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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
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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