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An Analytical Solution to Neumann-Type Mixed Boundary Poiseuille Microfluidic Flow in Rectangular Channel Cross-Sections (Slip/No-Slip) including a Numerical Technique to Derive It

Richter, Christiane; Kotz, Frederik; Keller, N.; Nargang, Tobias M.; Sachsenheimer, Kai; Helmer, Dorothea; Rapp, Bastian E.

In most microfluidic applications, pressure-driven Poiseuille flow in a contained cross-section with no-slip boundary conditions is the underlying fluid- mechanical model. Solutions for this problem exist for many known cross- sections. We have recently demonstrated a simple method to solve the relevant Poisson equation using a finite difference scheme in a spreadsheet analysis tool such as Microsoft Excel. The numerical solutions obtained from such a spreadsheet are close-to-exact to the analytical solutions with errors on the order of only a few percent. However, there are numerous applications in microfluidics for which the no-slip boundary condition is not valid. Examples include drag-reducing air-retaining surfaces as well as open-channel flow. For these scenarios few to no analytical models exist. In this paper, we derive an analytical model for mixed boundary conditions (slip/no-slip) in two dimensions in a rectangular channel cross-section. We also demonstrate that the equivalent numerical solution can be derived conveniently by adaption of the spreadsheet. In general, mixed boundary-type flow scenarios are especially difficult to solve analytically whereas numerical solutions can be derived using Microsoft Excel within seconds.

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DOI: 10.5445/IR/1000071600
DOI: 10.4236/jbise.2017.105016
Cover der Publikation
Zugehörige Institution(en) am KIT Institut für Mikrostrukturtechnik (IMT)
Publikationstyp Zeitschriftenaufsatz
Publikationsjahr 2017
Sprache Englisch
Identifikator ISSN: 1937-6871, 1937-688X
KITopen-ID: 1000071600
HGF-Programm 47.02.07 (POF III, LK 01) Zellpopul.auf Biofunk.Oberflächen IMT
Erschienen in Journal of biomedical science and engineering
Verlag Scientific Research Publishing (SCIRP)
Band 10
Heft 05
Seiten 205–218
Bemerkung zur Veröffentlichung
Gefördert durch den KIT-Publikationsfonds
Schlagwörter Microfluidics, Numerics, Navier-Stokes Equation, Slip Condition, No-Slip Condition
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