The melt viscosity of filled polymers depends on the filler particle packing. It is shown that the maximum particle packing for a low density polyethylene, filled with calcium carbonate, depends strongly on the filler surface treatment. This packing can be evaluated from melt viscosity measurements using the Quemada model. From contact angle measurements and using the Lee unified adhesion theory, it has been demonstrated that the maximum packing depends on particle-particle and matrix-filler interactions. The competition between both types of interaction leads to different organizations of particles in the composite.