Session R11: Non-Newtonian Flows III

Numerical simulation of particle migration in rotating eccentric cylinders

In this study we numerically investigate the particle migration in a concentrated suspension undergoing flow between rotating eccentric cylinders observed in an experiment by Subia et al. (1998) J. Fluid Mech., 373. There are two mathematical models developed to explain particle migration phenomenon, namely, suspension balance model and diffusive flux model. These models have been successfully applied to explain migration behavior in several two-dimensional flows. However, compared with two-dimensional simulation, three-dimensional simulation is able to produce relatively realistic results. In this work, we have carried out numerical simulation of concentrated suspension flow in 3D eccentric cylinder geometry using suspension balance model and finite element methods. The simulation method was validated with available analytical solutions for circular Couette flow. Therefore, the simulation technique was applied to study the flow of concentrated suspensions through rotating eccentric cylinders. The detailed comparison of numerical simulation results is made with the experimental data.   

Coarse-grained simulations of flow-induced morphology dynamics in dispersed graphene

We investigated how flow fields affect graphene morphology dynamics in liquid phase using a coarse-grained model. Past simulations of the dynamics of dispersed graphene sheets are limited to static fluids on small timescales, with little attention devoted to flow dynamics, which is critical given the importance of graphene solution-processing of multifunctional devices and materials. We developed a Brownian Dynamics (BD) algorithm to study the morphology of sheetlike macromolecules in dilute solutions with an applied external flow field. We used a bead-rod lattice to represent the mesoscopic conformation of individual two dimensional sheets. We then analyzed the morphology dynamic modes (stretching, tumbling, crumpling) of these molecules as a function of sheet size, Weissenberg number, and bending stiffness. The physical properties (e. g. viscosity) affected by the morphology are also studied. Our results demonstrate how bending stiffness relates to relaxation modes during startup of shear.   

Stretch and relax: a viscoelastic filament that displays thixotropic yield stress behavior

A filament with circular cross-sectional area is stretched by controlling the distance between the ends, and then stopped. The evolution of the filament radius in the presence of gravity and surface tension is studied. The constitutive model is a combination of a Newtonian solvent and the viscoelastic partially extending strand convection model (Larson 1986) with a large relaxation time. Time-dependent solutions show phenomena with thixotropy and yield stress.   

Ants cushion applied stress by active rearrangements

Fire ants, Solenopsis invicta, link their bodies together to form waterproof rafts, which in turn drip, spread, and coagulate, demonstrating properties of an active material that can change state from a liquid to a solid. This soft-matter phase transition is important when the raft interacts with environmental forces such as raindrops and crashing waves. We study this active behavior through plate-on-plate rheology on the ants, extracting the active components by comparison with the rheological behavior of a collection of dead ants. In controlled shear tests, both and live and dead ants show properties of a non-Newtonian fluid, specifically, shear-thinning behavior. In oscillatory tests, live ants exhibit a rare behavior in which their storage modulus (G') and loss modulus (G'') have approximately the same value over three orders magnitudes of frequency and two orders of magnitude of strain, indicating the ants are neither fluid nor solid. In comparison, dead ants are more solid-like, with a storage modulus twice as large as their loss modulus. This striking active behavior arises from rearrangement of their bodies and storage and dissipation of energy with the ants' muscles.   

Simulations of Shock Propagation in Viscoelastic Media

Understanding the mechanics of shock waves emitted by cavitation bubbles and propagating through viscoelastic media is important to various naval and medical applications, particularly in the context of cavitation damage. In such problems, the constitutive models describing the material are non-trivial, and include effects such as nonlinear elasticity, history and viscosity. Thus, the influence of the shock on the material and the response of the material to the shock are generally unknown. A novel numerical approach is proposed for simulating shock and acoustic-wave propagation in a Zener-like viscoelastic medium. The method is based on a high-order accurate weighted essentially non-oscillatory (WENO) scheme for shock capturing and introduces evolution equations for the stresses. The HLLC Riemann solver is used for upwinding, with a reconstruction of the primitive variables. The performance and accuracy of the numerical approach is presented for several one- and two-dimensional problems, including acoustic wave propagation and the Sod shock tube problem for various combinations of elasticities, viscosities and relaxation times. This work is supported by ONR grant N00014-12-1-0751.   

Viscoelastic Effects on Spraying and Fragmentation of Polymeric Solutions

The addition of small amounts of polymer to Newtonian fluids can inhibit the spray process, but the physical reasons behind these effects are still unclear. To explore this phenomenon, model viscoelastic fluids composed of very dilute solutions of polyethylene oxide are tested in a variety of fragmentation processes including air-assisted atomization, jet impact fragmentation, drop impact, and rotary atomization. Spray image analysis shows that when the fluid viscoelasticity is increased the average particle diameter and Sauter Mean Diameter both show a systematic increase before reaching an asymptotic plateau value. As observed for Newtonian fluids, the droplet size distributions are still well described by a Gamma distribution but the addition of viscoelasticity shifts the distribution to smaller values of \emph{n}, corresponding to a broader size distribution. A linear stability analysis indicates that the effects of fluid viscoelasticity are more pronounced in the final stage of ligament formation than in the initial stages of atomization. The linear analysis can predict the observed trends in the mean droplet sizes; however, the shift in the size distributions seems to rise from the nonlinear dynamics of the stretched viscoelastic ligaments close to break up.   

Elasto-Inertial Turbulence in polymeric flows

The dynamics of elasto-inertial turbulence (EIT) is investigated numerically from the perspective of the coupling between polymer dynamics and flow structures. In particular, direct numerical simulations of channel flow with Reynolds numbers ranging from 1000 to 6000 are used to study the formation and dynamics of elastic instabilities and their effects on the flow. Based on the splitting of the pressure into inertial and polymeric contributions, it is shown that the trains of cylindrical structures around thin sheets of high polymer extension that are characteristics to elasto-inertial turbulence are mostly driven by polymeric contributions.   

A numerical rheometer, or the time-dependent flow of dense suspensions

The ability to perform numerical simulations of realistic flow situations is an ongoing area of research of importance in the realm of academia, as well as industry. The goal of this project is to perform a proof-of-concept calculation on the measurement of the rheological properties for a dense suspension. The following measurement methods were chosen for evaluation: a) Couette rheometry, b) parallel plate rheometry and c) axial piezo-rheometry. In the case of Couette and parallel plate rheometry, the rotational motion of the cylinder or plate is controlled with respect to the rotational rate or induced strain, whereafter a torsional moment is measured. For the piezo-rheometry, the stress mode is in the normal direction with respect to the plate and a stress response is measured. Experimental data for a number of model fluids is used for validation The simulations are performed with IBOFlow, the multi phase flow solver developed at Fraunhofer-Chalmers Centre. The granular-suspension is modelled by a two-fluid model discretized in an Euler-Euler framework. From the simulations it is concluded that the proposed granular model accurately models the rheology of the general flux and that the relaxation time may vary from case to case.