data-mathml='<math xmlns=\\\"http://www.w3.org/1998/Math/MathML\\\" display=\\\"inline\\\"><msubsup><mrow><mi>t</mi></mrow><mrow><mi>p</mi></mrow><mrow><mi>c</mi></mrow></msubsup><mo>/</mo><msubsup><mrow><mi>t</mi></mrow><mrow><mi>p</mi></mrow><mrow><mi>f</mi></mrow></msubsup></math>' role=\\\"presentation\\\" style=\\\"position: relative;\\\" tabindex=\\\"0\\\"><nobr aria-hidden=\\\"true\\\"><span style=\\\"width: 2.564em; display: inline-block;\\\"><span style=\\\"display: inline-block; position: relative; width: 2.103em; height: 0px; font-size: 122%;\\\"><span style=\\\"position: absolute; clip: rect(1.078em, 1002.1em, 2.769em, -999.997em); top: -2.2em; left: 0em;\\\"><span><span><span style=\\\"display: inline-block; position: relative; width: 0.771em; height: 0px;\\\"><span style=\\\"position: absolute; clip: rect(3.23em, 1000.31em, 4.152em, -999.997em); top: -3.993em; left: 0em;\\\"><span><span style=\\\"font-family: MathJax_Math-italic;\\\">t</span></span><span style=\\\"display: inline-block; width: 0px; height: 3.998em;\\\"></span></span><span style=\\\"position: absolute; clip: rect(3.537em, 1000.36em, 4.152em, -999.997em); top: -4.352em; left: 0.361em;\\\"><span><span style=\\\"font-size: 70.7%; font-family: MathJax_Math-italic;\\\">c</span></span><span style=\\\"display: inline-block; width: 0px; height: 3.998em;\\\"></span></span><span style=\\\"position: absolute; clip: rect(3.537em, 1000.41em, 4.306em, -999.997em); top: -3.737em; left: 0.361em;\\\"><span><span style=\\\"font-size: 70.7%; font-family: MathJax_Math-italic;\\\">p</span></span><span style=\\\"display: inline-block; width: 0px; height: 3.998em;\\\"></span></span></span></span><span style=\\\"font-family: MathJax_Main;\\\">/</span><span><span style=\\\"display: inline-block; position: relative; width: 0.822em; height: 0px;\\\"><span style=\\\"position: absolute; clip: rect(3.23em, 1000.31em, 4.152em, -999.997em); top: -3.993em; left: 0em;\\\"><span><span style=\\\"font-family: MathJax_Math-italic;\\\">t</span></span><span style=\\\"display: inline-block; width: 0px; height: 3.998em;\\\"></span></span><span style=\\\"position: absolute; clip: rect(3.332em, 1000.46em, 4.306em, -999.997em); top: -4.506em; left: 0.361em;\\\"><span><span style=\\\"font-size: 70.7%; font-family: MathJax_Math-italic;\\\">f<span style=\\\"display: inline-block; overflow: hidden; height: 1px; width: 0.054em;\\\"></span></span></span><span style=\\\"display: inline-block; width: 0px; height: 3.998em;\\\"></span></span><span style=\\\"position: absolute; clip: rect(3.537em, 1000.41em, 4.306em, -999.997em); top: -3.84em; left: 0.361em;\\\"><span><span style=\\\"font-size: 70.7%; font-family: MathJax_Math-italic;\\\">p</span></span><span style=\\\"display: inline-block; width: 0px; height: 3.998em;\\\"></span></span></span></span></span><span style=\\\"display: inline-block; width: 0px; height: 2.205em;\\\"></span></span></span><span style=\\\"display: inline-block; overflow: hidden; vertical-align: -0.559em; border-left: 0px solid; width: 0px; height: 1.816em;\\\"></span></span></nobr><span role=\\\"presentation\\\"><math display=\\\"inline\\\" xmlns=\\\"http://www.w3.org/1998/Math/MathML\\\"><msubsup><mrow><mi>t</mi></mrow><mrow><mi>p</mi></mrow><mrow><mi>c</mi></mrow></msubsup><mo>/</mo><msubsup><mrow><mi>t</mi></mrow><mrow><mi>p</mi></mrow><mrow><mi>f</mi></mrow></msubsup></math></span></span><script type=\\\"math/mml\\\"><math display=\\\"inline\\\"><msubsup><mrow><mi>t</mi></mrow><mrow><mi>p</mi></mrow><mrow><mi>c</mi></mrow></msubsup><mo>/</mo><msubsup><mrow><mi>t</mi></mrow><mrow><mi>p</mi></mrow><mrow><mi>f</mi></mrow></msubsup></math></script>) increased significantly with increasing elutriation pipe width of the multiple-chamber fluidized bed, thus enabling the MRT ratio to exceed <i></i><span style=\\\"color: inherit;\\\"></span><span data-mathml='<math xmlns=\\\"http://www.w3.org/1998/Math/MathML\\\" display=\\\"inline\\\"><msup><mrow><mrow><mo stretchy=\\\"false\\\">(</mo></mrow><mrow><mrow><msubsup><mrow><mi>d</mi></mrow><mrow><mi>p</mi></mrow><mrow><mi>c</mi></mrow></msubsup></mrow><mrow><mo>/</mo></mrow><mrow><msubsup><mrow><mi>d</mi></mrow><mrow><mi>p</mi></mrow><mrow><mi>f</mi></mrow></msubsup></mrow></mrow><mrow><mo stretchy=\\\"false\\\">)</mo></mrow></mrow><mrow><mn>2</mn></mrow></msup></math>' role=\\\"presentation\\\" style=\\\"position: relative;\\\" tabindex=\\\"0\\\"><nobr aria-hidden=\\\"true\\\"><span style=\\\"width: 4.511em; display: inline-block;\\\"><span style=\\\"display: inline-block; position: relative; width: 3.691em; height: 0px; font-size: 122%;\\\"><span style=\\\"position: absolute; clip: rect(0.925em, 1003.69em, 2.769em, -999.997em); top: -2.2em; left: 0em;\\\"><span><span><span style=\\\"display: inline-block; position: relative; width: 3.691em; height: 0px;\\\"><span style=\\\"position: absolute; clip: rect(2.923em, 1003.18em, 4.562em, -999.997em); top: -3.993em; left: 0em;\\\"><span><span><span style=\\\"font-family: MathJax_Main;\\\">(</span></span><span><span><span><span style=\\\"display: inline-block; position: relative; width: 0.976em; height: 0px;\\\"><span style=\\\"position: absolute; clip: rect(3.128em, 1000.51em, 4.152em, -999.997em); top: -3.993em; left: 0em;\\\"><span><span style=\\\"font-family: MathJax_Math-italic;\\\">d<span style=\\\"display: inline-block; overflow: hidden; height: 1px; width: 0.003em;\\\"></span></span></span><span style=\\\"display: inline-block; width: 0px; height: 3.998em;\\\"></span></span><span style=\\\"position: absolute; clip: rect(3.537em, 1000.36em, 4.152em, -999.997em); top: -4.403em; left: 0.566em;\\\"><span><span style=\\\"font-size: 70.7%; font-family: MathJax_Math-italic;\\\">c</span></span><span style=\\\"display: inline-block; width: 0px; height: 3.998em;\\\"></span></span><span style=\\\"position: absolute; clip: rect(3.537em, 1000.41em, 4.306em, -999.997em); top: -3.737em; left: 0.515em;\\\"><span><span style=\\\"font-size: 70.7%; font-family: MathJax_Math-italic;\\\">p</span></span><span style=\\\"display: inline-block; width: 0px; height: 3.998em;\\\"></span></span></span></span></span><span><span style=\\\"font-family: MathJax_Main;\\\">/</span></span><span><span><span style=\\\"display: inline-block; position: relative; width: 1.027em; height: 0px;\\\"><span style=\\\"position: absolute; clip: rect(3.128em, 1000.51em, 4.152em, -999.997em); top: -3.993em; left: 0em;\\\"><span><span style=\\\"font-family: MathJax_Math-italic;\\\">d<span style=\\\"display: inline-block; overflow: hidden; height: 1px; width: 0.003em;\\\"></span></span></span><span style=\\\"display: inline-block; width: 0px; height: 3.998em;\\\"></span></span><span style=\\\"position: absolute; clip: rect(3.332em, 1000.46em, 4.306em, -999.997em); top: -4.403em; left: 0.566em;\\\"><span><span style=\\\"font-size: 70.7%; font-family: MathJax_Math-italic;\\\">f<span style=\\\"display: inline-block; overflow: hidden; height: 1px; width: 0.054em;\\\"></span></span></span><span style=\\\"display: inline-block; width: 0px; height: 3.998em;\\\"></span></span><span style=\\\"position: absolute; clip: rect(3.537em, 1000.41em, 4.306em, -999.997em); top: -3.737em; left: 0.515em;\\\"><span><span style=\\\"font-size: 70.7%; font-family: MathJax_Math-italic;\\\">p</span></span><span style=\\\"display: inline-block; width: 0px; height: 3.998em;\\\"></span></span></span></span></span></span><span><span style=\\\"font-family: MathJax_Main;\\\">)</span></span></span><span style=\\\"display: inline-block; width: 0px; height: 3.998em;\\\"></span></span><span style=\\\"position: absolute; top: -4.659em; left: 3.281em;\\\"><span><span style=\\\"font-size: 70.7%; font-family: MathJax_Main;\\\">2</span></span><span style=\\\"display: inline-block; width: 0px; height: 3.998em;\\\"></span></span></span></span></span><span style=\\\"display: inline-block; width: 0px; height: 2.205em;\\\"></span></span></span><span style=\\\"display: inline-block; overflow: hidden; vertical-align: -0.559em; border-left: 0px solid; width: 0px; height: 1.941em;\\\"></span></span></nobr><span role=\\\"presentation\\\"><math display=\\\"inline\\\" xmlns=\\\"http://www.w3.org/1998/Math/MathML\\\"><msup><mrow><mrow><mo stretchy=\\\"false\\\">(</mo></mrow><mrow><mrow><msubsup><mrow><mi>d</mi></mrow><mrow><mi>p</mi></mrow><mrow><mi>c</mi></mrow></msubsup></mrow><mrow><mo>/</mo></mrow><mrow><msubsup><mrow><mi>d</mi></mrow><mrow><mi>p</mi></mrow><mrow><mi>f</mi></mrow></msubsup></mrow></mrow><mrow><mo stretchy=\\\"false\\\">)</mo></mrow></mrow><mrow><mn>2</mn></mrow></msup></math></span></span><script type=\\\"math/mml\\\"><math display=\\\"inline\\\"><msup><mrow><mrow><mo stretchy=\\\"false\\\">(</mo></mrow><mrow><mrow><msubsup><mrow><mi>d</mi></mrow><mrow><mi>p</mi></mrow><mrow><mi>c</mi></mrow></msubsup></mrow><mrow><mo>/</mo></mrow><mrow><msubsup><mrow><mi>d</mi></mrow><mrow><mi>p</mi></mrow><mrow><mi>f</mi></mrow></msubsup></mrow></mrow><mrow><mo stretchy=\\\"false\\\">)</mo></mrow></mrow><mrow><mn>2</mn></mrow></msup></math></script>; however, the MRT ratio of medium and fine particles (<i></i><span style=\\\"color: inherit;\\\"></span><span data-mathml='<math xmlns=\\\"http://www.w3.org/1998/Math/MathML\\\" display=\\\"inline\\\"><msubsup><mrow><mi>t</mi></mrow><mrow><mi>p</mi></mrow><mrow><mi>m</mi></mrow></msubsup><mo>/</mo><msubsup><mrow><mi>t</mi></mrow><mrow><mi>p</mi></mrow><mrow><mi>f</mi></mrow></msubsup></math>' role=\\\"presentation\\\" style=\\\"position: relative;\\\" tabindex=\\\"0\\\"><nobr aria-hidden=\\\"true\\\"><span style=\\\"width: 2.974em; display: inline-block;\\\"><span style=\\\"display: inline-block; position: relative; width: 2.41em; height: 0px; font-size: 122%;\\\"><span style=\\\"position: absolute; clip: rect(1.078em, 1002.41em, 2.769em, -999.997em); top: -2.2em; left: 0em;\\\"><span><span><span style=\\\"display: inline-block; position: relative; width: 1.078em; height: 0px;\\\"><span style=\\\"position: absolute; clip: rect(3.23em, 1000.31em, 4.152em, -999.997em); top: -3.993em; left: 0em;\\\"><span><span style=\\\"font-family: MathJax_Math-italic;\\\">t</span></span><span style=\\\"display: inline-block; width: 0px; height: 3.998em;\\\"></span></span><span style=\\\"position: absolute; clip: rect(3.537em, 1000.72em, 4.152em, -999.997em); top: -4.352em; left: 0.361em;\\\"><span><span style=\\\"font-size: 70.7%; font-family: MathJax_Math-italic;\\\">m</span></span><span style=\\\"display: inline-block; width: 0px; height: 3.998em;\\\"></span></span><span style=\\\"position: absolute; clip: rect(3.537em, 1000.41em, 4.306em, -999.997em); top: -3.737em; left: 0.361em;\\\"><span><span style=\\\"font-size: 70.7%; font-family: MathJax_Math-italic;\\\">p</span></span><span style=\\\"display: inline-block; width: 0px; height: 3.998em;\\\"></span></span></span></span><span style=\\\"font-family: MathJax_Main;\\\">/</span><span><span style=\\\"display: inline-block; position: relative; width: 0.822em; height: 0px;\\\"><span style=\\\"position: absolute; clip: rect(3.23em, 1000.31em, 4.152em, -999.997em); top: -3.993em; left: 0em;\\\"><span><span style=\\\"font-family: MathJax_Math-italic;\\\">t</span></span><span style=\\\"display: