Jeffrey F. Morris (Levich Institute and Chemical Engineering CUNY City College of New York), Suspension physics: From osmotic pressure to force networks

Suspensions of solid particles in liquids represent an important model for the understanding of both engineering materials and the statistical physics of mixtures, particularly of non-equilibrium systems. Several physical phenomena in suspensions with relevance to both the engineering and scientific perspectives will be discussed. The first of these will be a consideration of the two-phase nature of suspensions, and how the shear-induced structure results in non-Newtonian rheology, including rate-dependent viscosity as well as normal stresses. The normal stress differences are well-known, but remain poorly characterized for suspensions. Less well-known, but perhaps of greater impact on their behavior is the non-equilibrium osmotic pressure, or particle pressure. This shear-driven pressure has been related to particle migration; experiments and simulation will be used to motivate its constitutive modeling, including the case of very highly loaded or “dense” suspensions which forms the second major topic of discussion.

Dense suspensions, with industrial examples including precursors to solid ceramics and cements, can be quite difficult to process because their properties are very sensitive to particle surface interactions and thus to components in the liquid. This leads to extreme rate dependence known as “discontinuous shear thickening” (DST) where the viscosity undergoes a finite (often large) discontinuous jump in viscosity at some shear rate. Computational simulations inclusive of lubrication hydrodynamics, repulsive forces and contact with friction have been shown to reproduce the primary features found in experimental studies of DST. Here, we consider the force network development in this phenomenon. The suspension rheology displays behavior analogous to phase transition, with the control variables being the volume fraction and shear rate. For solid fraction below the critical value (~ 0.55 for monodisperse spheres), the suspension exhibits continuous shear thickening, with a finite rate of viscosity increase as shear rate increases. At the critical volume fraction, as the shear rate is increased, the system reaches a critical point at which the viscosity (or stress) has infinite slope, but remains continuous (as would the density at a gas-liquid critical point) and at which the stress fluctuations simultaneously grow. The underlying basis for this behavior is analyzed by various network-theoretical measures.