It's probable that more microfluidic devices have been ruined by bubbles than any other problem. One key source is due to a higher temperature in the device compared to the stored solution: gas solubility goes down so bubbles come out.
It is very simple to estimate the size of a single bubble if all the excess gas in your capillary of radius r and length L accumulates into a single bubble. If this radius is greater than your capillary, then it's blocked. To avoid this sort of bubble, just keep your device a few °C lower than your stock solution.
You have the perfect microfluidic setup and everything should work, except for some pesky bubbles blocking a channel. Where did they come from? Assuming that you didn't introduce them from your syringes, pumps or connectors, the most likely answer is that they appeared because the temperature in the device is higher than the temperature of your stock solutions. The solubility of air in water goes down with temperature so a bubble can form at higher temperature. This rather trivial and obvious fact is surprisingly little known and many experiments that work well in simple room-temperature tests on biological systems will fail when the system is set to physiological temperatures.
The root cause cure is to make sure your stock solution is stabilised for some time at 1°C above your device temperature, then to remove all the bubbles before the liquid enters the device. Alternatively, a vacuum degassing at storage temperature achieves the same result.
The equation for gas solubility is somewhat inelegant, based on Tv=T°K/100:
Sol(g/cc) = Exp(-67.4 + 87.5 / Tv + 24.8 * Ln(Tv)) * 18 / 28
The calculation assumes that you have a capillary of radius r and length L - it's up to you to provide rough estimates from your real case. From the temperature rise ΔT (from a reference value of T=20°C) and a knowledge of the solubility of air in water, and from the total volume of your capillary, a theoretical radius for a single bubble is calculated. This assumes the worst case that all the excess air in this volume accumulates into this single bubble. If the calculated radius is much smaller than your capillary then you don't have to worry as the internal pressure (1/r) makes it unlikely that the bubble will appear.
Of course, if you are pumping fluid through the channel and a small bubble starts to appear, the dissolved air in the fresh liquid will be happy to join it. If you have a capillary length of, say, 10mm but pump through 10 volume equivalents, then set L to 100mm to get an idea of the size of the bubble that might accumulate.