Bulletin of the American Physical Society
66th Annual Meeting of the APS Division of Fluid Dynamics
Volume 58, Number 18
Sunday–Tuesday, November 24–26, 2013; Pittsburgh, Pennsylvania
Session L11: Non-Newtonian Flows I |
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Chair: Amy Shen, University of Washington Room: 335 |
Monday, November 25, 2013 3:35PM - 3:48PM |
L11.00001: Worst-case amplification of disturbances in inertialess shear-driven flows of viscoelastic fluids Mihailo Jovanovic, Binh Lieu, Satish Kumar Amplification of deterministic disturbances in inertialess shear-driven channel flows of viscoelastic fluids is examined by analyzing the frequency responses from spatio-temporal body forces to the velocity and polymer stress fluctuations. In strongly elastic flows, we show that disturbances with large streamwise length scales may be significantly amplified even in the absence of inertia. For fluctuations without streamwise variations, we derive explicit analytical expressions for the dependence of the worst-case amplification (from different forcing to different velocity and polymer stress components) on the Weissenberg number ($We$), the maximum extensibility of the polymer chains ($L$), the viscosity ratio and the spanwise wavenumber. For the Oldroyd-B model, the amplification of the most energetic components of velocity and polymer stress fields scales as $We^2$ and $We^4$. On the other hand, the finite extensibility of polymer molecules limits the largest achievable amplification even in flows with infinitely large Weissenberg numbers: in the presence of wall-normal and spanwise forces the amplification of the streamwise velocity and polymer stress fluctuations is bounded by quadratic and quartic functions of $L$. [Preview Abstract] |
Monday, November 25, 2013 3:48PM - 4:01PM |
L11.00002: Linear stability analysis of the stick-slip flow of a viscoelastic fluid following the Phan-Thien Tanner model John Tsamopoulos, George Karapetsas It is well known that during extrusion of viscoelastic fluids various flow instabilities may arise resulting in a distorted free surface. In order to investigate the factors generating these instabilities we perform a linear stability analysis at zero Reynolds number around the steady solution of the cylindrical or planar stick-slip flow for a viscoelastic fluid following the PTT model. The stick-slip flow is an important special case of the extrudate swell problem, since the latter reduces to it in the limit of infinite surface tension. We will show that the flow becomes unstable as the Weissenberg number increases above a critical value, due to a Hopf bifurcation suggesting that the flow will become periodic in time. Both the critical value of the Weissenberg number and the frequency of the instability depend strongly on the rheological parameters of the viscoelastic model. The elasticity alone can be responsible for the appearance of instabilities in the extrusion process of viscoelastic fluids and the often used assumptions of wall slip or compressibility, although they might be present, are not required. Finally, the mechanisms that produce these instabilities are examined through energy analysis of the disturbance flow. [Preview Abstract] |
Monday, November 25, 2013 4:01PM - 4:14PM |
L11.00003: Localized disturbances in channel flow of a viscoelastic fluid Akshat Agarwal, Luca Brandt, Tamer Zaki Linear and non-linear growth of a localized disturbance in polymeric channel flow is investigated using Direct Numerical Simulations. The polymeric stress is represented by the FENE-P model. When the amplitude of the intial disturbance is sufficiently small, the presence of the polymer reduces the linear amplification of the disturbance energy, and this stabilizing influence depends on the Weissenberg number, maximum polymer extensibility and the ratio of the solvent viscosity to the total viscosity. When the initial disturbance amplitude is increased, the same trend is identified in the early linear phase. In the subsequent non-linear phase, the behaviour of the Newtonian and polymeric flows are substantially different. In the Newtonian case, non-linear growth is followed by an ultimate decay of the disturbance energy due to viscosity. On the other hand, in the polymeric flow, the non-linear terms due to the solvent contribution are reduced. However, a new energy growth mechanism is present and leads to bypass transition. [Preview Abstract] |
Monday, November 25, 2013 4:14PM - 4:27PM |
L11.00004: Contravariant and covariant dumbbells in polymer-diluted viscoelastic turbulence Kiyosi Horiuti, Shohei Takeu We carried out numerical study to reveal the mechanism of drag reduction (DR) in polymer-diluted flows. The polymer chains are modeled as elastic dumbbells. Our aim is to elucidate the effect of non-affinity in the motion of dumbbells on DR, in which their motions do not precisely correspond to macroscopically-imposed deformation. We conduct analysis in forced homogeneous isotropic turbulence by connecting a macroscopic description (DNS) with a mesoscopic Brownian dynamics of dumbbells (BDS). The dumbbell connector vector is convected as either contravariant or covariant vectors. Contravariant dumbbells orient in the stretching direction of the strain and elasticity is incurred on the tubular structures. Covariant dumbbells orient in the direction which maximizes the stretching by the solvent deformation and direct outward perpendicularly on the planar structures. They exert an extra tension on vortex sheet, which leads to attenuation of energy cascade, resulting in a larger DR than in contravariant dumbbells. In the mixture of contravariant and covariant dumbbells, DR is intermediate between those caused in individually released cases. The two dumbbells form a unit in which contravariant dumbbell is transversely aligned with the covariant dumbbell. [Preview Abstract] |
