Session L7: Non-Newtonian Flows II

Dynamics of non Newtonian vortex rings

The dynamics of formation and evolution of non-Newtonian vortex rings generated in a piston-cylinder arrangement are studied. The ratio of the piston displacement $L_m$ to the internal cylinder diameter $D_0$, the piston velocity $U_p$ and fluid properties determine the vortex properties and evolution. Measurements of the 2D velocity field were obtained with a PIV technique. The vortex circulation $\Gamma$ was computed considering a vortex identification scheme ($Q$ criterion). Experiments with fluids with different rheological properties (shear thinning and viscoelastic) are presented. Our Newtonian experiments agree with previous investigations. For shear-thinning liquids, we observed that the final vortex circulation decreases with the fluid power index, $n$. We show that the total circulation ejected from the cylinder is reduced when the thinning property of the liquid increases; thus, the circulation confined inside the vortex ring, is reduced too. For vortex rings in a viscoelastic liquid, the formation of a `negative wake' (returning flow) and a second vortex ring with opposite whirl are observed. We show that the negative wake results from the high extension rates produced during the vortex formation.   

Flow Behavior near the Liquid-to-Solid Transition

Amorphous materials are studied experimentally in search for viscosity/elasticity properties in the approach of the liquid-to-solid transition from the liquid side (LSTLS). Two vastly different processes are considered, gelation and glass transition. While viscoelasticity in incipient gels is dominated by the shorter relaxation modes, expressed in a decaying relaxation time spectrum, it is the opposite in a glass forming liquid near LSTLS which exhibits an advancing. For both classes of amorphous materials, the relaxation time spectrum broadens significantly near LSTLS and it shares the same powerlaw format. Still, the relaxation behavior differs fundamentally for the two material classes since the powerlaw exponent is positive for the glass transition and negative for gelation, i.e. the relaxation patterns of gelling fluids and glass formers are inverse near LSTLS. The entire study is founded in Boltzmann's constitutive equation of linear viscoelasticity; the stress is caused by a wide range of modes where, as argued here, short modes dominate gelation and long modes dominate the glass transition. Several examples are shown for each class of materials in order to test the proposed transition behavior for glasses (colloidal and molecular) on the one side and chemical/physical gels on the other. One of the results of this experimental study is that it provides a decisive criterion that distinguishes the glass transition from gelation.   

Bending and buckling of viscoplastic threads

We use a slender body theory to describe the dynamics of a thin viscoplastic thread undergoing extrusion, such as occurs when squeezing toothpaste from a tube. The theory adopts the Bingham model for a yield stress fluid, together with an asymptotic approximation for the stress and strain-rate profiles across the narrow width of the thread, which imply that the thread must either be rigid or fully yielded across its entire width. A compact description of the resultant longitudinal stress and moment acting on the thread allows these yielded and unyielded regions to be identified for given external forces. The theory is applied to extrusion flows; the yield stress prevents any deformation until a critical length of extrusion is reached, after which the dynamically evolving yielded regions mediate a distinctive drooping of a horizontal beam, or a catastrophic collapse of an upright beam.   

Dynamics of Viscoplastic Sheets

A theory is presented for the dynamics of slender sheets of viscoplastic fluid, equivalent to classical analysis of elastic beams and viscous plates. The effect of a yield stress is highlighted. The theory is applied to the fall of a liquid bridge supported at its two ends. The yield stress halts the fall of the bridge; the final asymptotic state is calculated in various limits.   

Transient Non-Newtonian Screw Flow

The influence of axial flow on the transient response of the pseudoplastic rotating flow is carried out. The fluid is assumed to follow the Carreau-Bird model and mixed boundary conditions are imposed. The four-dimensional low-order dynamical system, resulted from Galerkin projection of the conservation of mass and momentum equations, includes additional nonlinear terms in the velocity components originated from the shear-dependent viscosity. In absence of axial flow the base flow loses its radial flow stability to the vortex structure at a lower critical Taylor number, as the pseudoplasticity increases. The emergence of the vortices corresponds to the onset of a supercritical bifurcation which is also seen in the flow of a linear fluid. However, unlike the Newtonian case, pseudoplastic Taylor vortices lose their stability as the Taylor number reaches a second critical number corresponding to the onset of a Hopf bifurcation. Existence of an axial flow, manifested by a pressure gradient appears to further advance each critical point on the bifurcation diagram. In addition to the simulation of spiral flow, the proposed formulation allows the axial flow to be independent of the main rotating flow. Complete transient flow field together with viscosity maps are also presented.   

