(123c) Why Is Everything Squishy?

A broad variety of different biomaterials, foods and personal products are found to have remarkably similar mechanical properties when deformed--which might typically be called 'squishy'. Technically termed soft-glassy materials (SGMs), these materials include such examples as soap foams, mayonnaise, ketchup, toothpaste, as well as remarkably, the actin cytoskeleton and the chromatin in cells' nuclei. When gently activated by internal energy sources, these SGMs display dynamic shear moduli that have a power-law frequency dependence, super-diffusive particle motion, and large cooperative particle rearrangements, or avalanches, all phenomena which are essentially unexplained. I will describe three-dimensional tracking experiments that show similar behavior in a transparent dense emulsion--essentially clear mayonnaise. We constructed a minimal computational model for SGMs whose physics was determined solely by energy minimization on an energy landscape spanning a high-dimensional configuration space (Nature Materials, 15, 1031-1036, 2016). The model is essentially a wet soap foam consisting of compressible spherical bubbles, whose sizes slowly evolve due to Ostwald Ripening. Surprisingly, we find that the steepest-descent configuration space path is a self-similar fractal curve, resembling a river cascading down a tortuous mountain canyon. The previously unexplained SGM rheology and Lévy-like super-diffusive motion in our model stem directly from these paths' fractal dimension and energy function. In the clear mayonnaise, we are able to show experimentally that the high-dimensional configuration space path is also a fractal.