Width of a planetary ring system and the C-ring of Saturn

The growth of particles in a planetary ring system is considered with reference to the C-ring of Saturn. Small particles arising from various sources collide with and temporarily adhere to larger particles, and the paper presents a mathematical analysis of the conditions under which the small particles will stay long enough on the surface of the larger ones so that a permanent bond will develop. It is initially assumed that the only force acting between the particles is gravitational attraction, and upper and lower limits for the width of a planetary ring are determined. The effects of van der Waals forces are then considered.