Risch, Patrick
[Author];
Helmer, Dorothea
[Author];
Kotz-Helmer, Frederik
[Author];
Rapp, Bastian E.
[Author]
Analytical solution of the time-dependent microfluidic poiseuille flow in rectangular channel cross-sections and its numerical implementation in microsoft excel
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Title:
Analytical solution of the time-dependent microfluidic poiseuille flow in rectangular channel cross-sections and its numerical implementation in microsoft excel
Description:
Abstract: We recently demonstrated that the Navier–Stokes equation for pressure-driven laminar (Poiseuille) flow can be solved in any channel cross-section using a finite difference scheme implemented in a spreadsheet analysis tool such as Microsoft Excel. We also showed that implementing different boundary conditions (slip, no-slip) is straight-forward. The results obtained in such calculations only deviated by a few percent from the (exact) analytical solution. In this paper we demonstrate that these approaches extend to cases where time-dependency is of importance, e.g., during initiation or after removal of the driving pressure. As will be shown, the developed spread-sheet can be used conveniently for almost any cross-section for which analytical solutions are close-to-impossible to obtain. We believe that providing researchers with convenient tools to derive solutions to complex flow problems in a fast and intuitive way will significantly enhance the understanding of the flow conditions as well as mass and heat transfer kinetics in microfluidic systems