Numerical Simulation of Nanoparticle Clustering with Experimental Validation

In this study a numerical approach for modeling the forces acting on nanoparticles was performed and the dynamics of transient nanoparticle agglomeration have been explored. The validity of the approach is demonstrated by examining a pair of nanoparticles in a fluid. The force interactions due to the presence of the electric double layer (EDL) were identified as a significant factor in determining the propensity for agglomerative of the nanoparticles. Simulations were performed to demonstrate the clustering and agglomeration of an ensemble of nanoparticles. The simulation results provide an estimate for the time scale for the agglomeration and the resultant structure of the agglomerated ensemble of nanoparticles. Subsequently simulations were performed using this numerical model corresponding to the available experimental data in the literature. The predictions from the numerical simulations show that the change in zeta potential (determined in part by the pH of the solvent phase) is a crucial parameter that affects the level of agglomeration of the nanoparticles.   

Numerical modeling of flowing soft materials

The structural properties of soft-flowing and non-ergodic materials, such as emulsions, foams and gels shares similarities with the three basic states of matter (solid, liquid and gas). The macroscopic properties are characterized by non-standard features such as non-Newtonian rheology, long-time relaxation, caging effects, enhanced viscosity, structural arrest, hysteresis, dynamic disorder, aging and related phenomena. Large scale non-homogeneities can develop, even under simple shear conditions, by means of the formation of macroscopic bands of widely different viscosities (``shear banding'' phenomena). We employ a numerical model based on the Lattice Boltzmann method to perform numerical simulations of soft-matter under flowing conditions. Results of 3d simulations are presented and compared to previous 2d investigations.   

Brownian Dynamics Simulations of Flow Induced Conformation of Single Polymer Chains

Coarse-grained molecular dynamics simulation of single polymer chains is conducted to examine flow induced conformational changes of single polymer chains in shear and extensional flows. Dynamic properties of polymeric molecules are described using bead-spring models; these models put coarse grain groups of atoms into single particles, connected to adjacent particles via spring like interactions. A common representation of the bonded interaction, or spring, is given by the Finitely Extensible Non-linear Elastic model. The constants used in the model are determined form single-molecule force spectroscopic experiments. Simulations and experiments will help to achieve a clear picture of how von Willebrand Factor, a blood clotting protein, model system for flow-induced activation, achieves flow sensing at the single protein/polymer level. The model includes bead-bead interactions, hydrodynamic interaction, the volume of the beads and spring-spring interaction for finitely extensible dumbbell and other spring models. The effects of walls on the dynamics of polymer chains are also presented. The results are presented for various chain lengths and flow conditions. Hydrodynamic interaction and the presence of wall have strong influences on the dynamics of the polymer chain.   

Computational modeling of dilute biomass slurries

The biochemical conversion of lignocellulosic biomass to liquid transportation fuels involves a multitude of physical and chemical transformations that occur in several distinct processing steps (e.g., pretreatment, enzymatic hydrolysis, and fermentation). In this work we focus on development of a computational fluid dynamics model of a dilute biomass slurry, which is a highly viscous particle-laden fluid that can exhibit yield-stress behavior. Here, we model the biomass slurry as a generalized Newtonian fluid that accommodates biomass transport due to settling and biomass-concentration-dependent viscosity. Within a typical mixing vessel, viscosity can vary over several orders of magnitude. We solve the model with the Nek5000 spectral-finite-element solver in a simple vane mixer, and validate against experimental results. This work is directed towards our goal of a fully coupled computational model of fluid dynamics and reaction kinetics for the enzymatic hydrolysis of lignocellulosic biomass.   

Stability of streamwise vortices in shear flows of viscoelastic fluids

Recent work on transient growth in viscoelastic shear flows [1] suggests that even though these flows are linearly stable, a non-modal perturbation could be sufficiently amplified resulting in long-living transient disturbances. Similar to Newtonian shear flows, these disturbances take form of the streamwise vortices. Here we perform a linear stability analysis of the streamwise vortices superimposed on the steady shear flow. We find that this flow is linearly unstable towards 3D perturbations. In Newtonian case, this instability is known to play an important role in sustaining exact coherent structures [2] that dynamically organise the transition to turbulence. We discuss the possibility that similar structures exist in viscoelastic shear flows.\\[4pt] [1] M. Jovanovic and S. Kumar, Phys. Fluids 22, 023101 (2010)\\[0pt] [2] F. Waleffe, Phys. Fluids 9, 883 (1997)