TY - JOUR

T1 - Numerics made easy: solving the Navier-Stokes equation for arbitrary channel cross-sections using Microsoft Excel

AU - Richter, Christiane

AU - Kotz, Frederik

AU - Giselbrecht, Stefan

AU - Helmer, Dorothea

AU - Rapp, Bastian E.

PY - 2016/6

Y1 - 2016/6

N2 - 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.

AB - 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.

KW - Numerics

KW - Navier-Stokes

KW - Microsoft Excel

KW - Finite differents method

KW - Velocity profile

U2 - 10.1007/s10544-016-0070-2

DO - 10.1007/s10544-016-0070-2

M3 - Article

C2 - 27233665

SN - 1387-2176

VL - 18

JO - Biomedical Microdevices

JF - Biomedical Microdevices

IS - 3

M1 - 52

ER -