inline-block; width: 0px; height: 3.998em;\\\"></span></span><span style=\\\"position: absolute; clip: rect(3.332em, 1000.46em, 4.306em, -999.997em); top: -4.506em; left: 0.361em;\\\"><span><span style=\\\"font-size: 70.7%; font-family: MathJax_Math-italic;\\\">f<span style=\\\"display: inline-block; overflow: hidden; height: 1px; width: 0.054em;\\\"></span></span></span><span style=\\\"display: inline-block; width: 0px; height: 3.998em;\\\"></span></span><span style=\\\"position: absolute; clip: rect(3.537em, 1000.41em, 4.306em, -999.997em); top: -3.84em; left: 0.361em;\\\"><span><span style=\\\"font-size: 70.7%; font-family: MathJax_Math-italic;\\\">p</span></span><span style=\\\"display: inline-block; width: 0px; height: 3.998em;\\\"></span></span></span></span></span><span style=\\\"display: inline-block; width: 0px; height: 2.205em;\\\"></span></span></span><span style=\\\"display: inline-block; overflow: hidden; vertical-align: -0.559em; border-left: 0px solid; width: 0px; height: 1.816em;\\\"></span></span></nobr><span role=\\\"presentation\\\"><math display=\\\"inline\\\" xmlns=\\\"http://www.w3.org/1998/Math/MathML\\\"><msubsup><mrow><mi>t</mi></mrow><mrow><mi>p</mi></mrow><mrow><mi>m</mi></mrow></msubsup><mo>/</mo><msubsup><mrow><mi>t</mi></mrow><mrow><mi>p</mi></mrow><mrow><mi>f</mi></mrow></msubsup></math></span></span><script type=\\\"math/mml\\\"><math display=\\\"inline\\\"><msubsup><mrow><mi>t</mi></mrow><mrow><mi>p</mi></mrow><mrow><mi>m</mi></mrow></msubsup><mo>/</mo><msubsup><mrow><mi>t</mi></mrow><mrow><mi>p</mi></mrow><mrow><mi>f</mi></mrow></msubsup></math></script>) is only slightly exceeded <i></i><span style=\\\"color: inherit;\\\"></span><span data-mathml='<math xmlns=\\\"http://www.w3.org/1998/Math/MathML\\\" display=\\\"inline\\\"><msubsup><mrow><mi>d</mi></mrow><mrow><mi>p</mi></mrow><mrow><mi>m</mi></mrow></msubsup><mo>/</mo><msubsup><mrow><mi>d</mi></mrow><mrow><mi>p</mi></mrow><mrow><mi>f</mi></mrow></msubsup></math>' role=\\\"presentation\\\" style=\\\"position: relative;\\\" tabindex=\\\"0\\\"><nobr aria-hidden=\\\"true\\\"><span style=\\\"width: 3.435em; display: inline-block;\\\"><span style=\\\"display: inline-block; position: relative; width: 2.82em; height: 0px; font-size: 122%;\\\"><span style=\\\"position: absolute; clip: rect(1.13em, 1002.82em, 2.769em, -999.997em); top: -2.2em; left: 0em;\\\"><span><span><span style=\\\"display: inline-block; position: relative; width: 1.283em; height: 0px;\\\"><span style=\\\"position: absolute; clip: rect(3.128em, 1000.51em, 4.152em, -999.997em); top: -3.993em; left: 0em;\\\"><span><span style=\\\"font-family: MathJax_Math-italic;\\\">d<span style=\\\"display: inline-block; overflow: hidden; height: 1px; width: 0.003em;\\\"></span></span></span><span style=\\\"display: inline-block; width: 0px; height: 3.998em;\\\"></span></span><span style=\\\"position: absolute; clip: rect(3.537em, 1000.72em, 4.152em, -999.997em); top: -4.403em; left: 0.566em;\\\"><span><span style=\\\"font-size: 70.7%; font-family: MathJax_Math-italic;\\\">m</span></span><span style=\\\"display: inline-block; width: 0px; height: 3.998em;\\\"></span></span><span style=\\\"position: absolute; clip: rect(3.537em, 1000.41em, 4.306em, -999.997em); top: -3.737em; left: 0.515em;\\\"><span><span style=\\\"font-size: 70.7%; font-family: MathJax_Math-italic;\\\">p</span></span><span style=\\\"display: inline-block; width: 0px; height: 3.998em;\\\"></span></span></span></span><span style=\\\"font-family: MathJax_Main;\\\">/</span><span><span style=\\\"display: inline-block; position: relative; width: 1.027em; height: 0px;\\\"><span style=\\\"position: absolute; clip: rect(3.128em, 1000.51em, 4.152em, -999.997em); top: -3.993em; left: 0em;\\\"><span><span style=\\\"font-family: MathJax_Math-italic;\\\">d<span style=\\\"display: inline-block; overflow: hidden; height: 1px; width: 0.003em;\\\"></span></span></span><span style=\\\"display: inline-block; width: 0px; height: 3.998em;\\\"></span></span><span style=\\\"position: absolute; clip: rect(3.332em, 1000.46em, 4.306em, -999.997em); top: -4.403em; left: 0.566em;\\\"><span><span style=\\\"font-size: 70.7%; font-family: MathJax_Math-italic;\\\">f<span style=\\\"display: inline-block; overflow: hidden; height: 1px; width: 0.054em;\\\"></span></span></span><span style=\\\"display: inline-block; width: 0px; height: 3.998em;\\\"></span></span><span style=\\\"position: absolute; clip: rect(3.537em, 1000.41em, 4.306em, -999.997em); top: -3.737em; left: 0.515em;\\\"><span><span style=\\\"font-size: 70.7%; font-family: MathJax_Math-italic;\\\">p</span></span><span style=\\\"display: inline-block; width: 0px; height: 3.998em;\\\"></span></span></span></span></span><span style=\\\"display: inline-block; width: 0px; height: 2.205em;\\\"></span></span></span><span style=\\\"display: inline-block; overflow: hidden; vertical-align: -0.559em; border-left: 0px solid; width: 0px; height: 1.691em;\\\"></span></span></nobr><span role=\\\"presentation\\\"><math display=\\\"inline\\\" xmlns=\\\"http://www.w3.org/1998/Math/MathML\\\"><msubsup><mrow><mi>d</mi></mrow><mrow><mi>p</mi></mrow><mrow><mi>m</mi></mrow></msubsup><mo>/</mo><msubsup><mrow><mi>d</mi></mrow><mrow><mi>p</mi></mrow><mrow><mi>f</mi></mrow></msubsup></math></span></span><script type=\\\"math/mml\\\"><math display=\\\"inline\\\"><msubsup><mrow><mi>d</mi></mrow><mrow><mi>p</mi></mrow><mrow><mi>m</mi></mrow></msubsup><mo>/</mo><msubsup><mrow><mi>d</mi></mrow><mrow><mi>p</mi></mrow><mrow><mi>f</mi></mrow></msubsup></math></script>. Moreover, by further optimizing the elutriation