The role of elasticity in particle-fluid interactions and its effect on suspension rheology [electronic resource]
Keywords: Chemical Engineering.

We leverage numerical methods to study two problems that require a detailed understanding of particle-fluid interactions and, in particular, the effect of elasticity in these interactions. The first project is on understanding the bulk shear properties (viscosity, first and second normal stress difference coefficients) of non-Brownian rigid sphere suspensions in highly elastic fluids. We use numerical tools to compute the stress contributions due to the interaction of the particles with the elastic fluid. This work was motivated by 1) interesting shear-thickening behavior observed in experimental measurements of suspensions in highly elastic fluids that could not be explained by our understanding of suspension rheology, and 2) conflicting results in theoretical attempts at deriving even the first order correction to the suspension bulk stress due to fluid elasticity. Thus there is a great opportunity to use high performance computing to bridge the gap between theory and empirical observations. First we investigate the viscometric functions of dilute suspensions for a wide range of Weissenberg numbers. The Weissenberg number is the shear rate non-dimensionalized by the fluid relaxation time and compares elastic forces to viscous forces in the flow. We show that two extra stress contributions come from the addition of rigid particles to the nonlinear elastic fluid: 1) the contribution directly from the particles as they resist deformation leading to an increase in the internal stress —this contribution is known as the stresslet; and 2) the contribution from the fluid as it deforms around the particles leading to extra stresses in the fluid phase —this contribution is known as the particle-induced fluid stress. In the Wi < < 1 regime, we resolve previous discrepancies in the O(Wi) theory for the bulk stress of a dilute suspension by correctly calculating the two stress contributions from the particles. We also numerically determine the Wi scaling for the particle contribution to the viscometric functions of a dilute suspension in an Oldroyd-B fluid (a model that represents polymer fluids as dumb- bells suspended in a Newtonian solvent) and aid in the development of a theory that gives the first correction to the suspension viscosity due to fluid elasticity. We show that in weak flows, all the viscometric functions shear-thicken. At moderate to high Wi, this shear-thickening behavior remains prominent for the viscosity and first nor- mal stress coefficient, though in the latter, the behavior can be non-monotonic if the suspending fluid is slightly shear-thinning. We also explore the microstructural origins of the particle-induced fluid stress, which is the dominant contribution to the shear-thickening behavior. We determine the scalings of the magnitude and the "volume of interest" for the particle-induced fluid stress to understand the overall suspension behavior. Furthermore, we analyze the flow type in the regions of significant particle-induced fluid stress and find that the stretch of polymers in strain-dominated flow within closed streamlines around the particles generates the large stresses that contribute to the thickening behavior. Thus, understanding the properties of the suspending fluid in extensional deformation is important for predicting the shear rheology of the suspension. We give experimental evidence that quantitative differences between simulation results and experimental data can be explained by the shortcomings of existing closed-form constitutive equations to adequately describe both the shear and extensional rheology of dilute polymer solutions. Finally, we study, via simulation and experiments, non-dilute suspensions in Boger fluids to elucidate the effect of particle-particle hydrodynamic interactions on the stress contributions. In the numerical study, we use an immersed boundary method to simulate an ensemble of particles as a function of time until they achieve steady average bulk properties. The simulations include fully resolved particle-scale hydro- dynamics and fluid stresses. They show that for low volume fraction, non-dilute suspensions, the shear-thickening of the viscosity can be fully determined by considering a single particle's interactions with the suspending fluid. In fact, we show that the viscosity for suspensions up to a volume fraction of about 0.25 can be characterized by a shift factor that determines the zero-shear viscosity and a master curve that describes the viscosity thickening as a function of the suspension shear stress. This "master curve" for the thickening of the shear viscosity is not only demonstrated in the simulations but also shown to be consistent with all available experimental data, including our own. We also show that the first normal stress difference coefficient can be described similarly by a shift factor and a master curve. The second project is a study of particle separation via continuous flow through microfluidic devices. Within the last decade, a plethora of such microfluidic devices have been developed, largely based on observation and intuition. This is particularly true in the development of vector chromatography, where particles separate out laterally in two dimensions, at vanishingly small Reynolds number for non-Brownian particles. This phenomenon has its origins in the irreversible forces that are at work in the device, since Stokes flow reversibility typically prohibits their function otherwise. We present Boundary Element Method simulations of the vector separation of non-Brownian particles with different sizes and elasticities in Stokes flow through channels whose lower surface is composed of slanted cavities. The simulations are designed to understand the physical principles behind the separation as well as to provide design criteria for devices for separating particles in a given size/flexibility range. We first show that we can get quantitative agreement with the experimental separation data. We then vary the geometric parameters of the simulated devices to demonstrate the sensitivity of the separation efficiency to those parameters —thus making design predictions as to which devices are appropriate for separating particles in different size, shape, and deformability ranges.