How the Poly Density Bottle Works:
Water and isopropanol are soluble with one another in any porportion; they are miscible. Both the water molecules and the alcohol molecules have -OH groups that easily hydrogen bond to each other. The sodium chloride salt particles, Na1+ and Cl1-, however, preferentially bind with the water molecules forcing the alcohol molecules out of the water solution. This causes two layers to form: the isopropanol on top and the more dense water and salt layer on the bottom. This is because isopropanol and salt water are immiscible; they are not soluble with one another in all proportions. This 'salting out effect' is commonly used to remove organic molecules from an aqueous solution.
When the bottle is shaken, the two liquid layers momentarily mix, forming a pseudo-homogenous mixture with a density between the two separate liquid densities. The white beads with a lesser density than the liquid mixture float on top, and the blue beads with a greater density sink to the bottom. Then, as the aqueous salt layer separates from the alcohol, the blue beads rise in the bottom aqueous layer and the white beads sink in the top alcohol layer until they meet in the center. From lowest density to highest density the order is as follows: isopropanol, white beads, blue beads, and salt water. Because the beads float between the two liquids, the actual isopropanol/salt water interface is difficult to observe, adding to the mystery.