Next Article in Journal
Casein-Conjugated Gold Nanoparticles for Amperometric Detection of Leishmania infantum
Next Article in Special Issue
Acoustofluidic Micromixing Enabled Hybrid Integrated Colorimetric Sensing, for Rapid Point-of-Care Measurement of Salivary Potassium
Previous Article in Journal
Rapid Profiling of Soybean Aromatic Compounds Using Electronic Nose
Previous Article in Special Issue
Integrated Microfluidic Devices Fabricated in Poly (Methyl Methacrylate) (PMMA) for On-site Therapeutic Drug Monitoring of Aminoglycosides in Whole Blood
Open AccessArticle

Analytical Solution of the Time-Dependent Microfluidic Poiseuille Flow in Rectangular Channel Cross-Sections and Its Numerical Implementation in Microsoft Excel

Department of Microsystems Engineering (IMTEK), Laboratory of Process Technology | NeptunLab, Albert-Ludwigs University of Freiburg, 79085 Freiburg im Breisgau, Germany
*
Author to whom correspondence should be addressed.
Biosensors 2019, 9(2), 67; https://doi.org/10.3390/bios9020067
Received: 15 April 2019 / Revised: 16 May 2019 / Accepted: 22 May 2019 / Published: 24 May 2019
(This article belongs to the Special Issue Microfluidics for Biosensing and Diagnostics)
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. View Full-Text
Keywords: microfluidics; numerical techniques; Microsoft Excel; finite difference method; Navier–Stokes; time dependent flow; dynamic flow; initiation of flow; Poiseuille flow microfluidics; numerical techniques; Microsoft Excel; finite difference method; Navier–Stokes; time dependent flow; dynamic flow; initiation of flow; Poiseuille flow
Show Figures

Figure 1

MDPI and ACS Style

Risch, P.; Helmer, D.; Kotz, F.; Rapp, B.E. Analytical Solution of the Time-Dependent Microfluidic Poiseuille Flow in Rectangular Channel Cross-Sections and Its Numerical Implementation in Microsoft Excel. Biosensors 2019, 9, 67.

Show more citation formats Show less citations formats
Note that from the first issue of 2016, MDPI journals use article numbers instead of page numbers. See further details here.

Article Access Map by Country/Region

1
Search more from Scilit
 
Search
Back to TopTop