Casein micelles dispersions have been concentrated and equilibrated at different osmotic pressures using equilibrium dialysis. This technique measured an equation of state of the dispersions over a wide range of pressures and concentrations and at different ionic strengths. Three regimes were found. i), A dilute regime in which the osmotic pressure is proportional to the casein concentration. In this regime, the casein micelles are well separated and rarely interact, whereas the osmotic pressure is dominated by the contribution from small residual peptides that are dissolved in the aqueous phase. ii), A transition range that starts when the casein micelles begin to interact through their kappa-casein brushes and ends when the micelles are forced to get into contact with each other. At the end of this regime, the dispersions behave as coherent solids that do not fully redisperse when osmotic stress is released. iii), A concentrated regime in which compression removes water from within the micelles, and increases the fraction of micelles that are irreversibly linked to each other. In this regime the osmotic pressure profile is a power law of the residual free volume. It is well described by a simple model that considers the micelle to be made of dense regions separated by a continuous phase. The amount of water in the dense regions matches the usual hydration of proteins.