Mixing should be limited even if nothing special is done, due to the temperature and phase of matter and short timeframe. One could of course pay the weight penalty of a piston (need not have a perfect seal) or collapsing bag.
Doing a heat exchanger (to boil and thus pressurize) is another option, but then you're back to needing a place for the exhaust. It would let you do a sort of full-flow engine without turbopumps however, which is great. All those issues with cavitation and lubrication and stress cracking just go away.