The pattern may be not repulsion, but the result of attractive forces between grains. It seems a case of crystal formation by nucleation and accretion. Smaller grains are joining by intermolecular forces into larger particles, so the space between a large grain and smaller ones is growing at a rate related with the accretion process. At some point, the grain can no longer grow fast enough and reaches a maximum size.

I think the small particles may be distributed as a dark rim due to an effect described by Nagel el al and reported in New Scientist back in 1997 (http://www.newscientist.com/article/mg15621054.900-the-thrill-of-the-spill--theres-more-to-coffee-stains-than-meets.html).

They concluded that a rim was formed when the edge of a liquid was pinned to a surface by the slight roughness of most surfaces. This prevents the patch of liquid from shrinking in size and it evaporates. Instead, the patch of liquid shrinks in height and, as more liquid evaporates from the edges (due to the greater surface area here from exposure of the sides as well as the top of the patch to air), liquid has to flow towards the edges to replace the lost liquid here. As it flows outwards it brings particles with it, forming a dark rim when all the water has evaporated.

Each large coffee particle in this photo may have held around it  its own drop of water, which once evaporated, left the pattern seen in the photo.

It looks to me as if there is some surfactant (soap) or oil in the solids that is leaking out slowly.  There are a lot of oily compounds in coffee that could be to blame.  The larger particles will have more soluble material still present due to the time required for it to diffuse out of a larger solid particle.  If you take a water surface covered with powder (flour often  works well, but inly dust a little on lightly)  you can cause the particles to retreat into a distant ring by toughing the surface with a pin or matchstick that has been dipped into washing up liquid or wiped on a bar of soap and then wiped with a tissue to reduce the amount present.  This is a local reduction in surface tension causing the water surface to retreat and the particles are dragged with it.  A similar effect can be caused by adding a drop of oil at a point.