Methods comprising: evaporating a catalyst source to produce a catalyst gas; condensing the catalyst gas to produce a catalyst vapor comprising catalyst droplets suspended in a gas phase; and contacting the catalyst vapor with a hydrocarbon gas to catalyze a decomposition reaction of the hydrocarbon gas into hydrogen gas and carbon. And, systems comprising: a catalyst source evaporator that provides a first stream to a reactor; a hydrocarbon source that provides a second stream to the reactor; a cooling column coupled to the reactor via a third stream comprising hydrogen, catalyst liquid, solid carbon, optionally catalyst gas, and optionally unreacted hydrocarbon gas such that the cooling column receives the third stream from the reactor; and wherein the cooling column has effluent streams that include (a) a fourth stream that comprises hydrogen and optionally catalyst gas and (b) a fifth stream that comprises catalyst liquid.