Evolution of vapor pressure at contact with liquid

Two phase gas-liquid flow in pipes often appear in space applications. We consider the problem of reducing vapor pressure of steam in a closed vessel due to condensation at the interface with the cold liquid. We obtain integro-differential equations describing the drop in pressure first at the interface of the steam and a horizontal liquid layer and second when water droplets are injected into the steam. We analyze the effect of the initial state, the liquid content, and the geometric size of the closed vessel on the rate of decrease in pressure.