  We discuss the time variation of dust-to-gas mass ratio in spiral galaxies
using the multi-phase model of interstellar medium. The typical timescale of
the phase change of an interstellar gas is $\sim 10^7$--$10^8$ yr in spiral
galaxies. Since the phase transition changes the filling factor of the cold gas
where the dust growth occurs, the dust growth rate varies on that timescale. In
order to examine the response of the dust-to-gas ratio to the phase transition,
we construct a model of the time evolution of the dust-to-gas ratio. We adopt
the three phase model for the interstellar gas and the Ikeuchi-Tomita model for
the mass exchange among the phases. According to the model, three types of
solutions are possible: [1] all the gas is transformed to a hot gas; [2] a
stable stationary state of three phases is realized; [3] the filling factor of
each phase cyclically changes. For each of the three types of solutions, the
dust-to-gas ratio behaves as follows: [1] almost all the dust is destroyed (the
dust-to-gas ratio becomes $\sim 0$); [2] the dust-to-gas ratio converges to a
stationary state; [3] the dust-to-gas ratio varies cyclically in response to
the phase transition. In the case of [3], the amplitude of the variation of the
dust-to-gas ratio is large (nearly an order of magnitude) if the dust growth
timescale is shorter than the phase transition timescale. This condition is
easily satisfied in spiral galaxies. However, it is difficult for dwarf
galaxies to realize the condition because their small metallicity makes the
dust growth timescale long.
