Abstract
A quasi-3D model has been developed to simulate the flow in planar microfluidic systems with low Reynolds numbers. The model was developed by decomposing the flow profile along the height of a microfluidic system into a Fourier series. It was validated against the analytical solution for flow in a straight rectangular channel and the full 3D numerical COMSOL Navier-Stokes solver for flow in a T-channel. Comparable accuracy to the full 3D numerical solution was achieved by using only three Fourier terms with a significant decrease in computation time. The quasi-3D model was used to model flows in a micro-flow cytometer chip on a desktop computer and good agreement between the simulation and the experimental results was found.
Highlights
The development of microfluidic devices fabricated using microfabrication technologies began several decades ago [1]
We have presented a Q3D hydrodynamic flow model for planar microfluidic devices
The Q3D model solution was accurate to within 1% of the analytical solution with only three Fourier only three Fourier terms
Summary
The development of microfluidic devices fabricated using microfabrication technologies began several decades ago [1]. For complex three-dimensional (3D) flow geometries and systems, numerical techniques including finite difference, finite volume, and finite element methods have been used for many years [25,26,27], and a number of commercial software packages are currently available These packages are designed to handle general and arbitrary boundary conditions and require extensive computing resources and time for solving realistic problems. As will be shown below, a Fourier series decomposition of the velocity profile in the direction normal to the planar layers reduces the 3D flow problem to a limited number of 2D problems which can be solved more rapidly than a single full 3D problem without sacrificing accuracy significantly This approach has been used in the past [28] for simulations of electromagnetic waves in networks of rectangular waveguides
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