What is Microfluidics?

Microfluidics is the flow and mixing of microlitre volumes of fluids via capillary action, where the fluids are contained within wells and channels made of glass and polydimethylsiloxane gel (PDMS). Figure 1 shows how the cured gel creates an enclosure between itself and the glass slide beneath. Essentially, this forms what you call a “lab-on-a-chip” device.

Figure 1. Lab-on-a-chip.

Identifying Requirements

The implementation of our engineered biological system into a device required to meet the following criteria: Solutions have to mixed in the right order and the correct times and incubated for specified durations to allow any reaction to take place. We looked into microfluidics as a solution that could potentially meet these requirements. We also identified that an external pneumatic pump should not be used to drive flow in the chip as doctors would not have access to such a pump when using the chip in an ordinary clinical setting.

Figure 2. Photo of a microfluidics chip showing 3 channels.

A schematic diagram of the potential chip is shown in figure 3. The chip would require two inlets: one where the blood sample is deposited (Start chamber) and one where the stock solution is deposited (Middle chamber). The stock solution contains the siderophore-iron complexes that lipocalin in the blood sample would bind to. The two solutions would mix completely in the main channel before entering the end chamber where the bacteria will be contained. Once the mixed solution flows into the end chamber, it can stay there indefinitely until the bacteria takes up the siderophore-iron complexes and produces fluorescent proteins. As an extension of this project, an albumin chelator could be added just before the middle chamber in order to chelate albumin before it could come into contact with the siderophore-iron complexes.

Figure 3. Schematic diagram of a potential microfluidics chip for detecting lipocalin.

Why Microfluidics?

Not only did microfluidics enable our device requirements to be met, but also offered several additional advantages such as:

• Ease of use: in order for the reactions to be carried out at the right times, one need only add the blood sample onto the chip in order for it to work.
• Low cost: a single chip only costs a few cents each to make, so it would be cheap to manufacture in bulk. The small volumes of reagents used would also result in costs savings.
• Parallel processing: if there needs to be a control during the diagnosis, a microfluidics chip could provide an easy means of conducting the two tests simultaneously.
• Speed: With the small size of a glass slide/chip, the total flow time within the chip should be no more than 20 minutes, which means this is a sure way to ensure that the reactions are within 20 mins.
• Ease of coupling to a fluorometer: due to the transparency of the materials, it is easy to connect a chip to a fluorometer/spectrometer in order to detect minute amounts of fluorescence/colour change.
• Possibility of automation: reagents can be added automatically and at the right times to the blood sample in the chip.
• Biosafety: the chip could contain bacteria and blood with less risk of contamination. It is also easy to dispose of when the test is done since all the reagents are contained within the chip.
• Flexibility in testing: it is quick and easy to make and test multiple designs. Each batch of test designs would take around 1 day to make and 1 day to test. Food colouring is used in place of blood and ferric enterobactin solution to test how well the solutions mixed.

In order to determine the best microfluidics design for our project, we tested out different mixing designs as well as the fluid flow rate in different channel lengths.

References

1. Falkovich, G. (2011). Fluid Mechanics. Cambridge University Press.

2. Bruus, H. Theoretical Microfluidics. Oxford University Press, 2007

3. C. H. Mastrangelo, A. Burns, D. T. Burke, C. Science, and A. Arbor, Microfabricated Capillary-Driven Stop Valve And Sample Injector,‖ in Eleventh Annual International Workshop On Micro Electrical Mechanical Systems, 1998, pp. 45–50.>

4. Boldock, L, 2013. Developing A Microfluidic Device With Passive Valves And Capillary Pump. Postgraduate. Sheffield: The University of Sheffield.

5. Tabeling, P. (2005). Introduction to microfluidics. Oxford University Press on Demand.

The Theory

Mixing in microfluidics occurs in two ways: via diffusion or the introduction of turbulence. In order to encourage mixing in a microfluidics chip, one must induce it in either or both ways.

