The reaction between Diet Coke and mentos is caused by nucleation. This is where the carbon dioxide in the pop goes to the mentos (EpyBird.com), and create a bubbly stream that had so much pressure it shoots out of the container. According to the Diet Coke and Mentos Eruption article, pop is supersaturated with gas. This reaction is a physical reaction (DC&M Eruptions).
To speed up this physical reaction you can change multiple things. Warming up the Diet Coke before dropping the mentos