Need help- calculating clearing of bubbles from a microfluidic channel

[RedneckPhysics]

TL;DR Summary

(Unsure of where to post) Trying to determine (semi-quantitatively), the amount of water flow needed to clear away bubbles in a 2-material, sharp-cornered micro-fluidic channel.

Hi All,

I need some help to figure out how to best go about setting-up and analyzing a micro-fluidics design problem I ran across in my research. It's not the typical single-surface contact angle adhesion kind of analysis.

Basically, I have a wide micro-fluidic channel that's formed by a nickel-plated metal transducer surface on the top wall, and a 3D printed acrylate plastic part for the bottom wall, with a very gradually sloping fillet forming the side walls. The part starts empty (air-filled), and water is pumped through the channel, ideally displacing all of the air inside (in other words, fills the entire channel with water). The channel may not be fully wet-able, leaving behind pockets of air, or bubbles in the corners. Bubbles will inevitably be formed within the water circuit, and passed through this channel, and could be lodged inside. I expect the flow rate in the corners to be far lower than the center, due to the boundary effect, combined with the inlet and outlet geometry.

Basic dimensions aren't drawn... the full channel is approximately 0.5mm in height (boundary 1 to boundary 2, at the widest part in this diagram), and about 8mm wide in total. The radius of curvature on that fillet as-is varies between 3mm and 0.5mm.

Here's a simple cross section diagram of the right 1/2 of the channel (Water flow is into or out of the page):

I'm trying to get a sense of how this design will trap or expel any air bubbles, at some specified average flow rate. I'm guessing we can assume flow is laminar through the majority of the channel. I'll use that information to optimize the average radius of curvature on that fillet, or otherwise alter the shape of the channel. The channel can't just be a simple rectangular shape... it will need at a minimum of a circular 0.5mm radius fillet on the right wall. The more material in that fillet, the better, in this use case.

Also, how would changes in effective surface energy of each material influence bubble retention? My intuition says, wetability might be a plus in this case... basically decreasing the amount of gas in the bubble in contact with the 2 solid interfaces.
I'm wondering if surface etching, or micro-patterning or the like could positively influence bubble clearing. Or, in the opposite case, smoothing and polishing.

The outlet is situated at the bottom center of the channel, and water flows from the ends of the channel, towards the center. To successfully clear a bubble from the system, it will need to be pulled away from the wall, towards the center of the channel. The side walls near the outlet area aren't going to see much flow... but that's a different ball of wax (or bubble of gas), best saved for another day.

In setting up the analysis, my best guess at the problem's end goal, is to obtain the work required to separate an air bubble from the edge of the channel, and then, to minimize that. Or perhaps, just get the overall adhesion force instead, if that's easy to calculate?

Aside from that, my best guess at a starting point is with Young's relations, and approximating the curved surface as locally flat for simplicity's sake.

Perhaps it's a lot more simple than that? In the end, I just need to know if there's a design that's more conducive to clearing away bubbles, and not trapping them in the first place.

Any thoughts? I'm a bit overwhelmed when it comes to connecting the dots.

Thanks for your help!

Michael

Edit: 04/28/20 Re-uploaded diagram

 

[Dullard]

I understand your question, but have no idea how to answer it (usefully) in a quantitative way. I do know that if you can re-orient things so that flow is against gravity (up), buoyancy will improve bubble clearance.

 

[Baluncore]

Likewise.
I see three possible mechanical solutions.
The first is to pull a vacuum on the channel while it is under water, so bubbles expand and can be replaced by water.
The second is to fit an ultrasonic transducer nearby, as used in ultrasonic cleaners, that will break up the bubble contact with the wall.
Third, flush the system with cold deionised or boiled water that may disolve the air.

 

[Baluncore]

1. How much pure water is needed to dissolve air?
At 20°C and a pressure of 1 bar, the solubility of O₂ in water is 8.5 mg/litre while N₂ is 20 mg/l.
The limiting factor will be N₂ solubility because air has 4 times more N₂ than O₂.
A 1 mm³ bubble of N₂ weighs 1 uL * 28 (g/mole) / 22.4 (L/mole) = 1.25 ug.
So it would require only 1.25 ug / 20 mg = 0.0625 ml of water to dissolve 1 mm³ of gas.
That is possible.

2. Maybe you could change the thermal profile of the system. Regulate the temperature of the channel. Introduce warmer water to the system, then cool it to channel temperature before it enters the channel. That way the water will not release dissolved gas into the channel and it will always have some capacity to remove gas from existing bubbles in the channel.

3. Another possibility would be to flush the cavity with steam. Maybe install a thin wire heating element that will boil the water in, or just upstream of the cavity.

 

[256bits]

Summary:: (Unsure of where to post) Trying to determine (semi-quantitatively), the amount of water flow needed to clear away bubbles in a 2-material, sharp-cornered micro-fluidic channel.

I'm wondering if surface etching, or micro-patterning or the like could positively influence bubble clearing. Or, in the opposite case, smoothing and polishing.

Possibly.
You will run into the Rose petal effect or the Lotus effect on the indentations.
Capillary effect may fill the indentations, ( and the corner interface you have drawn ) or have entrapped air over-ridden with water.
https://en.wikipedia.org/wiki/Lotus_effect

See the Cassie-Baxter equation and the Wenzel equation of a water bubble on a surface, even though you are actually looking at an air bubble, so will have to adapt to that scenario.
https://www.intechopen.com/books/su...assie-baxter-equation-based-on-energy-minimiz
if you are looking at energy considerations.
Do take into account if the bubble moves, there would be hysterisis at the leading and trailing edges.

rose petal
https://royalsocietypublishing.org/doi/10.1098/rsta.2010.0203