Jan Leppert, Tillman Brehmer, Peter Boeker, Matthias Wüst
{"title":"气相色谱法所用毛细管网络中气体流量的通用流量计算。","authors":"Jan Leppert, Tillman Brehmer, Peter Boeker, Matthias Wüst","doi":"10.1002/jssc.202400419","DOIUrl":null,"url":null,"abstract":"<p>A general method for the calculation of the flow and pressure of a gas in a network of cylindrical capillaries is presented. This method is used specifically for gas chromatographic systems in this work. With this approach, it is possible to easily calculate flow and pressures in complex gas chromatographic systems, like flow-modulated or thermal-modulated multidimensional gas chromatographic systems, or systems with multiple outlets at different pressures. A mathematic abstraction using graph theory is used to represent the system of capillaries. With this graph, the flow balance equations at the connections of the capillaries can easily be set up. Using a computer algebra system, the system of flow balance equations can be solved for the pressures at the connection points. For simple systems, this approach is presented, and calculated flows, pressures, and hold-up times are compared with measured values. In addition, two complex systems (4-Way-Splitter, Deans Switch system) of capillaries are presented with calculations only. For these systems, certain conditions were formulated, that is, a certain difference in hold-up times and a defined split ratio between different paths of these systems. Using a numeric non-linear solver, configurations of these systems were found, that fulfill these conditions.</p>","PeriodicalId":17098,"journal":{"name":"Journal of separation science","volume":"47 16","pages":""},"PeriodicalIF":2.8000,"publicationDate":"2024-08-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://onlinelibrary.wiley.com/doi/epdf/10.1002/jssc.202400419","citationCount":"0","resultStr":"{\"title\":\"Generalized flow calculation of the gas flow in a network of capillaries used in gas chromatography\",\"authors\":\"Jan Leppert, Tillman Brehmer, Peter Boeker, Matthias Wüst\",\"doi\":\"10.1002/jssc.202400419\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"<p>A general method for the calculation of the flow and pressure of a gas in a network of cylindrical capillaries is presented. This method is used specifically for gas chromatographic systems in this work. With this approach, it is possible to easily calculate flow and pressures in complex gas chromatographic systems, like flow-modulated or thermal-modulated multidimensional gas chromatographic systems, or systems with multiple outlets at different pressures. A mathematic abstraction using graph theory is used to represent the system of capillaries. With this graph, the flow balance equations at the connections of the capillaries can easily be set up. Using a computer algebra system, the system of flow balance equations can be solved for the pressures at the connection points. For simple systems, this approach is presented, and calculated flows, pressures, and hold-up times are compared with measured values. In addition, two complex systems (4-Way-Splitter, Deans Switch system) of capillaries are presented with calculations only. For these systems, certain conditions were formulated, that is, a certain difference in hold-up times and a defined split ratio between different paths of these systems. Using a numeric non-linear solver, configurations of these systems were found, that fulfill these conditions.</p>\",\"PeriodicalId\":17098,\"journal\":{\"name\":\"Journal of separation science\",\"volume\":\"47 16\",\"pages\":\"\"},\"PeriodicalIF\":2.8000,\"publicationDate\":\"2024-08-23\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"https://onlinelibrary.wiley.com/doi/epdf/10.1002/jssc.202400419\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Journal of separation science\",\"FirstCategoryId\":\"5\",\"ListUrlMain\":\"https://onlinelibrary.wiley.com/doi/10.1002/jssc.202400419\",\"RegionNum\":3,\"RegionCategory\":\"工程技术\",\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q2\",\"JCRName\":\"CHEMISTRY, ANALYTICAL\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Journal of separation science","FirstCategoryId":"5","ListUrlMain":"https://onlinelibrary.wiley.com/doi/10.1002/jssc.202400419","RegionNum":3,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q2","JCRName":"CHEMISTRY, ANALYTICAL","Score":null,"Total":0}
Generalized flow calculation of the gas flow in a network of capillaries used in gas chromatography
A general method for the calculation of the flow and pressure of a gas in a network of cylindrical capillaries is presented. This method is used specifically for gas chromatographic systems in this work. With this approach, it is possible to easily calculate flow and pressures in complex gas chromatographic systems, like flow-modulated or thermal-modulated multidimensional gas chromatographic systems, or systems with multiple outlets at different pressures. A mathematic abstraction using graph theory is used to represent the system of capillaries. With this graph, the flow balance equations at the connections of the capillaries can easily be set up. Using a computer algebra system, the system of flow balance equations can be solved for the pressures at the connection points. For simple systems, this approach is presented, and calculated flows, pressures, and hold-up times are compared with measured values. In addition, two complex systems (4-Way-Splitter, Deans Switch system) of capillaries are presented with calculations only. For these systems, certain conditions were formulated, that is, a certain difference in hold-up times and a defined split ratio between different paths of these systems. Using a numeric non-linear solver, configurations of these systems were found, that fulfill these conditions.
期刊介绍:
The Journal of Separation Science (JSS) is the most comprehensive source in separation science, since it covers all areas of chromatographic and electrophoretic separation methods in theory and practice, both in the analytical and in the preparative mode, solid phase extraction, sample preparation, and related techniques. Manuscripts on methodological or instrumental developments, including detection aspects, in particular mass spectrometry, as well as on innovative applications will also be published. Manuscripts on hyphenation, automation, and miniaturization are particularly welcome. Pre- and post-separation facets of a total analysis may be covered as well as the underlying logic of the development or application of a method.