pipe gas velocity, the latter can be adjusted to be exceed <i></i><span style=\\\"color: inherit;\\\"></span><span data-mathml='<math xmlns=\\\"http://www.w3.org/1998/Math/MathML\\\" display=\\\"inline\\\"><msup><mrow><mrow><mo stretchy=\\\"false\\\">(</mo></mrow><mrow><mrow><msubsup><mrow><mi>d</mi></mrow><mrow><mi>p</mi></mrow><mrow><mi>m</mi></mrow></msubsup></mrow><mrow><mo>/</mo></mrow><mrow><msubsup><mrow><mi>d</mi></mrow><mrow><mi>p</mi></mrow><mrow><mi>f</mi></mrow></msubsup></mrow></mrow><mrow><mo stretchy=\\\"false\\\">)</mo></mrow></mrow><mrow><mn>1.5</mn></mrow></msup></math>' role=\\\"presentation\\\" style=\\\"position: relative;\\\" tabindex=\\\"0\\\"><nobr aria-hidden=\\\"true\\\"><span style=\\\"width: 5.587em; display: inline-block;\\\"><span style=\\\"display: inline-block; position: relative; width: 4.562em; height: 0px; font-size: 122%;\\\"><span style=\\\"position: absolute; clip: rect(0.925em, 1004.56em, 2.769em, -999.997em); top: -2.2em; left: 0em;\\\"><span><span><span style=\\\"display: inline-block; position: relative; width: 4.562em; height: 0px;\\\"><span style=\\\"position: absolute; clip: rect(2.923em, 1003.49em, 4.562em, -999.997em); top: -3.993em; left: 0em;\\\"><span><span><span style=\\\"font-family: MathJax_Main;\\\">(</span></span><span><span><span><span style=\\\"display: inline-block; position: relative; width: 1.283em; height: 0px;\\\"><span style=\\\"position: absolute; clip: rect(3.128em, 1000.51em, 4.152em, -999.997em); top: -3.993em; left: 0em;\\\"><span><span style=\\\"font-family: MathJax_Math-italic;\\\">d<span style=\\\"display: inline-block; overflow: hidden; height: 1px; width: 0.003em;\\\"></span></span></span><span style=\\\"display: inline-block; width: 0px; height: 3.998em;\\\"></span></span><span style=\\\"position: absolute; clip: rect(3.537em, 1000.72em, 4.152em, -999.997em); top: -4.403em; left: 0.566em;\\\"><span><span style=\\\"font-size: 70.7%; font-family: MathJax_Math-italic;\\\">m</span></span><span style=\\\"display: inline-block; width: 0px; height: 3.998em;\\\"></span></span><span style=\\\"position: absolute; clip: rect(3.537em, 1000.41em, 4.306em, -999.997em); top: -3.737em; left: 0.515em;\\\"><span><span style=\\\"font-size: 70.7%; font-family: MathJax_Math-italic;\\\">p</span></span><span style=\\\"display: inline-block; width: 0px; height: 3.998em;\\\"></span></span></span></span></span><span><span style=\\\"font-family: MathJax_Main;\\\">/</span></span><span><span><span style=\\\"display: inline-block; position: relative; width: 1.027em; height: 0px;\\\"><span style=\\\"position: absolute; clip: rect(3.128em, 1000.51em, 4.152em, -999.997em); top: -3.993em; left: 0em;\\\"><span><span style=\\\"font-family: MathJax_Math-italic;\\\">d<span style=\\\"display: inline-block; overflow: hidden; height: 1px; width: 0.003em;\\\"></span></span></span><span style=\\\"display: inline-block; width: 0px; height: 3.998em;\\\"></span></span><span style=\\\"position: absolute; clip: rect(3.332em, 1000.46em, 4.306em, -999.997em); top: -4.403em; left: 0.566em;\\\"><span><span style=\\\"font-size: 70.7%; font-family: MathJax_Math-italic;\\\">f<span style=\\\"display: inline-block; overflow: hidden; height: 1px; width: 0.054em;\\\"></span></span></span><span style=\\\"display: inline-block; width: 0px; height: 3.998em;\\\"></span></span><span style=\\\"position: absolute; clip: rect(3.537em, 1000.41em, 4.306em, -999.997em); top: -3.737em; left: 0.515em;\\\"><span><span style=\\\"font-size: 70.7%; font-family: MathJax_Math-italic;\\\">p</span></span><span style=\\\"display: inline-block; width: 0px; height: 3.998em;\\\"></span></span></span></span></span></span><span><span style=\\\"font-family: MathJax_Main;\\\">)</span></span></span><span style=\\\"display: inline-block; width: 0px; height: 3.998em;\\\"></span></span><span style=\\\"position: absolute; top: -4.659em; left: 3.589em;\\\"><span><span style=\\\"font-size: 70.7%; font-family: MathJax_Main;\\\">1.5</span></span><span style=\\\"display: inline-block; width: 0px; height: 3.998em;\\\"></span></span></span></span></span><span style=\\\"display: inline-block; width: 0px; height: 2.205em;\\\"></span></span></span><span style=\\\"display: inline-block; overflow: hidden; vertical-align: -0.559em; border-left: 0px solid; width: 0px; height: 1.941em;\\\"></span></span></nobr><span role=\\\"presentation\\\"><math display=\\\"inline\\\" xmlns=\\\"http://www.w3.org/1998/Math/MathML\\\"><msup><mrow><mrow><mo stretchy=\\\"false\\\">(</mo></mrow><mrow><mrow><msubsup><mrow><mi>d</mi></mrow><mrow><mi>p</mi></mrow><mrow><mi>m</mi></mrow></msubsup></mrow><mrow><mo>/</mo></mrow><mrow><msubsup><mrow><mi>d</mi></mrow><mrow><mi>p</mi></mrow><mrow><mi>f</mi></mrow></msubsup></mrow></mrow><mrow><mo stretchy=\\\"false\\\">)</mo></mrow></mrow><mrow><mn>1.5</mn></mrow></msup></math></span></span><script type=\\\"math/mml\\\"><math display=\\\"inline\\\"><msup><mrow><mrow><mo stretchy=\\\"false\\\">(</mo></mrow><mrow><mrow><msubsup><mrow><mi>d</mi></mrow><mrow><mi>p</mi></mrow><mrow><mi>m</mi></mrow></msubsup></mrow><mrow><mo>/</mo></mrow><mrow><msubsup><mrow><mi>d</mi></mrow><mrow><mi>p</mi></mrow><mrow><mi>f</mi></mrow></msubsup></mrow></mrow><mrow><mo stretchy=\\\"false\\\">)</mo></mrow></mrow><mrow><mn>1.5</mn></mrow></msup></math></script>. Finally, <i></i><span style=\\\"color: inherit;\\\"></span><span data-mathml='<math xmlns=\\\"http://www.w3.org/1998/Math/MathML\\\" display=\\\"inline\\\"><msubsup><mrow><mi>t</mi></mrow><mrow><mi>p</mi></mrow><mrow><mi>c</mi></mrow></msubsup><mo>/</mo><msubsup><mrow><mi>t</mi></mrow><mrow><mi>p</mi></mrow><mrow><mi>f</mi></mrow></msubsup></math>' role=\\\"presentation\\\" style=\\\"position: