title: Numerics made easy: solving the Navier-Stokes equation for arbitrary channel cross-sections using Microsoft Excel.
abstract: The fluid mechanics of microfluidics is distinctively simpler than the fluid mechanics of macroscopic systems. In macroscopic systems effects such as non-laminar flow, convection, gravity etc. need to be accounted for all of which can usually be neglected in microfluidic systems. Still, there exists only a very limited selection of channel cross-sections for which the Navier-Stokes equation for pressure-driven Poiseuille flow can be solved analytically. From these equations, velocity profiles as well as flow rates can be calculated. However, whenever a cross-section is not highly symmetric (rectangular, elliptical or circular) the Navier-Stokes equation can usually not be solved analytically. In all of these cases, numerical methods are required. However, in many instances it is not necessary to turn to complex numerical solver packages for deriving, e.g., the velocity profile of a more complex microfluidic channel cross-section. In this paper, a simple spreadsheet analysis tool (here: Microsoft Excel) will be used to implement a simple numerical scheme which allows solving the Navier-Stokes equation for arbitrary channel cross-sections.
authors.affiliation: Institute of Microstructure Technology (IMT), Karlsruhe Institute of Technology (KIT), Hermann-von-Helmholtz-Platz 1, 76344, Eggenstein-Leopoldshafen, Germany.
authors.forename: Christiane
authors.initials: C
authors.lastname: Richter
authors.affiliation: Institute of Microstructure Technology (IMT), Karlsruhe Institute of Technology (KIT), Hermann-von-Helmholtz-Platz 1, 76344, Eggenstein-Leopoldshafen, Germany.
authors.forename: Frederik
authors.initials: F
authors.lastname: Kotz
authors.affiliation: Department of Complex Tissue Regeneration (CTR), MERLN Institute for Technology-Inspired Regenerative Medicine, Maastricht University, Maastricht, The Netherlands.
authors.forename: Stefan
authors.initials: S
authors.lastname: Giselbrecht
authors.affiliation: Institute of Microstructure Technology (IMT), Karlsruhe Institute of Technology (KIT), Hermann-von-Helmholtz-Platz 1, 76344, Eggenstein-Leopoldshafen, Germany.
authors.forename: Dorothea
authors.initials: D
authors.lastname: Helmer
authors.affiliation: Institute of Microstructure Technology (IMT), Karlsruhe Institute of Technology (KIT), Hermann-von-Helmholtz-Platz 1, 76344, Eggenstein-Leopoldshafen, Germany. bastian.rapp@kit.edu.
authors.forename: Bastian E
authors.initials: BE
authors.lastname: Rapp
mesh_terms: D003198:Computer Simulation; D044085:Microfluidics / Q000295:instrumentation* / Q000379:methods; D009716:Numerical Analysis, Computer-Assisted
keywords: Finite differents method; Microsoft Excel; Navier–Stokes; Numerics; Velocity profile