(226e) Prediction of Rheological Properties of Structured Fluids in Homogeneous Shear Flows Based on a Realizable Model for the Orientation Dyad

Non-spherical particles dispersed in a Newtonian fluid have a tendency to align in shear flows because of viscous drag. This phenomenon is opposed by rotary diffusion induced by particle-particle interactions. At high concentrations and in the absence of hydrodynamic couples, self-alignment can also occur because excluded volume interactions prevent the return-to-isotropy of anisotropic states by rotary Brownian motion. The foregoing balance between hydrodynamic and diffusive alignment phenomena on the microstructure has a direct impact on the rheological properties of structured fluids.

Low-order moments of the orientation density function governed by Smoluchowski's equation are commonly used to characterize the microstructure of "rigid-rod" fluids. This classical approach has also been employed to study the flow-induced alignment of other fluids, such as lyotropic liquid crystalline polymers.

This research has identified an improved model for the microstructure of axisymmetric ellipsoidal particle suspensions by addressing a specific barrier problem related to the closure of the fourth-order moment of the orientation density function. The resulting theory for the instantaneous orientation dyad depends on four dimensionless groups: the particle aspect ratio, L/d; the Péclet number; a neumatic coefficient associated with the Maier-Saupe excluded volume potential, U; and, a dimensionless time associated with the rotary diffusion coefficient. A critical step in the practical application of the theory is the development of an algebraic closure that relates the orientation tetrad to the orientation dyad. The improved closure predicts that all two-dimensional and three-dimensional realizable microstructures subjected to a homogeneous shear flow will relax to either an anisotropic realizable steady state or an anisotropic realizable periodic state. The results, which agree qualitatively with previous theories and with experimental observations, show how the Péclet number and the neumatic coefficient influences the shear viscosity and the normal stress differences.

The theory predicts the existence of biphasic regions with and without an external hydrocynamic force field. For U < 25, the predominant feature is the existence of a unique nematic-like microstructure with a steady alignment of the director that becomes fully aligned with the flow as the Péclet number increases. For U > 25, tumbling and wagging of the director occurs at low to moderate values of the Péclet number. If the initial state has a director with a component in the vorticity direction, then director kayaking and director log-rolling may occur. For selected values of the governing parameters, the theory predicts shear thinning and shear thickening phenomena, Newtonian plateau regions at low and high Péclet numbers, positive (and negative) first normal stress differences as well as negative (and positive) second normal stress differences.