relative;\\\" tabindex=\\\"0\\\"><nobr aria-hidden=\\\"true\\\"><span style=\\\"width: 2.564em; display: inline-block;\\\"><span style=\\\"display: inline-block; position: relative; width: 2.103em; height: 0px; font-size: 122%;\\\"><span style=\\\"position: absolute; clip: rect(1.078em, 1002.1em, 2.769em, -999.997em); top: -2.2em; left: 0em;\\\"><span><span><span style=\\\"display: inline-block; position: relative; width: 0.771em; height: 0px;\\\"><span style=\\\"position: absolute; clip: rect(3.23em, 1000.31em, 4.152em, -999.997em); top: -3.993em; left: 0em;\\\"><span><span style=\\\"font-family: MathJax_Math-italic;\\\">t</span></span><span style=\\\"display: inline-block; width: 0px; height: 3.998em;\\\"></span></span><span style=\\\"position: absolute; clip: rect(3.537em, 1000.36em, 4.152em, -999.997em); top: -4.352em; left: 0.361em;\\\"><span><span style=\\\"font-size: 70.7%; font-family: MathJax_Math-italic;\\\">c</span></span><span style=\\\"display: inline-block; width: 0px; height: 3.998em;\\\"></span></span><span style=\\\"position: absolute; clip: rect(3.537em, 1000.41em, 4.306em, -999.997em); top: -3.737em; left: 0.361em;\\\"><span><span style=\\\"font-size: 70.7%; font-family: MathJax_Math-italic;\\\">p</span></span><span style=\\\"display: inline-block; width: 0px; height: 3.998em;\\\"></span></span></span></span><span style=\\\"font-family: MathJax_Main;\\\">/</span><span><span style=\\\"display: inline-block; position: relative; width: 0.822em; height: 0px;\\\"><span style=\\\"position: absolute; clip: rect(3.23em, 1000.31em, 4.152em, -999.997em); top: -3.993em; left: 0em;\\\"><span><span style=\\\"font-family: MathJax_Math-italic;\\\">t</span></span><span style=\\\"display: inline-block; width: 0px; height: 3.998em;\\\"></span></span><span style=\\\"position: absolute; clip: rect(3.332em, 1000.46em, 4.306em, -999.997em); top: -4.506em; left: 0.361em;\\\"><span><span style=\\\"font-size: 70.7%; font-family: MathJax_Math-italic;\\\">f<span style=\\\"display: inline-block; overflow: hidden; height: 1px; width: 0.054em;\\\"></span></span></span><span style=\\\"display: inline-block; width: 0px; height: 3.998em;\\\"></span></span><span style=\\\"position: absolute; clip: rect(3.537em, 1000.41em, 4.306em, -999.997em); top: -3.84em; left: 0.361em;\\\"><span><span style=\\\"font-size: 70.7%; font-family: MathJax_Math-italic;\\\">p</span></span><span style=\\\"display: inline-block; width: 0px; height: 3.998em;\\\"></span></span></span></span></span><span style=\\\"display: inline-block; width: 0px; height: 2.205em;\\\"></span></span></span><span style=\\\"display: inline-block; overflow: hidden; vertical-align: -0.559em; border-left: 0px solid; width: 0px; height: 1.816em;\\\"></span></span></nobr><span role=\\\"presentation\\\"><math display=\\\"inline\\\" xmlns=\\\"http://www.w3.org/1998/Math/MathML\\\"><msubsup><mrow><mi>t</mi></mrow><mrow><mi>p</mi></mrow><mrow><mi>c</mi></mrow></msubsup><mo>/</mo><msubsup><mrow><mi>t</mi></mrow><mrow><mi>p</mi></mrow><mrow><mi>f</mi></mrow></msubsup></math></span></span><script type=\\\"math/mml\\\"><math display=\\\"inline\\\"><msubsup><mrow><mi>t</mi></mrow><mrow><mi>p</mi></mrow><mrow><mi>c</mi></mrow></msubsup><mo>/</mo><msubsup><mrow><mi>t</mi></mrow><mrow><mi>p</mi></mrow><mrow><mi>f</mi></mrow></msubsup></math></script> and <i></i><span style=\\\"color: inherit;\\\"></span><span data-mathml='<math xmlns=\\\"http://www.w3.org/1998/Math/MathML\\\" display=\\\"inline\\\"><msubsup><mrow><mi>t</mi></mrow><mrow><mi>p</mi></mrow><mrow><mi>m</mi></mrow></msubsup><mo>/</mo><msubsup><mrow><mi>t</mi></mrow><mrow><mi>p</mi></mrow><mrow><mi>f</mi></mrow></msubsup></math>' role=\\\"presentation\\\" style=\\\"position: relative;\\\" tabindex=\\\"0\\\"><nobr aria-hidden=\\\"true\\\"><span style=\\\"width: 2.974em; display: inline-block;\\\"><span style=\\\"display: inline-block; position: relative; width: 2.41em; height: 0px; font-size: 122%;\\\"><span style=\\\"position: absolute; clip: rect(1.078em, 1002.41em, 2.769em, -999.997em); top: -2.2em; left: 0em;\\\"><span><span><span style=\\\"display: inline-block; position: relative; width: 1.078em; height: 0px;\\\"><span style=\\\"position: absolute; clip: rect(3.23em, 1000.31em, 4.152em, -999.997em); top: -3.993em; left: 0em;\\\"><span><span style=\\\"font-family: MathJax_Math-italic;\\\">t</span></span><span style=\\\"display: inline-block; width: 0px; height: 3.998em;\\\"></span></span><span style=\\\"position: absolute; clip: rect(3.537em, 1000.72em, 4.152em, -999.997em); top: -4.352em; left: 0.361em;\\\"><span><span style=\\\"font-size: 70.7%; font-family: MathJax_Math-italic;\\\">m</span></span><span style=\\\"display: inline-block; width: 0px; height: 3.998em;\\\"></span></span><span style=\\\"position: absolute; clip: rect(3.537em, 1000.41em, 4.306em, -999.997em); top: -3.737em; left: 0.361em;\\\"><span><span style=\\\"font-size: 70.7%; font-family: MathJax_Math-italic;\\\">p</span></span><span style=\\\"display: inline-block; width: 0px; height: 3.998em;\\\"></span></span></span></span><span style=\\\"font-family: MathJax_Main;\\\">/</span><span><span style=\\\"display: inline-block; position: relative; width: 0.822em; height: 0px;\\\"><span style=\\\"position: absolute; clip: rect(3.23em, 1000.31em, 4.152em, -999.997em); top: -3.993em; left: 0em;\\\"><span><span style=\\\"font-family: MathJax_Math-italic;\\\">t</span></span><span style=\\\"display: inline-block; width: 0px; height: 3.998em;\\\"></span></span><span