How do amines react with flue gases to absorb CO₂? I'm reading this article about carbon capture from the combustion of fossil fuels.  In this article, it says that amines are used as a chemical absorbent to capture the $\ce{CO2}$ from the exhaust of the combustion.  

In particular, I have read that N-Methyl diethanolamine (MDEA) is used (a  reference  lists the formula as $\ce{CH3N (C2H4OH)2}$).  I am curious if anyone can explain what happens during the reaction with $\ce{CO2}$ and how it absorbs the $\ce{CO2}$ from the flue gas.
In addition to the reaction in permeakra's answer, some amines may react with $\ce{CO2}$ in absence of water also. This type of reaction is a Lewis acid-base reaction forming a zwitterionic complex: $\ce{R3N + CO2 -&gt; R3NCO2}$.

 

MDEA adds some stability to this complex. The alcohol groups can stabilize the carboxylate group through hydrogen bonding.