Generalized flow calculation of the gas flow in a network of capillaries used in gas chromatography

• Published in: Journal of separation science Vol. 47; no. 16; pp. e2400419 - n/a
• Main Authors: Leppert, Jan, Brehmer, Tillman, Boeker, Peter, Wüst, Matthias
• Format: Journal Article
• Language: English
• 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
• ISSN: 1615-9306; 1615-9314; 1615-9314
• DOI: 10.1002/jssc.202400419

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.