text: The final case described by Asakura and Oosawa describes two large, hard spheres of diameter , in a solution of small, hard spheres of diameter . If the distance between the center of the spheres, , is less than , then the small spheres are excluded from the space between the large spheres. This results in the area between the large spheres having a reduced concentration of small spheres and therefore reduced entropy. This reduced entropy causes a force to act upon the large spheres pushing them together. This effect was convincingly demonstrated in experiments with vibrofluidized granular materials where attraction can be directly visualized.