Scaling behaviors of colloidal aggregates under uniform pressure

We present a theoretical model for the compaction of a colloidal sediment under uniaxial mechanical pressure in the continuous three-dimensional space. The initial system is formed with aggregated particles dispersed in a fluid, and softly sedimented in a vessel. When a uniform pressure is applied, it evolves irreversibly through successive creation and destruction of bonds between the particles. The rules governing the bonds depend on both geometrical constraints and current stresses. Numerical simulations of such systems exhibit three different scenarios, corresponding, respectively, to the fragile, elastic, and plastic behaviors. In the elastic regime, where most bonds are permanent, the pressure scales as a power law of the volume fraction of particles, with a numerical exponent equal to 4.4. In the plastic regime, where many bonds are broken and many others created, the pressure also scales with volume fraction, but the exponent is much lower, equal to 1.7. These scaling behaviors agree remarkably well with recent experiments realized on the compaction of systems with aggregated silica particles in the oedometer cell. They also can be explained with simple theoretical arguments using a plausible morphology of the resistant paths acting throughout the system. Finally, at very large applied pressures, all these regimes converge to the random close packing of spheres.