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The size distribution of interstellar grains is governed by the coagulation of small grains and shattering of large grains in grain-grain collisions. Observations imply that grain motions in interstellar clouds are driven by turbulence. A simple model is constructed wherein a Kolmogorov spectrum of turbulent eddies drives collisions between spherical grains in a uniform density gas. A collision between two grains results in either coagulation of both into a single, larger grain or shattering of both into a power-law spectrum of fragments.
Steady-state dust distributions are sought for various physically reasonable values of the maximum and minimum sizes of the turbulent eddies, turbulent velocities, grain-grain sticking efficiencies and the distribution of fragments produced by grain shattering. Extinction curves are calculated for these distributions and the sensitivity of the optical and ultraviolet extinction to the parameters is examined. Diffuse cloud extinction can be reproduced with a plausible choice of parameters.
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