Firstly, diffusion is the movement of particles from a region of higher concentration to a region of lower concentration. For instance, when the blood and stock solution are flowing side by side, lipocalin would move from the blood into the stock solution since there is higher a concentration of lipocalin in the blood as compared to the stock solution. This also holds true for the siderophore-iron complexes, which diffuse from the stock solution into the blood. Over time, there is an equal concentration of reagents on both sides and thus the solutions are mixed. In order to increase the rate of diffusion and hence mixing, the distance that the particles need to diffuse across needs to be shortened by minimising the width of the channel. For the protocol used, the minimum width that is feasible is 0.5 mm.

Introducing turbulence encourages mixing much like how stirring liquid in a mug helps to mix the contents.There are two types of flow: laminar and turbulent. Laminar flow is when the liquid particles travel in an orderly manner parallel to the channel length and in a single direction. The velocity of the liquid can be represented well using equations. In turbulent flow, the direction and speed at which each particle moves is unpredictable. The Reynolds number quantifies whether a flow is laminar or turbulent¹. It is defined as follows, where a higher Reynolds number indicates a more turbulent regime.

With respect to the lengths of a microfluidics chip (maximum 10 cm) , viscosity (3.5 × 10⁻³ Pa.s) and density (1060 kg/M³) of blood, the Reynolds number is around 10², which indicates laminar flow with minimal turbulence. The viscosity and density of blood remains constant throughout the test and the velocity cannot be easily controlled. However, the flow can be made more turbulent by increasing the length of the channel.

The Design Ideas

Design 1: The Capillary Stop Valve Idea

The initial design for mixing is shown in figure 4. Due to the surface tension of the liquid, the stock solution contained within the middle chamber would not flow out into the main channel. This design is called a capillary stop valve and has been shown to work in literature³. The flow of liquid from the middle channel can only be initiated when the blood sample flows past it.

Figure 4. Diagram of the mixing idea 1 containing a capillary stop valve. Surface tension holds the blue liquid in place like a valve until the red liquid flows past, pulling the blue liquid into the main channel where they mix.

This design allows the stock solution to be contained in a chamber prior to a blood sample being taken. The length of the main channel between the middle chamber and the end chamber can be specified so that the binding of siderophores to lipocalin would have reached equilibrium by the time the solution reaches the end chamber. A potential pitfall of this design is that the surface tension is inadequate to contain the stock solution.

Design 2: The Well Idea

The second design consists of two layers of PDMS (figure 5). The bottom layer has a well holding the stock solution (blue). The middle well needs to be filled to the brim but should not flow into the channels when the top layer is placed on it. This can be done by calculating the volume that the well can hold prior to adding the stock solution. The blood sample (here shown in yellow) will flow across the well, mix with the blue solution and flow out of the well as the mixed green solution.

This design is harder to manufacture, as two layers of PDMS have to be made and aligned with each other and this often incorporates considerable amount of human error and poor reproducibility. It has also not been seen in literature before, thus the effectiveness of this design is unknown. The advantage to this design is that it is a simple idea that does not depend on the quality of the manufactured PDMS, unlike capillary stop valves (design 1). The timing could also be easily controlled by varying the lengths of the channels.

Figure 5. Diagram of how mixing design 2 should work. The yellow fluid flows over the bottom well and mixes with the blue fluid contained there before flowing to the end chamber.

Design 3: The Mixing Chamber Idea

The third design consists of a large mixing chamber where the two fluids will spread out over a larger area and thus flow over a longer distance, which would give them a higher chance of mixing. A longer distance to flow over also means we can extend the time for which the reagents are in contact, further promoting adequate mixing. The final channel is deliberately made to be long so that if the fluids are not mixed by the time they enter the final channel, they could mix via diffusion within the smaller width of the channel. When the fluid flows from the mixing chamber to the final chamber, the reduction in width of the channel promotes the fluid to reach the end chamber. This is important as one of the problems we faced in the lab was the fluid stopping in the final chamber mid-way before reaching the end.

