What is Laminar Flow in Microchannels & Reynolds Number?

Author: Rabia Rana Atlan, University of Ankara, Department of Biomedical Engineering

   Macro/Micro-channel applications have been researched for many years by their advantages in improving mass and heat transfer. After the development of microsystems which was predicated on macro systems, the flow and heat transfer techniques in channels are getting more and more understood. Nowadays, microchannels are widely used in the automotive industry, the cooling of microprocessors and especially in biomedical systems.
The use of mini and micro terms for channels has made the classification of channels necessary according to their diameters.

   The first classification was made in 2000 thereby, the hydraulic diameter channel from 1 to 100 μm was named as microchannel [1]. Today, it was accepted that microchannels have characteristic dimensions with a hydraulic diameter below 1 mm in microtechnology.

   There are several materials to be fabricated such as molding, micromachining, etc. Regardless of fabrication techniques, microchannels offer some opportunities which are benefited from their high surface-to-volume ratio. For instance, MEMS (Micro-Electro-Mechanical Systems) devices are used for biological and chemical analysis in microscale. High-precise match with the scale of biological structure and also the possibility for placing several functions in a chemical process of MEMS are considered as essential advantages of microscale chips [2]. Within this scope, this review focuses on flow characteristics in microchannels.

Flow characteristics

   In fluid mechanics, some flows are quite turbulent, while others are smooth and regular. The regular movement of flow which is specified by smooth flow lines is called laminar flow. The motion of high viscous fluids at low speeds is generally laminar. On the other hand, a high degree of irregular fluid motion at high speeds is defined as turbulent. Since the transition from laminar flow the turbulent flow does not occur suddenly, between these flow regimes there is another type of fluid characteristic which is called transient. 

Reynolds Number & Laminar Flow Patterning in Microchannels

   Using laminar flow pattern is a novel method in microchannels that allows two or more fluids (e.g. samples, analytes, biological fluids, solutions, etc.) to move side-by-side in a channel without interference [3, 4]. This terminology is applied in microfluidic systems as a result of their microscale dimensions and correspondingly low Reynolds number flow.

   Osborne Reynolds, the British scientist, found that all flow regimes depend on surface roughness, geometries, the flow velocity, and the type of material in addition to other factors.

After detailed experiments, he defined a non-dimensional number which is called Reynolds number as the ratio of inertial forces to viscous forces in a significant flow configuration [5]:

Re=(ρ×u×L)/μ=(u×L)/ν

where:
    ρ is the density of the fluid
    u is the velocity of the fluid
    L is the typical length scale
    μ is the dynamic viscosity of the fluid
    ν is the kinematic viscosity of the fluid

   If the Reynolds number is larger than about 2300, it corresponds to turbulent flow at which inertial forces are dominant. The region in which Reynolds number is smaller than about 1000, it is called laminar flow regime. When the microchannels are considered, small dimensions of these channels generally just let to obtain much less than 1000 Re.

   It is possible to make Reynolds number clear by animating proof of concept: A man is running through the hallway in order to pass the corner. Suppose that another man is calling him from the opposite direction at that moment. Naturally, it is predicted that the running man will not change his direction suddenly because his momentum is high. Then, let’s define the viscosity as the desire to stick to the wall. In the end, as the running man is pulled by the wall, Re decreases, or viscosity increases, he will turn the corner as much as possible.

   This is the simplified representation of the Reynolds number. If the Reynolds number is low, you will run almost adherent to the wall (laminar flow); but if Re is high, you will break away from the corner, then you will be dispersed (turbulent flow).

   Now, imagine a microchannel. In relation to this microchannel, the numerator of the Reynolds formula is very small due to low dimensions of the channel which is scaled from nano to millimeter, while the denominator usually states constantly for most fluids that relevant to Newtonian fluids. At that point, velocity is the only consideration which is capable to manipulate the flow whether turbulent or not.

   Generally, a high-velocity profile of fluid inside the microfluidic systems cannot be achieved. It means that in any microchannel, flow is completely laminar and the emergence of turbulence is nearly impossible. More importantly, the laminar flow regime allows the straight parallel line of fluid to flow next to each other without mixing in microchannels except diffusion [4]. Because the laminar flow is represented as straight parallel lines which are also called profile of the flow. These lines move directly into the microchannels without any warping away from its route.

Examples in Microfluidics Utilizing Laminar Flow

   Micro-fuel cells are being considered as an alternative power source at microscale range. The two flows (which are oxidant and fuel streams) are distinguished in a single microchannel. Laminar flow allows a controllable diffusion region for oxidant and fuel streams in micro-fuel cells [6].

   Microfluidics is also used for the diagnostic device in chemical processes e.g. measurement of diffusion coefficients. In these devices (T-cells), two streams are introduced from the input. Then, the flows are run by laminar flow, it means that transportation only occurs via diffusion. This feature helps to find diffusion coefficients of materials [7].

   Laminar flow is mostly utilized in lab-on-a-chip devices. It exploits of easily generated laminar flows to move fluids and to deliver them for patterning. Patterning ability of growth medium is the unique feature which provides to modeling delicate structures of mammalian cells [4]. 

Conclusion

   To sum up, several investigations have been undertaken in the current literature to better understand fluid flow in microfluidics and how to be utilized. Furthermore, these researches expanded with macro and microscale studies. As opposed to macro systems, microscale ones provide much more fit to the purpose of fluidic systems such as fuel cells, lab-on-a-chip devices, etc.

   The flow regimes are specified by Reynolds number which depends on density, velocity, and viscosity of the fluid. Turbulent flow is a type of fluid regimes in which the fluid forms irregular fluctuations. In microfluidic systems, the dominant fluid regime is laminar flow which moves in smooth layers or path. It just offers diffusion transportation between two fluids, otherwise given two different streams cannot be mixed through the microchannels. These features will continue to open new research fields in science.

References

[1] Mehendale S., et al., (2000), doi: 10.1115/1.3097347
[2] Sharp, K.V., et al., (2019), ISBN: 9780849321061 
[3] Takayama, S., et al.,(1999), 10.1073/pnas.96.10.5545.
[4] Jiang, X., et al., (2014), ISBN: 9780123983701
[5] Launder, B.E., (2011), ISBN: 978-0-521-19868-4 
[6] Tanveer, M. and K.Kim, (2018), doi: 10.3390/mi9100479
[7] Kamholz, A.E. and P.Yager, (2001), doi: 10.1016/S0006-3495(01)76003-1