Evaporation

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What drives evaporation of water when it's at the same temperature as the air? I know dry air absorbs more water than saturated air and that hot air carries more water but what drives the water to evaporate, absorb heat (cool down the liquid) and change phases? How can I quantify it?
I just want to use this to run some scenarios for my future evaporative cooler. Currently it works but I'd like to understand it better.