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Shear and Extensional Rheology of Particle-Laden Viscoelastic Suspensions
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Dissertation
Shear and Extensional Rheology of Particle-Laden Viscoelastic Suspensions
2021
Overview
Recent discoveries have allowed a mathematical and computational foundation for understanding the rheology of particles suspended in viscoelastic fluids. We employ these new tools to understand the shear and the extensional rheology of such suspensions.0.1 Shear rheologyIn this project, we study the time dependent evolution and steady values of the bulk shear stress in non-Brownian rigid particle suspensions during start-up of shear flow via experiments and numerical simulations. We compute the per-particle “extra” stress contribution to suspensions due to the interaction of the particles with the elastic fluid as well as the particle-particle hydrodynamic interactions. Previously, non-colloidal suspensions in viscoelastic fluids have been studied in steady shear flows mostly through experiments for relatively concentrated suspensions but there are very few computational simulation studies that may shed light into these experiments. We are not aware of any theoretical or 3D direct numerical studies in the literature that compute the viscometric functions of viscoelastic suspensions in the start-up of shear flow. We are also not aware of any experimental data regarding rigid particle suspensions in polymeric fluid undergoing start-up of shear flow appearing in any previous work. Thus, there is a great opportunity to use high performance computing to study the evolution of stress in viscoelastic suspensions starting from rest and compare with transient shear experiments.First, we compute the viscometric functions (viscosity and first normal stress di↵erence coe- cient) of dilute suspensions as a function of shear strain for a wide range of Weissenberg numbers. The Weissenberg number, Wi, is the ratio of fluid relaxation timescale to flow timescale 1 ˙ . We show that the “extra” per-particle stress contribution can be decomposed into two components: 1) the direct contribution from the rigid particles as they resist deformation in the flow, known as the iv stresslet; and 2) the contribution from the polymeric fluid as it deforms around the particles, leading to extra stresses in the fluid phase, known as the particle-induced fluid stress (PIFS).We validate our “single particle” numerical simulations in the Wi << 1 regime by comparing the stresslet and the PIFS results with small Wi theory that we develop for the time-dependent evolution of average stress in a dilute particle suspension. We perform numerical simulations using both the Oldroyd-B equation and the Giesekus equation. The parameters of both models are chosen such that they fit to the steady shear rheology of the Boger fluid used by Dai et al. [14]. We find that the per-particle viscosity and the primary normal stress coecient evolve monotonically to steady state with strain at all Wi studied. The steady viscosity values show shear-thickening with Wi but the steady primary normal coecient values are non-monotonic with Wi in agreement with Yang et al. [88].We also study non-dilute suspensions in Boger fluids via numerical simulations to elucidate the e↵ect of particle-particle hydrodynamic interactions on the stress contributions. We use an implementation based on the class of Immersed Boundary (IB) methods to simulate multiple moving particles in computational domain. These simulations include fully resolved particle-scale hydrodynamics and fluid stresses. The IB method has a main disadvantage, the loss of resolution near the particle boundaries due to interpolation of information between the Lagrangian and Eulerian meshes - consequently the solid-fluid interface is not sharp.
Publisher
ProQuest Dissertations & Theses
Subject
ISBN
9798357500021
