We investigate shattering and coagulation of dust grains in turbulent interstellar medium ( ISM ) .
The typical velocity of dust grain as a function of grain size has been calculated for various ISM phases based on a theory of grain dynamics in compressible magnetohydrodynamic turbulence .
In this paper , we develop a scheme of grain shattering and coagulation and apply it to turbulent ISM by using the grain velocities predicted by the above turbulence theory .
Since large grains tend to acquire large velocity dispersions as shown by earlier studies , large grains tend to be shattered .
Large shattering effects are indeed seen in warm ionized medium ( WIM ) within a few Myr for grains with radius a \ga 10 ^ { -6 } cm .
We also show that shattering in warm neutral medium ( WNM ) can limit the largest grain size in ISM ( a \sim 2 \times 10 ^ { -5 } ~ { } \mathrm { cm } ) .
On the other hand , coagulation tends to modify small grains since it only occurs when the grain velocity is small enough .
Coagulation significantly modifies the grain size distribution in dense clouds ( DC ) , where a large fraction of the grains with a < 10 ^ { -6 } cm coagulate in 10 Myr .
In fact , the correlation among R _ { V } , the carbon bump strength , and the ultraviolet slope in the observed Milky Way extinction curves can be explained by the coagulation in DC .
It is possible that the grain size distribution in the Milky Way is determined by a combination of all the above effects of shattering and coagulation .
Considering that shattering and coagulation in turbulence are effective if dust-to-gas ratio is typically more than \sim 1 / 10 of the Galactic value , the regulation mechanism of grain size distribution should be different between metal-poor and metal-rich environments .