Figure 1: An example of laminar and turbulent flow in the macroscale (Image taken from here)
When they hear the words fluid flow, most people think of a river. Water flows from a higher point to a lower one, primarily due to gravity and height gradient effects. Sure, that is a great example. However, most of this cannot be applied to microfluidic chips. That is because fluid flow can generally be split into turbulent and laminar [1]. In turbulent flow (the river case), the fluid under investigation – either a gas or a liquid – moves in such a way that it is constantly subject to mixing and irregular fluctuations. In addition, another characteristic of turbulent flow is the constant change in the speed of the fluid, both in direction and in magnitude at a certain point. On the contrary, in laminar flow, a fluid moves in parallel smooth layers (or laminae). To ensure the existence of laminar flow, the requirements are a slow motion of a fluid, a relatively small flow channel and a relatively viscous fluid. The profile of laminar flow through a small straight pipe may be approximated by small concentric cylinders towards the direction of the flow. At the outmost cylinder, which also coincides with the tube boundary, the fluid’s velocity is zero, gradually increasing until a maximum at the center of the tube. But how could one describe or even predict flow patterns?
Figure 2: Reynolds number and its implications
The Reynolds number, named after Osborne Reynolds, is a unitless indicator of whether fluid flow is turbulent or steady [2]. In general, for values of the Reynolds number less than 2000, the fluid is considered to exhibit a laminar flow, while for higher values it is considered to have a turbulent flow [3]. Unfortunately, there is no magic cut-off number, rather than a transition gradient from a value of 1000 to 5000 where the flow switches state [4]. The Reynolds number, derived by the uncompressed Navier-Stokes equation [5], is expressed as a mathematical quantity that links the average flow, the tube diameter, the fluid’s mass density and its absolute viscosity [6]. Or, more simply, it can be expressed as the ratio between the inertial and viscous forces acting on a fluid. Its importance for the microfluidic domain does not only come from the ability to predict flow profiles but also as it can be applied to interactions such as microparticles inflows, like bacteria or microspheres [7].
Figure 3: Different microfluidic drop maker geometries [8]
Laminar flows with low Reynolds number values are sought after in a microfluidic chip. Since there are two main types of flow control in such devices, pressure control and volume control, and the devices are very limited in size and volume, it is typically challenging to create turbulent flow.
However, some microfluidic devices take advantage of the capillary flow. This is utilized in passive designs, as the capillary flow does not rely on external forces such as pressure controllers or syringe pumps to induce the fluid motion but relies on the principle of spontaneous wicking of liquids, or more accurately, the capillary action that happens when the cohesive forces among the fluid molecules are weaker than their adhesion to the vessel walls. One could think of a filter coffee maker to visualize easily capillary flow in the macroscale, where coffee grounds are placed inside a funnel-shaped paper filter, and then hot water is poured over. Even if someone is extremely precise about not spilling any water and directly targets the center of the coffee grounds, after a while, the entire filter paper will have been wetted, and some brown color will also transfer in areas no coffee grounds exist. That is an example of how capillary flow works. A more fitting example of microfluidic work, while simultaneously known to everyone in the recent past, is the existence of lateral flow tests, such as the COVID-19 self-tests, which rely on a droplet of fluid for detection. Due to capillary flow, the small droplet of liquid travels along the surface of the pad until it reaches the points where the antibody and test control stripes are. If antigens are present in the liquid, the “positive test” line appears.
On the other hand, active microfluidic devices rely on external instruments to drive the flow by volume or pressure controllers. In addition, they might employ other methods to control the fluidic flow, such as electrodes for electrophoresis. Precise control is crucial and can impact the devices’ intended performance. However, owing to such precise control, contrary to macro systems, microfluidic devices have a key advantage in controlling multiphase flow systems with much higher precision and efficacy. Multiphase flow is simply the simultaneous flow of more than one liquid phase through a porous medium. For microfluidic applications, that translates into droplet creation, nanoparticle suspension, diffusion etc.
Figure 4: “Matryoshka droplets” by Iacopo Mattich, ETH Zurich (image taken from flickr).
Even though the discussed flow phenomena can be used to the advantage of numerous microfluidic devices, one should also be mindful of making the correct choices not only in terms of device design and fluid formulation, but also int terms of the material interactions of the device as well. Microfluidics nowadays are made using a variety of mostly optically transparent materials such as glass, polymers (PDMS,PMMA, etc.), wax, paper and many other plastics. However, the device performance might be impacted by the material choice. For example PDMS is highly permeable to organic solvents, while other plastics are not. On the contrary, it remains flexible when cross-linked, unlike PMMA. Some microchannels might also lose their shape if the material of choice is not strong enough, rendering the fluid flow through it abrasive.
In addition, another material problem is the interfacing of the device. There are various connectors available, but not all fixtures and fittings are created equal. Some flexible tubing might also inflate or deflate like a balloon if pressure differentiates significantly, which can change its effective diameter, and in turn, the whole fluid flow behavior. However, this precise peculiarity can be exploited to form a flow stop switch. Moreover, to avoid fabrication complexity or balance devices, microfluidic resistance is sometimes added outside of the device by changing the effective tubing diameter.
Shaping and accurate positioning is another important parameter. Some connectors, such as Luer-lock systems or ferruled barb fittings, don’t leave a lot of margin for error. However, some attachments, like inserting tubing into a punched hole through PDMS, rely on the skill of the user to not clog a channel and to shape the tubing at a correct bevel angle (or absence thereof) to ensure optimal fluid flow through the interface to the design. For example, needle hubs are notorious microsphere traps due to the combined change in geometry, material, and diameter of the interface from the syringe to the needle tip.
Figure 5: An example of airflow simulation using computational fluid dynamics (image taken from here)
In recent years, primarily due to the advances in computers in processing power and their accessibility, digital simulations gained popularity in many fields, as very complex problems can be analyzed profoundly quickly. One of these fields is computational fluid dynamics. Having been around since the 20th century, computational fluid dynamics has been recently popularized in research with the rise of computers capable of running multiple calculations simultaneously and at an acceptable cost. As a result, modern computational fluid dynamics implementations are, in essence, processes of numerically solving a mathematical model of a physical phenomenon involving fluid flow by utilizing the maximum computational power available. Thus, the number of necessary physical prototypes of a device can significantly be reduced owing to CFD, while many parameters can be optimized before the manufacturing process starts.
This report was written as part of the project STRENTEX, funded under the Horizon 2020 research and innovation programme under grant agreement No. 854194
This review was written by Adrian Stavrakis, doctoral researcher at University of Novi Sad.
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