A complex fluid, whether blood or mud, can exhibit a tremendous range of mechanical properties determined, among other things, by the liquid’s viscosity, the particles’ composition and chemistry, and the concentration of particles. Other effects being equal, whether the particles are hard or soft doesn’t matter much at low or intermediate concentrations. But that should change at the highest concentrations, more in the realm of cosmetics (as shown here) than of paint. In a conceptually simple model with hard spheres (HSs), a particle’s motion is confined to a cage formed by its nearest neighbors. As the concentration increases, the cage shrinks and motion decreases until, at a HS volume fraction of about 0.64, there remains no more available space for a particle to move. Soft spheres (SSs) are expected to behave differently—they deform each other at close quarters—but the details and implications of that behavior have been unclear. A...

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