style=\\\"position: absolute; clip: rect(3.332em, 1000.46em, 4.306em, -999.997em); top: -4.506em; left: 0.361em;\\\"><span><span style=\\\"font-size: 70.7%; font-family: MathJax_Math-italic;\\\">f<span style=\\\"display: inline-block; overflow: hidden; height: 1px; width: 0.054em;\\\"></span></span></span><span style=\\\"display: inline-block; width: 0px; height: 3.998em;\\\"></span></span><span style=\\\"position: absolute; clip: rect(3.537em, 1000.41em, 4.306em, -999.997em); top: -3.84em; left: 0.361em;\\\"><span><span style=\\\"font-size: 70.7%; font-family: MathJax_Math-italic;\\\">p</span></span><span style=\\\"display: inline-block; width: 0px; height: 3.998em;\\\"></span></span></span></span></span><span style=\\\"display: inline-block; width: 0px; height: 2.205em;\\\"></span></span></span><span style=\\\"display: inline-block; overflow: hidden; vertical-align: -0.559em; border-left: 0px solid; width: 0px; height: 1.816em;\\\"></span></span></nobr><span role=\\\"presentation\\\"><math display=\\\"inline\\\" xmlns=\\\"http://www.w3.org/1998/Math/MathML\\\"><msubsup><mrow><mi>t</mi></mrow><mrow><mi>p</mi></mrow><mrow><mi>m</mi></mrow></msubsup><mo>/</mo><msubsup><mrow><mi>t</mi></mrow><mrow><mi>p</mi></mrow><mrow><mi>f</mi></mrow></msubsup></math></span></span><script type=\\\"math/mml\\\"><math display=\\\"inline\\\"><msubsup><mrow><mi>t</mi></mrow><mrow><mi>p</mi></mrow><mrow><mi>m</mi></mrow></msubsup><mo>/</mo><msubsup><mrow><mi>t</mi></mrow><mrow><mi>p</mi></mrow><mrow><mi>f</mi></mrow></msubsup></math></script> can be simultaneously adjusted to exceed <i></i><span style=\\\"color: inherit;\\\"></span><span data-mathml='<math xmlns=\\\"http://www.w3.org/1998/Math/MathML\\\" display=\\\"inline\\\"><msup><mrow><mrow><mo stretchy=\\\"false\\\">(</mo></mrow><mrow><mrow><msub><mrow><mi>d</mi></mrow><mrow><mi>p</mi></mrow></msub></mrow><mrow><mo>/</mo></mrow><mrow><msubsup><mrow><mi>d</mi></mrow><mrow><mi>p</mi></mrow><mrow><mi>f</mi></mrow></msubsup></mrow></mrow><mrow><mo stretchy=\\\"false\\\">)</mo></mrow></mrow><mrow><mn>2</mn></mrow></msup></math>' role=\\\"presentation\\\" style=\\\"position: relative;\\\" tabindex=\\\"0\\\"><nobr aria-hidden=\\\"true\\\"><span style=\\\"width: 4.511em; display: inline-block;\\\"><span style=\\\"display: inline-block; position: relative; width: 3.691em; height: 0px; font-size: 122%;\\\"><span style=\\\"position: absolute; clip: rect(0.925em, 1003.69em, 2.769em, -999.997em); top: -2.2em; left: 0em;\\\"><span><span><span style=\\\"display: inline-block; position: relative; width: 3.691em; height: 0px;\\\"><span style=\\\"position: absolute; clip: rect(2.923em, 1003.18em, 4.562em, -999.997em); top: -3.993em; left: 0em;\\\"><span><span><span style=\\\"font-family: MathJax_Main;\\\">(</span></span><span><span><span><span style=\\\"display: inline-block; position: relative; width: 0.976em; height: 0px;\\\"><span style=\\\"position: absolute; clip: rect(3.128em, 1000.51em, 4.152em, -999.997em); top: -3.993em; left: 0em;\\\"><span><span style=\\\"font-family: MathJax_Math-italic;\\\">d<span style=\\\"display: inline-block; overflow: hidden; height: 1px; width: 0.003em;\\\"></span></span></span><span style=\\\"display: inline-block; width: 0px; height: 3.998em;\\\"></span></span><span style=\\\"position: absolute; top: -3.84em; left: 0.515em;\\\"><span><span style=\\\"font-size: 70.7%; font-family: MathJax_Math-italic;\\\">p</span></span><span style=\\\"display: inline-block; width: 0px; height: 3.998em;\\\"></span></span></span></span></span><span><span style=\\\"font-family: MathJax_Main;\\\">/</span></span><span><span><span style=\\\"display: inline-block; position: relative; width: 1.027em; height: 0px;\\\"><span style=\\\"position: absolute; clip: rect(3.128em, 1000.51em, 4.152em, -999.997em); top: -3.993em; left: 0em;\\\"><span><span style=\\\"font-family: MathJax_Math-italic;\\\">d<span style=\\\"display: inline-block; overflow: hidden; height: 1px; width: 0.003em;\\\"></span></span></span><span style=\\\"display: inline-block; width: 0px; height: 3.998em;\\\"></span></span><span style=\\\"position: absolute; clip: rect(3.332em, 1000.46em, 4.306em, -999.997em); top: -4.403em; left: 0.566em;\\\"><span><span style=\\\"font-size: 70.7%; font-family: MathJax_Math-italic;\\\">f<span style=\\\"display: inline-block; overflow: hidden; height: 1px; width: 0.054em;\\\"></span></span></span><span style=\\\"display: inline-block; width: 0px; height: 3.998em;\\\"></span></span><span style=\\\"position: absolute; clip: rect(3.537em, 1000.41em, 4.306em, -999.997em); top: -3.737em; left: 0.515em;\\\"><span><span style=\\\"font-size: 70.7%; font-family: MathJax_Math-italic;\\\">p</span></span><span style=\\\"display: inline-block; width: 0px; height: 3.998em;\\\"></span></span></span></span></span></span><span><span style=\\\"font-family: MathJax_Main;\\\">)</span></span></span><span style=\\\"display: inline-block; width: 0px; height: 3.998em;\\\"></span></span><span style=\\\"position: absolute; top: -4.659em; left: 3.281em;\\\"><span><span style=\\\"font-size: 70.7%; font-family: MathJax_Main;\\\">2</span></span><span style=\\\"display: inline-block; width: 0px; height: 3.998em;\\\"></span></span></span></span></span><span style=\\\"display: inline-block; width: 0px; height: 2.205em;\\\"></span></span></span><span style=\\\"display: inline-block; overflow: hidden; vertical-align: -0.559em; border-left: 0px solid; width: 0px; height: 1.941em;\\\"></span></span></nobr><span role=\\\"presentation\\\"><math display=\\\"inline\\\" xmlns=\\\"http://www.w3.org/1998/Math/MathML\\\"><msup><mrow><mrow><mo