The surface of Mentos candies are high in surface area, and are bumpy and pitted. Bumpy surfaces tend to "seed" bubbles out of carbonated drinks. What is meant by "seeding" this means is that when a gas is dissolved in a solution, it remains within the solution in microscopic bubbles. If there is an area where these microscopic bubbles can gather, they will do so to create a larger bubble (due to the hydrophobic effect). Areas that promote these microscopic bubbles to gather are called "seeds". Eventually the bubble will be too large to simply stay in solution and begin to rise to the surface, often as a visible tiny bubble. This is the same reason why after pouring yourself a glass of your favorite carbonated beverage, you may see small bubbling trails seemingly coming from the side of the glass out of nowhere. The "source" or origin of the bubbling is likely a small imperfection of the glass seeding bubbles.
When you drop the Mentos in, the carbon dioxide bubbles in the soda becomes seeded all over the entire surface of the candy's surface. Due to its high surface area, it seeds millions of bubbles at once, creating rapid gas release from solution. Additionally, gum arabic coating the surface of the candy acts as a surfactant, decreasing surface tension of the bubbles on its surface. Low surface tension also helps bubbles grow quickly. Aspartame (the artificial sweetener in diet coke) also works as a surfactant in solution, further decreasing surface area and increasing bubbling. Finally, Mentos are also fairly dense and sink rapidly, quickly creating bubbles that seed further bubbles as they rise, creating an exponential effect as the bubbles rise to the surface, as the bubbles are given more time to gather more bubbles as they rise.
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