Gravity-Driven System
Utilizing a system that relies on gravity to drive flow rates through the channels allows for live imaging of cells for prolonged periods of time. A holder with two large reservoirs (compared to the size of the channels) was designed to drive physiological flow through the channels. More fluid is added in the inlet reservoir than the outlet to force fluid flow in a single direction. The volume of the inlet reservoir can be restored over time to increase the time span of experiments while maintaining desired flow conditions.
Outer Holder Design
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The holder was designed using 3D Builder and SolidWorks. The top component of the holder was made of polycarbonate and the bottom component was made from polyether ether ketone (PEEK). Polycarbonate was chosen for the top as it is a durable, clear plastic material. PEEK was used for the bottom as it more flexible than polycarbonate, which was necessary to support the strain caused by tight screws in such a thin section of material. Both of these materials can be safely autoclaved for reusability to support sterile conditions. The collagen gel on a glass slide is put in the indent between the top and bottom holder pieces. The screws in the bottom allow for precise alignment of the top and bottom components of the device as well as a tight seal to avoid the leakage of media from the device. The square opening in the bottom piece of the holder also allows for live imaging of the microchannels through the glass slide holding the collagen.
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Images from the 3D Builder program showing dimensions of the outer holder. The 600μm holes in each reservoir are the inlet and outlet that connect the reservoirs to the microchannels. Images of the final fabricated product are also shown.
While the details for making the collagen gel with microchannels are detailed in the soft lithography page, this procedure is adapted so that the gel could be made directly on the underside of the top component of the device. The PDMS stamp is aligned at the bottom of the holder top and collagen is injected through the inlet/outlet channels into the empty space between the holder and the stamp. After the collagen has gelled completely, the PDMS is then peeled off and a collagen coated glass slide is added to seal off the produced channels in the gel. The bottom piece of the holder is then screwed in to hold the entire system together.
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Afterwards, pins are also inserted through the reservoir inlet and outlet to align and open up channels connecting to the microchannels inlet and outlet. This ensures flow between the reservoirs and channels indeed happens.
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Navier-Stokes and Bernoulli
The Navier Stokes equation, which can be further simplified to the Bernoulli equation, in conjunction with the formula for wall shear stress, is used to determine the desired height difference of fluid (∆z) between the two reservoirs of the outer holder in order to achieve a physiological flow within our system that is purely gravity-driven and can be sustained over a longer period of time. As seen below, the solution to the Bernoulli equation directly correlates to the flow rate solved for initially (refer to microfluidics page).
The change in pressure (∆p) is cancelled out as the reservoirs are open to the atmosphere. The velocity of fluid at the top of the inlet reservoir is very small since the reservoir size is much larger than the microchannels. Hence, the inlet velocity is considered negligible and cancels out as well. We are then left with a solution for the height difference, ∆z in terms of v out.
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Fluid can then be added into the inlet and outlet reservoir to the calculated height difference. This drives flow in the correct direction and at the right speed. When the fluid levels in the reservoirs start to equilibrate, the height difference is re-established by adding fluid into the inlet reservoir again. After establishing flow, the microchannels can be live imaged through the glass slide holding the collagen.
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