Comprehensive theory of the Deans' switch as a variable flow splitter: fluid mechanics, mass balance, and system behavior.

The Deans' switch is an effluent switching device based on controlling flows of carrier gas instead of mechanical valves in the analytical flow path. This technique offers high inertness and a wear-free operation. Recently new monolithic microfluidic devices have become available. In these devices the whole flow system is integrated into a small metal device with low thermal mass and leak-tight connections. In contrast to a mechanical valve-based system, a flow-controlled system is more difficult to calculate. Usually the Deans' switch is used to switch one inlet to one of two outlets, by means of two auxiliary flows. However, the Deans' switch can also be used to deliver the GC effluent with a specific split ratio to both outlets. The calculation of the split ratio of the inlet flow to the two outlets is challenging because of the asymmetries of the flow resistances. This is especially the case, if one of the outlets is a vacuum device, such as a mass spectrometer, and the other an atmospheric detector, e.g. a flame ionization detector (FID) or an olfactory (sniffing) port. The capillary flows in gas chromatography are calculated with the Hagen-Poiseuille equation of the laminar, isothermal and compressible flow in circular tubes. The flow resistances in the new microfluidic devices have to be calculated with the corresponding equation for rectangular cross-section microchannels. The Hagen-Poiseuille equation underestimates the flow to a vacuum outlet. A corrected equation originating from the theory of rarefied flows is presented. The calculation of pressures and flows of a Deans' switch based chromatographic system is done by the solution of mass balances. A specific challenge is the consideration of the antidiffusion resistor between the two auxiliary gas lines of the Deans' switch. A full solution for the calculation of the Deans' switch including this restrictor is presented. Results from validation measurements are in good accordance with the developed theories. A spreadsheet-based flow calculator is part of the Supporting Information.