# Water bubble inside a microchannel

1. Feb 3, 2010

### Excom

Hi

I need to calculate the force needed to move a water bubble inside a microchannel. Initially, the bubble is at rest and then the air pressure is increased on one side of the bubble.

I am new in microfluidic and need some help about where to start in order to solve this problem.

Thanks

2. Feb 3, 2010

### nona

hi
i didn't understand for you
can you tall us whether more,please
thanks

3. Feb 3, 2010

### Excom

I have a water bubble inside at microchannel. There is air on both sides of the bubble. I then increase the air pressure on one side of the bubble. The air pressure on the other sides is not changed. How much do I have to increase the pressure before the bubble starts to move?

4. Feb 3, 2010

### Andy Resnick

This is a great question! I'm not sure I have an answer, but let's see..

What are forces involved? We can ignore gravity. So it's really wetting: the air/water/glass common line must move in order for the bubble to move. Now, wetting is not understood and there are a lot of microscopic models that have been proposed, but macroscopically, we can maybe estimate:

Young's equation relates the contact angle and interfacial energies. To make the text here easier, let's assume the contact angle is 90 degrees (It's not, but you can work this out later). The air-water interfacial energy is 70 dyn/cm, so multiply this by the circumference of the bubble and you have a certain force to overcome in order to move the contact line. Now, if the glass surface is dirty or otherwise rough all bets are off, but for now, let's just consider the surface to be clean, flat, chemically homogeneous, etc. And I've neglected the air-glass and water-glass interfacial energies.

Then the required pressure difference will be 2*70*2*pi*r/(2*pi*r^2)= 140/r dyn/cm^2. As the channel size goes down, r decreases, requiring a larger pressure difference- that agrees with reality, at least.

It's fairly easy to measure- try it out and see how well it agrees, I'm curious.