# Laminar Flow - Jay Mistri

CHEM-ENG 590E: Microfluidics and Microscale Analysis in Materials and Biology

# Laminar Flow

Figure 1 Laminar flow streams parallel to each other with minimal mixing.

Laminar, or streamline, flow is a fluid flow that is characterized by parallel streams with no disruption between their layers. [1] Laminar flow is commonly seen at low velocities, which is a result of a lower Reynold's number (less than 2000). The Reynolds number is a dimensionless value that is the ratio of the inertial forces to the viscous forces of a fluid (see Reynolds Number - Blayne Sarazin). The equation for Reynolds number is as follows:

$\mathrm{Re} = \frac{ \mbox{inertial forces} }{ \mbox{viscous forces} } = \frac{\rho v D}{\mu}$

where:

• $\rho$ is the density of the fluid
• v is the average velocity of the fluid
• D is the diameter of the channel
• $\mu$ is the viscosity of the fluid

# Applications in Microfluidics

Microfluidic devices have a very small tube diameter (<1 cm) which results in a lower Reynolds number. This allows the fluid flow to be laminar even at higher velocities, making processes faster. Because layers are not disrupted in laminar flow, microfluidic devices can control particular separations or mixing at desired points. Separating out components of a mixture using a gradient or a charge will allow the laminar flow to continue undisturbed throughout the device. For example, hydrodynamic lift is used to sort cells in a red blood flow [3].

# References

1. Bird, R. Byron, Warren E. Stewart, and Edwin N. Lightfoot. Transport phenomena. John Wiley & Sons, 2007.
2. Nave, R. (2005). "Laminar Flow". HyperPhysics. Georgia State University. Retrieved 23 November 2010. http://hyperphysics.phy-astr.gsu.edu/hbase/pfric.html
3. Geislinger, T. M.; Franke, T. Hydrodynamic lift of vesicles and red blood cells in flow — from Fåhræus & Lindqvist to microfluidic cell sorting. Advances in Colloid and Interface Science 2014, 208, 161-176. http://dx.doi.org/10.1016/j.cis.2014.03.002
4. Salafi, T.; - Zeming, K. K.; - Zhang, Y. - Advancements in microfluidics for nanoparticle separation. - Lab Chip. http://dx.doi.org/https://doi.org/10.1039/c6lc01045h
5. Kim, S. & Karrila, S. J. (2005) Microhydrodynamics: Principles and Selected Applications, Dover. ISBN 0-486-44219-5.