How to correct collision between particles In the use particle system how to avoid two particles intersect each other as in the following figure:



Our settings for particles:
Physics = Newtonian, [checked] Size deflect,
Render: Object: dupli object : icosphere 

Update:
The original aim was to simulate separation of sands by some structures (combinations of tubes) due to their weights and the system configuration. So in our model, we used particle system to generate a continuous feed of sands into the system. Finally some sands are collected in some containers somewhere in the system.
The Figure shows a collector in which the intersection problem discovered. We also realised that not having self-collision between sand particles may bias the separation procedure as the particles do not collide each other, they were expected to do.
There is a free addon for blender name "Molecular"
this addon is exactly what you need

http://pyroevil.com/category/scripts-addons/molecular-script/

http://blenderartists.org/forum/showthread.php?233643-Addon-Moleculars-physics