stretchy=\\\"false\\\">(</mo></mrow><mrow><mrow><msub><mrow><mi>d</mi></mrow><mrow><mi>p</mi></mrow></msub></mrow><mrow><mo>/</mo></mrow><mrow><msubsup><mrow><mi>d</mi></mrow><mrow><mi>p</mi></mrow><mrow><mi>f</mi></mrow></msubsup></mrow></mrow><mrow><mo stretchy=\\\"false\\\">)</mo></mrow></mrow><mrow><mn>2</mn></mrow></msup></math></span></span><script type=\\\"math/mml\\\"><math display=\\\"inline\\\"><msup><mrow><mrow><mo stretchy=\\\"false\\\">(</mo></mrow><mrow><mrow><msub><mrow><mi>d</mi></mrow><mrow><mi>p</mi></mrow></msub></mrow><mrow><mo>/</mo></mrow><mrow><msubsup><mrow><mi>d</mi></mrow><mrow><mi>p</mi></mrow><mrow><mi>f</mi></mrow></msubsup></mrow></mrow><mrow><mo stretchy=\\\"false\\\">)</mo></mrow></mrow><mrow><mn>2</mn></mrow></msup></math></script> by increasing the number of elutriation pipes. Therefore, present study enables the controllable range of the MRT ratio of polydisperse particles covering from <i></i><span style=\\\"color: inherit;\\\"></span><span data-mathml='<math xmlns=\\\"http://www.w3.org/1998/Math/MathML\\\" display=\\\"inline\\\"><msup><mrow><mrow><mrow><msub><mrow><mi>d</mi></mrow><mrow><mi>p</mi></mrow></msub></mrow><mrow><mo>/</mo></mrow><mrow><msubsup><mrow><mi>d</mi></mrow><mrow><mi>p</mi></mrow><mrow><mi>f</mi></mrow></msubsup></mrow></mrow></mrow><mrow><mn>2</mn></mrow></msup></math>' role=\\\"presentation\\\" style=\\\"position: relative;\\\" tabindex=\\\"0\\\"><nobr aria-hidden=\\\"true\\\"><span style=\\\"width: 3.589em; display: inline-block;\\\"><span style=\\\"display: inline-block; position: relative; width: 2.923em; height: 0px; font-size: 122%;\\\"><span style=\\\"position: absolute; clip: rect(0.925em, 1002.92em, 2.769em, -999.997em); top: -2.2em; left: 0em;\\\"><span><span><span style=\\\"display: inline-block; position: relative; width: 2.923em; height: 0px;\\\"><span style=\\\"position: absolute; clip: rect(2.923em, 1002.51em, 4.562em, -999.997em); top: -3.993em; left: 0em;\\\"><span><span><span><span><span style=\\\"display: inline-block; position: relative; width: 0.976em; height: 0px;\\\"><span style=\\\"position: absolute; clip: rect(3.128em, 1000.51em, 4.152em, -999.997em); top: -3.993em; left: 0em;\\\"><span><span style=\\\"font-family: MathJax_Math-italic;\\\">d<span style=\\\"display: inline-block; overflow: hidden; height: 1px; width: 0.003em;\\\"></span></span></span><span style=\\\"display: inline-block; width: 0px; height: 3.998em;\\\"></span></span><span style=\\\"position: absolute; top: -3.84em; left: 0.515em;\\\"><span><span style=\\\"font-size: 70.7%; font-family: MathJax_Math-italic;\\\">p</span></span><span style=\\\"display: inline-block; width: 0px; height: 3.998em;\\\"></span></span></span></span></span><span><span style=\\\"font-family: MathJax_Main;\\\">/</span></span><span><span><span style=\\\"display: inline-block; position: relative; width: 1.027em; height: 0px;\\\"><span style=\\\"position: absolute; clip: rect(3.128em, 1000.51em, 4.152em, -999.997em); top: -3.993em; left: 0em;\\\"><span><span style=\\\"font-family: MathJax_Math-italic;\\\">d<span style=\\\"display: inline-block; overflow: hidden; height: 1px; width: 0.003em;\\\"></span></span></span><span style=\\\"display: inline-block; width: 0px; height: 3.998em;\\\"></span></span><span style=\\\"position: absolute; clip: rect(3.332em, 1000.46em, 4.306em, -999.997em); top: -4.403em; left: 0.566em;\\\"><span><span style=\\\"font-size: 70.7%; font-family: MathJax_Math-italic;\\\">f<span style=\\\"display: inline-block; overflow: hidden; height: 1px; width: 0.054em;\\\"></span></span></span><span style=\\\"display: inline-block; width: 0px; height: 3.998em;\\\"></span></span><span style=\\\"position: absolute; clip: rect(3.537em, 1000.41em, 4.306em, -999.997em); top: -3.737em; left: 0.515em;\\\"><span><span style=\\\"font-size: 70.7%; font-family: MathJax_Math-italic;\\\">p</span></span><span style=\\\"display: inline-block; width: 0px; height: 3.998em;\\\"></span></span></span></span></span></span></span><span style=\\\"display: inline-block; width: 0px; height: 3.998em;\\\"></span></span><span style=\\\"position: absolute; top: -4.659em; left: 2.513em;\\\"><span><span style=\\\"font-size: 70.7%; font-family: MathJax_Main;\\\">2</span></span><span style=\\\"display: inline-block; width: 0px; height: 3.998em;\\\"></span></span></span></span></span><span style=\\\"display: inline-block; width: 0px; height: 2.205em;\\\"></span></span></span><span style=\\\"display: inline-block; overflow: hidden; vertical-align: -0.559em; border-left: 0px solid; width: 0px; height: 1.941em;\\\"></span></span></nobr><span role=\\\"presentation\\\"><math display=\\\"inline\\\" xmlns=\\\"http://www.w3.org/1998/Math/MathML\\\"><msup><mrow><mrow><mrow><msub><mrow><mi>d</mi></mrow><mrow><mi>p</mi></mrow></msub></mrow><mrow><mo>/</mo></mrow><mrow><msubsup><mrow><mi>d</mi></mrow><mrow><mi>p</mi></mrow><mrow><mi>f</mi></mrow></msubsup></mrow></mrow></mrow><mrow><mn>2</mn></mrow></msup></math></span></span><script type=\\\"math/mml\\\"><math display=\\\"inline\\\"><msup><mrow><mrow><mrow><msub><mrow><mi>d</mi></mrow><mrow><mi>p</mi></mrow></msub></mrow><mrow><mo>/</mo></mrow><mrow><msubsup><mrow><mi>d</mi></mrow><mrow><mi>p</mi></mrow><mrow><mi>f</mi></mrow></msubsup></mrow></mrow></mrow><mrow><mn>2</mn></mrow></msup></math></script> to <i></i><span style=\\\"color: inherit;\\\"></span><span data-mathml='<math xmlns=\\\"http://www.w3.org/1998/Math/MathML\\\" display=\\\"inline\\\"><msup><mrow><mrow><mo