Figure 6. Diagram (top view) of mixing design 3 containing a large mixing chamber. The yellow and blue fluids should mix within the mixing chamber.

This design has already been shown to work in the lab before and thus should be more foolproof. However, there might be difficulty controlling when the 2 solutions mix, thus potentially resulting in one solution entering the end chamber before the mixed solution does. Since the blood can enter the last chamber without any adverse effects on the bacterial cells and the results obtained, this disadvantage can be mitigated by adding the blood before adding the siderophore-iron solution into their respective inlet chambers.

The Results

Design 1: The Capillary Stop Valve Idea

Capillary stop valves have been shown to work in literature³ but did not seem to work in our lab. We assume this is due to the quality of the PDMS chip produced when using our equipment and protocol⁴.

Figure 7 contains a photo of our result. The yellow solution, which represented the stock solution, did not stay in the chamber and flowed out into the main channel instead. Thus, it had to be quickly added after the red solution, representing the blood sample. The addition of the yellow solution had to be timed perfectly, as the red solution had the tendency to flow into both chambers. As can be seen from the photo, there is some leakage of red solution into the inlet chamber containing the yellow solution.

Figure 7. Photo showing the result of mixing design 1. Red food colouring representing the blood is added in the leftmost chamber, while yellow food colouring representing the stock solution is added in the middle chamber. Both fluids flowed towards rightmost end chamber.

The two solutions are not fully mixed by the time they reach the end chamber. The channel between the end chamber and the yellow chamber should have been longer and/or narrower to allow mixing via diffusion to take place.

Design 2: The Well Idea

Overall, the results indicate that the design did not work as expected.

In the first test, with a well of 4 mm diameter, blue dye from the inlet chamber entered the well and sank to the bottom. When the well was eventually filled, the yellow dye at the top of the well was pushed out into the channel (figure 8). Thus, while mixing did occur at the bottom of the well, the liquid going out of the well was completely yellow. Furthermore, when the well was covered by the top layer of PDMS, an air bubble was formed on top of the well, preventing the blue dye from entering the well. This was mitigated by punching a hole in the top layer to release the air.

Figure 8. Results of mixing design 2 with a 4 mm yellow well. The blue dye sank to the bottom of the well and pushed the yellow dye out into the channel. The top two photos show the results from the top and side views; the bottom image is a diagram that represents the results.

Since the blue dye seemed to be denser than the yellow dye, as indicated by how it sank to the bottom of the well, we tested what would happen if the dye in the well was denser instead (Fig.9). The two dyes were able to mix as shown by the green solution flowing out of the well. The green solution also managed to flow back towards the start chamber. However, this would not pose a problem as what matters is that a green solution reaches the end chamber.

Figure 9. Results of mixing design 2 with a 4 mm blue well. As the yellow dye was less dense than the blue dye, it was able to mix with the blue dye.

As blood is denser than the stock solution, it would be better to place the blood in the well rather than in the start chamber. Punching a hole in the top PDMS layer above the well to prevent an air bubble from forming has also helped in allowing blood to be deposited in the well.

It would be preferable for the well to hold the stock solution instead, as that would allow the stock solution to be transported with the chip instead of separately. Hence, we tested what would happen if we reduced the diameter of the well while using the same design (top view of Fig.5). As predicted from earlier experiments, the blue dye sank to the bottom of the well due to its higher density. The blue dye also managed to flow in the channel around the well so that both the yellow and blue dye were in the main channel. Mixing did occur, as shown by the green solution in between the yellow and blue dyes. However, the blue dye reached the end chamber before the green solution and there is no way of knowing how much blue dye will reach the end chamber before the green solution arrives.

Figure 10. Results of mixing design 2 with a 3 mm yellow well.

