Leppert Jan, Brehmer Tillman, Boeker Peter, Wüst Matthias
Department Fast GC, Institute of Nutritional and Food Sciences, Chair of Food Chemistry, University of Bonn, Bonn, Germany.
Hyperchrom GmbH Germany, Alfter, Germany.
J Sep Sci. 2024 Aug;47(16):e2400419. 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 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.
本文提出了一种计算圆柱形毛细管网络中气体流量和压力的通用方法。在本工作中，该方法专门用于气相色谱系统。通过这种方法，可以轻松计算复杂气相色谱系统中的流量和压力，如流量调制或热调制多维气相色谱系统，或具有不同压力下多个出口的系统。使用图论的数学抽象来表示毛细管系统。利用这个图，可以轻松建立毛细管连接处的流量平衡方程。使用计算机代数系统，可以求解流量平衡方程组以得到连接点处的压力。对于简单系统，给出了这种方法，并将计算得到的流量、压力和保留时间与测量值进行了比较。此外，还仅给出了两个复杂的毛细管系统（四通分流器、迪恩斯切换系统）的计算结果。对于这些系统，制定了某些条件，即这些系统不同路径之间保留时间的一定差异和定义的分流比。使用数值非线性求解器，找到了满足这些条件的这些系统的配置。
