Normally, we think of combustion as occurring only in the gas phase. I think I understand the main reason for this - in the gas phase it's very hard for a bimolecular reaction to produce a single product, which makes it more likely for radical chain reactions to propagate rather than being terminated - but I'm curious about whether it's possible for combustion to occur in the liquid state at all.
For example: suppose I mixed liquid $\ce{CH4}$ with liquid $\ce{O2}$ under high pressure and reasonably low temperature. Would they react immediately? If not, could I 'ignite' the mixture in the same way as I could in the gas phase? (Note that the combustion of $\ce{CH4}$ into $\ce{H2O}$ and $\ce{CO2}$ doesn't change the mole number, so the volume change should be relatively small.) Would the reactions that occur be similar to the reactions that occur during combustion of $\ce{CH4}$ in the gas phase, or would they be completely different?
If this reaction wouldn't resemble combustion, is there some other example of a self-propagating oxidation reaction in liquid or aqueous phase with similar properties to combustion?