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In order for the air not to rise in a liquid, that liquid would have to have the same density as air, which isn`t possible.

However, you can slow down the rise of air bubbles using very viscous liquid, honey for example. In general, making a liquid cooler also increases its viscosity, e.g. glycerin or gelatin that is liquid when hot and gel-liked when cool. There are also thixotropic liquids, ketchup is an example  that is liquid when moved, but pretty much solid when static.