Design 3: The Mixing Chamber Idea

The results of design 3 are rather promising, as the two dyes managed to mix (see Fig.11). Even though the yellow dye was added first, a green solution flowed out of the mixing chamber into the final channel. An air bubble was trapped within the mixing chamber once once fluid filled the final chamber. The quality of the PDMS produced could have also contributed to the formation of the air bubble. A close up photo of the chip (Fig.12) showed that the PDMS was uneven, so the quality of the PDMS produced could also have contributed to the formation of the air bubble. In this design, the solution also did not manage to reach the end chamber. This can be mitigated by shortening the length of the final channel.

Figure 11. Results of mixing design 3. The blue and yellow dyes mixed well to give a green solution.

Figure 12. A close up photo of the PDMS of mixing design 3.The channels are not smooth and that reflects the quality of the PDMS manufactured, which may affect the results.

The Theory

According to literature, the inlet chamber is similar to a capacitor of an electric circuit⁵. As the blood in the inlet chamber reduces, the pressure exerted on the channels also reduces, which should slow down the flow rate. However, since the volume of solution in the inlet chamber is much more than the total volume in the channel, it can be assumed that the pressure exerted by the inlet chamber remains constant throughout the duration of the flow. Thus, the main factor that affects flow rate is the resistance of the channels.

The resistance of the channel is similar to a resistor of an electric circuit. The higher the resistance, the slower the flow rate. The resistance of a channel can be represented by the equation shown below, where resistance is dependent on the dimensions of the channel (height 50 µm, varying lengths and widths) and the viscosity of the liquid⁵. C(X) is a constant that depends on the aspect ratio (the ratio between the width and the height of the channel); for the dimensions that we are considering (50 µm height, 1-2 mm width), C(X) tends to a constant of 0.0833.

By rearranging the equation, we find that the width of the channel does not affect the total flow rate. The total flow rate is defined as the total volume of the channel over the time taken for fluid to flow through the entire channel. The time taken is proportional to the square of the total channel length.

To test how length and width affect the total time taken for the dye to reach the end chamber, we carried out two sets of experiments; one where we kept width constant at 1 mm and 2 mm respectively and varied the length and two, where we kept length and width constant at 28 mm and 2 mm respectively, and measured the time taken to travel an incremental distance of 2 mm from 10 mm onwards. The latter allowed us to create a time lapse and see how fluid velocity changed with increasing distance. The reason behind this experiment was to determine the maximum length we could push for our final design.

The Results

At a constant width of 1 mm, the length was varied from 5 to 28 mm to determine the optimum channel length at this width. It was observed that the time taken for the dye to reach the end chamber increased as length of channel was increased. Dye travelled fastest at a channel length of 7 mm, reaching the end chamber in 2 seconds. For channel lengths under 7 mm, the chip had to be tapped against the bench surface to initiate flow.

At a constant width of 2 mm, the length was varied from 8 to 28 mm. The aim of doing this was to determine the optimum channel length at this width. It was observed that the time taken for the dye to reach the end chamber increased with increasing channel length. Here, the main challenge we face with lengths under 8 mm was the requirement of an external force to start flow. With channel lengths over and including 16 mm, flow started slowing down and eventually, stopping before reaching the end chamber. Another challenge was the collapsing of channels at lengths over 20 mm. This happened due to the weight of the PDMS causing the channel to bow into the space encapsulated by it and the glass slide. Figure 1 below demonstrates how flow rate changes with increasing channel length at 1 mm and 2 mm width respectively.

Figure 1. The effect of channel length on flow rate at constant widths of 1 mm and 2 mm. For 1 mm wide channels, the time taken for the dye to reach the end chamber increased as the channel length increases. For 2 mm wide channels, flow started slowing down significantly over lengths of 16 mm.

The final time lapse experiment proved that flow rate reduces over length. This is because of channel resistance that slows down the fluid over time. Figure 2 demonstrates reducing flow rate over distance travelled.

Figure 2. Flow rate over distance. Flow rate decreases over time as channel resistance slows down as the fluid travels through the channel.