Quasi-3D Modeling and Efficient Simulation of Laminar Flows in Microfluidic Devices
Abstract
:1. Introduction
2. Theoretical Background
- The boundary condition at a channel wall is assumed to be the “no-slip” condition, (wall) = 0. This condition is well established even at the submicron level [30];
- The flow is quasi-static. Therefore, the time derivative in Equation (2) can be neglected. By this, it is assumed that the fluid velocities are sufficiently low so that any change in the boundary conditions results in an instantaneous rearrangement of the velocity and pressure fields to conform to the new conditions;
- Low-Reynolds-number flow is dominated by viscous forces. So the term can be ignored for low Reynolds number; i.e., [31]. For aqueous flows in microchannels with scale lengths on the order of 50 μm, velocities only need to be much less than 1 m·s−1 for this to be valid. For the majority of the cases of interest, their velocities are significantly less than 1 m·s−1. Equation (2) then reduces to the much simpler equation:
- Finally, there are no free-moving bodies (particles) in the flow that can locally disrupt the velocity profile, a condition commonly assumed in microfluidic simulations containing cells or particles in low concentrations, so that the particle-induced hydro-dynamic disturbances in the flow field can be neglected [32].
2.1. Fourier Expansion of the Flow Field
3. Testing of the Model
3.1. Straight Rectangular Channel
3.2. Flow in a T-cell
3.3. Computation Resources
4. Comparison of Experimental and Simulation Results
4.1. Flow Speed Characterization in the Main Microchannel
4.2. Flow Focusing Characterization
5. Conclusions
Acknowledgments
Author Contributions
Conflicts of Interest
Appendix A. Approximation of Symmetric Flow
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Islam, M.Z.; Tsui, Y.Y. Quasi-3D Modeling and Efficient Simulation of Laminar Flows in Microfluidic Devices. Sensors 2016, 16, 1639. https://doi.org/10.3390/s16101639
Islam MZ, Tsui YY. Quasi-3D Modeling and Efficient Simulation of Laminar Flows in Microfluidic Devices. Sensors. 2016; 16(10):1639. https://doi.org/10.3390/s16101639
Chicago/Turabian StyleIslam, Md. Zahurul, and Ying Yin Tsui. 2016. "Quasi-3D Modeling and Efficient Simulation of Laminar Flows in Microfluidic Devices" Sensors 16, no. 10: 1639. https://doi.org/10.3390/s16101639
APA StyleIslam, M. Z., & Tsui, Y. Y. (2016). Quasi-3D Modeling and Efficient Simulation of Laminar Flows in Microfluidic Devices. Sensors, 16(10), 1639. https://doi.org/10.3390/s16101639