The stresses and forces of particle suspensions in viscoelastic shear flow
Keywords: Chemical Engineering.

Particle suspensions in viscoelastic fluids can be found across a wide array of engineering processes. As such, there is great interest in understanding the mechanical properties of the suspensions from both an academic and an industrial perspective. In this thesis, we employ a blend of direct numerical simulations, analytical theory, and experiments to study two main problems regarding the behavior of particles and the stresses arising from the presence of the particles in a viscoelastic shear flow. In the first project, we study the steady shear rheology of rigid particle suspensions in viscoelastic fluids via experiments and direct numerical simulations. Previous research on the study of noncolloidal suspension rheology has primarily been focused on particles in Boger fluids, which are highly elastic, nearly constant viscosity fluids. These Boger fluids are often created by suspending small concentrations of polymers in a Newtonian matrix. However, the vast majority of the viscoelastic fluids found in nature or used in industrial applications span a wide range of polymer concentrations and are often highly shear-thinning. To study the bulk shear rheology of a viscoelastic suspension, we compute the viscometric functions in terms of the per-particle viscosity and per-particle first normal stress difference coefficient as a function of Weissenberg number, Wi (the ratio of the elastic and viscous forces). These stress components are from the "extra" stress that arises in the suspension due to the addition of the particles, on a per-particle basis. The "extra" stress is comprised of two components: 1) the stresslet, or the stress arising from the rigid particles resistance to deformation from the flow and 2) the particle induced fluid stress (PIFS), or the extra stress in the polymers of the fluid changing conformations due to the presence of the added particles. We first study the effect of varying polymer concentration, measured by the dimensionless polymer viscosity partition function β, on the steady shear rheology of rigid particle suspensions using direct numerical simulation of the Oldroyd-B model. We perform both simulations of dilute and non-dilute suspensions using a single-particle body fitted (BF) method and a multi-particle immersed boundary (IB) method respectively. We compare the bulk rheology of our simulations at Φ = 2.5% and 5% to our dilute single particle simulations, and find that the per-particle viscosity and first normal stress difference coefficient are always shear-thickening at all values of β considered. However, as β decreases, the polymer stress transforms the flow field near each particle from closed concentric streamlines to helical streamlines that advect polymers away from the particle surface. Thus, at low β, the polymer stress is diffuse and can be significantly affected by particle-particle interactions. Therefore, in multi-particle simulations at low values of β, the stress generated by a given particle is disrupted by the presence of particles in its vicinity, leading to a significantly lower polymer induced fluid stress (PIFS) than that of the single particle simulations. We then studied the shear rheology of particle suspensions in shear-thinning viscoelastic fluids experimentally using cone-and-plate measurements, and numerically using fully resolved, 3D finite volume simulations with the Giesekus fluid model. We show in our experiments that the steady shear viscosity and first normal stress difference coefficient of the suspension evolve from shear-thickening to substantially shear-thinning as the degree of shear-thinning of the suspending fluid increases. In highly shear-thinning fluids, the suspension exhibits greater shear-thinning of the viscosity than the suspending fluid itself at high shear rates. Moreover, we find that the per-particle viscosity for the Φ = 2.5% particle suspension in the highly shear-thinning fluid is non-monotonic in Wi; it shear-thickens at low Wi and shear-thins above Wi = 1. We show that multi-particle simulations are necessary to obtain the shear-thinning behavior of the per-particle viscosity of suspensions in shear-thinning fluids at moderate values of β. Particle-particle interactions lead to a substantial decrease in the PIFS and an enhancement of the shear-thinning of the stresslet compared to the single particle simulations. This combination leads to the shear-thinning of the per-particle viscosity seen in experiments. In the second project, we present a comprehensive 3D numerical study of particles with imposed velocities relative to the local bulk flow (termed "slip velocities") in a viscoelastic shear flow. We consider the force on a spherical particle sedimenting in, a spherical bubble rising, and a spherical neutral squirmer swimming in an imposed viscoelastic shear flow. For the rigid particle, we show that the drag force increases from the Newtonian stokes drag for translation in any direction of the shear flow. We then demonstrate that any particle (rigid, bubble, and squirmer) moving with a slip velocity in the flow or gradient direction of the shear flow experience a lateral lift force. We calculate and compare the magnitude and direction of the lift force in all situations. At small Deborah (De) and Weissenberg (Wi) numbers, our results show good agreement with an existing perturbation theory for rigid particles and new perturbation theories for drops and for squirmers respectively. Our simulations extend these results to higher De and Wi regimes. Through our simulations, we uncover the physical mechanism of the lateral force on all particles. For rigid particles, we find the lift force arises from an imbalance in polymer stress on either side of the particle, which in turn is due to the imbalance of polymer stretch surrounding the particle. If this lift force is not balanced by an external force, a lateral drift velocity arises. We discuss implications of this lateral drift on the augmentation of concentration fluctuations of particles in viscoelastic suspensions