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 chromat...

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Published inJournal of separation science Vol. 47; no. 16; pp. e2400419 - n/a
Main Authors Leppert, Jan, Brehmer, Tillman, Boeker, Peter, Wüst, Matthias
Format Journal Article
LanguageEnglish
Published Germany Wiley Subscription Services, Inc 01.08.2024
Subjects
Algebra
Blood vessels
Capillaries
Chromatography
Complex systems
Computer algebra
computers
flow calculation
Gas chromatography
Gas flow
Graph theory
Graphs
hold‐up time calculation
mathematical theory
pressure calculation
separation
hold‐up time calculation
pressure calculation
graph theory
gas chromatography
flow calculation
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Abstract 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 ion 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.
AbstractList 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.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.
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.
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 ion 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.
Author Leppert, Jan
Brehmer, Tillman
Wüst, Matthias
Boeker, Peter
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Issue 16
Keywords hold‐up time calculation
pressure calculation
graph theory
gas chromatography
flow calculation
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Snippet 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...
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StartPage e2400419
SubjectTerms Algebra
Blood vessels
Capillaries
Chromatography
Complex systems
Computer algebra
computers
flow calculation
Gas chromatography
Gas flow
Graph theory
Graphs
hold‐up time calculation
mathematical theory
pressure calculation
separation
Title Generalized flow calculation of the gas flow in a network of capillaries used in gas chromatography
URI https://onlinelibrary.wiley.com/doi/abs/10.1002%2Fjssc.202400419
https://www.ncbi.nlm.nih.gov/pubmed/39178022
https://www.proquest.com/docview/3097657707
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https://www.proquest.com/docview/3153710308
Volume 47
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