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.

By combining the osmotic stress technique with small-angle x-ray scattering measurements, we followed the structural response of the casein micelle to an overall increase in concentration. When the aqueous phase that separates the micelles is extracted, they behave as polydisperse repelling spheres and their internal structure is not affected. When they are compressed, the micelles lose water and shrink to a smaller volume. Our results indicate that this compression is nonaffine, i.e., some parts of the micelle collapse, whereas other parts resist deformation. We suggest that this behavior is consistent with a spongelike casein micelle having a triple hierarchical structure. The lowest level of the structure consists of the CaP nanoclusters that serve as anchors for the casein molecules. The intermediate level consists of 10- to 40-nm hard regions that resist compression and contain the nanoclusters. Those regions are connected and/or partially merged with each other, thus forming a continuous and porous material. The third level of structure is the casein micelle itself, with an average size of 100 nm. In our view, such a structure is consistent with the observation of 10- to 20-nm casein particles in the Golgi vesicles of lactating cells: upon aggregation, those particles would rearrange, fuse, and/or swell to form the spongelike micelle.

Casein micelle dispersions have been concentrated through osmotic stress and examined through rheological experiments. In conditions where the casein micelles are separated from each other, i.e., below random-close packing, the dispersions have exactly the flow and dynamic properties of the polydisperse hard-sphere fluid, demonstrating that the micelles interact only through excluded volume effects in this regime. These interactions cause the viscosity and the elastic modulus to increase by three orders of magnitude approaching the concentration of random-close packing estimated at C(max) approximately 178 g/l. Above C(max), the dispersions progressively turn into "gels" (i.e., soft solids) as C increases, with elastic moduli G(') that are nearly frequency independent. In this second regime, the micelles deform and/or deswell as C increases, and the resistance to deformation results from the formation of bonds between micelles combined with the intrinsic mechanical resistance of the micelles. The variation in G(') with C is then very similar to that observed with concentrated emulsions where the resistance to deformation originates from a set of membranes that separate the droplets. As in the case of emulsions, the G(') values at high frequency are also nearly identical to the osmotic pressures required to compress the casein dispersions. The rheology of sodium caseinate dispersions in which the caseins are not structured into micelles is also reported. Such dispersions have the behavior of associative polymer solutions at all the concentrations investigated, further confirming the importance of structure in determining the rheological properties of casein micelle systems.