Dust-to-Gas Ratio and Phase Transition of Interstellar Medium

We discuss the time evolution of dust-to-gas mass ratio in the context of multi-phase model of interstellar medium. Phase transition of interstellar gas is considered to occur on a timescale of $10^{7--8}$ yr, according to a nonlinear open system model of interstellar medium. Since the phase transition changes the dust formation and destruction rates, the dust-to-gas ratio also fluctuates on the same timescale. This explains the scatter of the dust-to-gas ratios of spiral galaxies quantitatively, though we should note the large observational uncertainty.