Mechanical and Civil Engineering Seminar
Complex fluids -- suspensions, emulsions, foams, etc. -- can exhibit many of the same behavior as conventional solids: crystallization, dynamical arrest, and development of a shear modulus and yield stress. The volume fraction, φ, of the suspended particles/droplets/bubbles can play the role of temperature in conventional solids. In particular, the random close packing volume fraction, φrcp, -- very roughly speaking, the volume fraction gumballs occupy when thrown at random into a gumball machine -- plays an analogous role to the glass transition temperature in conventional glass-forming materials like molecular, polymeric, or metallic glasses. Below φrcp, the suspension is a fluid -- albeit with a huge viscosity -- while above φrcp, the suspension has a bonafide zero frequency shear modulus and a corresponding yield stress. This φ-controlled transition from a fluid-like to a solid-like state is called a jamming transition. We will present results on properties of model suspensions of soft, deformable, particles in the jammed state near this transition. In particular, we will show that the internal stresses show anomalous long range correlations with a correlation length that grows as φ approaches φrcp. We will also discuss how, during steady, quasi-static shearing, long range correlations in the local plastic rearrangements give rise to anomalous behavior in the particle-scale diffusion and how this impacts the rheology.