stretchy=\\\"false\\\">(</mo></mrow><mrow><mrow><msub><mrow><mi>d</mi></mrow><mrow><mi>p</mi></mrow></msub></mrow><mrow><mo>/</mo></mrow><mrow><msubsup><mrow><mi>d</mi></mrow><mrow><mi>p</mi></mrow><mrow><mi>f</mi></mrow></msubsup></mrow></mrow><mrow><mo stretchy=\\\"false\\\">)</mo></mrow></mrow><mrow><mn>2</mn></mrow></msup></math>' role=\\\"presentation\\\" style=\\\"position: relative;\\\" tabindex=\\\"0\\\"><nobr aria-hidden=\\\"true\\\"><span style=\\\"width: 4.511em; display: inline-block;\\\"><span style=\\\"display: inline-block; position: relative; width: 3.691em; height: 0px; font-size: 122%;\\\"><span style=\\\"position: absolute; clip: rect(0.925em, 1003.69em, 2.769em, -999.997em); top: -2.2em; left: 0em;\\\"><span><span><span style=\\\"display: inline-block; position: relative; width: 3.691em; height: 0px;\\\"><span style=\\\"position: absolute; clip: rect(2.923em, 1003.18em, 4.562em, -999.997em); top: -3.993em; left: 0em;\\\"><span><span><span style=\\\"font-family: MathJax_Main;\\\">(</span></span><span><span><span><span style=\\\"display: inline-block; position: relative; width: 0.976em; height: 0px;\\\"><span style=\\\"position: absolute; clip: rect(3.128em, 1000.51em, 4.152em, -999.997em); top: -3.993em; left: 0em;\\\"><span><span style=\\\"font-family: MathJax_Math-italic;\\\">d<span style=\\\"display: inline-block; overflow: hidden; height: 1px; width: 0.003em;\\\"></span></span></span><span style=\\\"display: inline-block; width: 0px; height: 3.998em;\\\"></span></span><span style=\\\"position: absolute; top: -3.84em; left: 0.515em;\\\"><span><span style=\\\"font-size: 70.7%; font-family: MathJax_Math-italic;\\\">p</span></span><span style=\\\"display: inline-block; width: 0px; height: 3.998em;\\\"></span></span></span></span></span><span><span style=\\\"font-family: MathJax_Main;\\\">/</span></span><span><span><span style=\\\"display: inline-block; position: relative; width: 1.027em; height: 0px;\\\"><span style=\\\"position: absolute; clip: rect(3.128em, 1000.51em, 4.152em, -999.997em); top: -3.993em; left: 0em;\\\"><span><span style=\\\"font-family: MathJax_Math-italic;\\\">d<span style=\\\"display: inline-block; overflow: hidden; height: 1px; width: 0.003em;\\\"></span></span></span><span style=\\\"display: inline-block; width: 0px; height: 3.998em;\\\"></span></span><span style=\\\"position: absolute; clip: rect(3.332em, 1000.46em, 4.306em, -999.997em); top: -4.403em; left: 0.566em;\\\"><span><span style=\\\"font-size: 70.7%; font-family: MathJax_Math-italic;\\\">f<span style=\\\"display: inline-block; overflow: hidden; height: 1px; width: 0.054em;\\\"></span></span></span><span style=\\\"display: inline-block; width: 0px; height: 3.998em;\\\"></span></span><span style=\\\"position: absolute; clip: rect(3.537em, 1000.41em, 4.306em, -999.997em); top: -3.737em; left: 0.515em;\\\"><span><span style=\\\"font-size: 70.7%; font-family: MathJax_Math-italic;\\\">p</span></span><span style=\\\"display: inline-block; width: 0px; height: 3.998em;\\\"></span></span></span></span></span></span><span><span style=\\\"font-family: MathJax_Main;\\\">)</span></span></span><span style=\\\"display: inline-block; width: 0px; height: 3.998em;\\\"></span></span><span style=\\\"position: absolute; top: -4.659em; left: 3.281em;\\\"><span><span style=\\\"font-size: 70.7%; font-family: MathJax_Main;\\\">2</span></span><span style=\\\"display: inline-block; width: 0px; height: 3.998em;\\\"></span></span></span></span></span><span style=\\\"display: inline-block; width: 0px; height: 2.205em;\\\"></span></span></span><span style=\\\"display: inline-block; overflow: hidden; vertical-align: -0.559em; border-left: 0px solid; width: 0px; height: 1.941em;\\\"></span></span></nobr><span role=\\\"presentation\\\"><math display=\\\"inline\\\" xmlns=\\\"http://www.w3.org/1998/Math/MathML\\\"><msup><mrow><mrow><mo stretchy=\\\"false\\\">(</mo></mrow><mrow><mrow><msub><mrow><mi>d</mi></mrow><mrow><mi>p</mi></mrow></msub></mrow><mrow><mo>/</mo></mrow><mrow><msubsup><mrow><mi>d</mi></mrow><mrow><mi>p</mi></mrow><mrow><mi>f</mi></mrow></msubsup></mrow></mrow><mrow><mo stretchy=\\\"false\\\">)</mo></mrow></mrow><mrow><mn>2</mn></mrow></msup></math></span></span><script type=\\\"math/mml\\\"><math display=\\\"inline\\\"><msup><mrow><mrow><mo stretchy=\\\"false\\\">(</mo></mrow><mrow><mrow><msub><mrow><mi>d</mi></mrow><mrow><mi>p</mi></mrow></msub></mrow><mrow><mo>/</mo></mrow><mrow><msubsup><mrow><mi>d</mi></mrow><mrow><mi>p</mi></mrow><mrow><mi>f</mi></mrow></msubsup></mrow></mrow><mrow><mo stretchy=\\\"false\\\">)</mo></mrow></mrow><mrow><mn>2</mn></mrow></msup></math></script> that meets the required reaction time ratio of different particle sizes, which is of great interest for realizing the synchronous conversion of polydisperse particles.\",\"PeriodicalId\":39,\"journal\":{\"name\":\"Industrial & Engineering Chemistry Research\",\"volume\":null,\"pages\":null},\"PeriodicalIF\":3.8000,\"publicationDate\":\"2024-09-20\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Industrial & Engineering Chemistry Research\",\"FirstCategoryId\":\"5\",\"ListUrlMain\":\"https://doi.org/10.1021/acs.iecr.4c02112\",\"RegionNum\":3,\"RegionCategory\":\"工程技术\",\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q2\",\"JCRName\":\"ENGINEERING, CHEMICAL\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Industrial & Engineering Chemistry Research","FirstCategoryId":"5","ListUrlMain":"https://doi.org/10.1021/acs.iecr.4c02112","RegionNum":3,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q2","JCRName":"ENGINEERING, CHEMICAL","Score":null,"Total":0}
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