Monday, November 25, 2013 4:27PM - 4:40PM |
L11.00005: Turbulence in dilute polymer solutions Alexandre de Chaumont Quitry, Nicholas T. Ouellette Turbulence in complex fluids encompasses many fascinating phenomena, ranging from drag reduction to elastic turbulence. We focus on inertial turbulence in a dilute polymer solution in order to understand how small changes a fluid's micro-scale properties result in large-scale flow changes. While there has been considerable progress in identifying such a mechanism in wall-bounded flows, it remains unclear in unbounded flows. We use Lagrangian Particle Tracking to measure the effect of 5 p.p.m by weight of polyacrylamide in water by imaging the central region of an experimental Von Karman flow, generated by placing counter-rotating impellers in a cylindrical chamber. While the fluid's viscosity hardly departs from that of water at such low concentrations, we observe a strong suppression of velocity fluctuations in the inertial range. [Preview Abstract] |
Monday, November 25, 2013 4:40PM - 4:53PM |
L11.00006: ABSTRACT WITHDRAWN |
Monday, November 25, 2013 4:53PM - 5:06PM |
L11.00007: Suppression of the Rayleigh-Plateau instability on a vertical fibre coated with wormlike micelle solutions Fran\c{c}ois Boulogne, Ludovic Pauchard, Fr\'ed\'erique Giorgiutti-Dauphin\'e, Marc-Antoine Fardin, Sandra Lerouge When a liquid film is coating a fibre, it undergoes spatial thickness variations due to the Rayleigh-Plateau instability. We report on the Rayleigh-Plateau instability in films of giant micelles solutions coating a vertical fibre. We observe that the dynamics of thin films coating the fibre could be very different from the Newtonian or standard Non-Newtonian cases. By varying the concentration of the components of the solutions and depending on the film thickness, we show for the first time that the Rayleigh-Plateau instability can be stabilized using surfactant solutions. Using global rheology and optical visualisations, we show that the development of shear-induced structures is required to stabilize the micellar film along the fibre. Assuming that the viscoelastic properties of the shear-induced state can be described by a simple model, we suggest that, in addition to the presence of shear-induced structures, the latter must have an elastic modulus greater than a critical value evaluated from a linear stability analysis. Finally, our analysis provides a way of estimating the bulk elasticity of the shear-induced state. [Preview Abstract] |
Monday, November 25, 2013 5:06PM - 5:19PM |
L11.00008: Irreversible Gelation in Wormlike Micellar Solutions via Microfluidics Joshua Cardiel, Ya Zhao, Perry Cheung, Amy Shen Surfactant molecules can self-assemble into various morphologies under proper combinations of ionic strength, temperature, and flow conditions. At equilibrium, the wormlike micelles can transition from entangled to branched and multi-connected structures with increasing salt concentration. Under specific flow conditions, micellar structure transition can follow different trajectories. In this work we consider the flow of two semi-dilute wormlike micellar solutions through microposts, focusing on their microstructural and rheological evolution. Both solutions contain cetyltrimethylammonium bromide (CTAB) and sodium salicylate (NaSal). One is weakly viscoelastic and shear thickening while the other is strongly viscoelastic and shear thinning. When subject to strain rates $\sim$10$^{3}$~s$^{-1}$ and strain~$\sim$10$^{3}$, we observe irreversible gelation, with entangled, branched, and multi-connected micellar bundles, evidenced by electron microscopy. We also show that the rheological properties of the shear-thickening precursor are smaller than those of the gel, while the rheological properties of the shear-thinning precursor are several times larger than those of the ge. This rheological property variation is associated with their respective structural evolution. [Preview Abstract] |
Monday, November 25, 2013 5:19PM - 5:32PM |
L11.00009: On the origin and evolution of streaks in polymeric shear flows Jacob Page, Tamer Zaki Streaks are a ubiquitous feature in transitional shear flows of both Newtonian and complex fluids. A model problem is formulated where streaks are generated in response to forcing by a decaying streamwise vortex in an Oldroyd-B fluid, and the effects of inertia and elasticity are examined. The dynamics are found to be largely governed by a single parameter: the ratio of the solvent diffusion to the polymer relaxation timescales. When the time scales are disparate, the ``quasi-Newtonian'' and ``elastic'' dynamics can be distinguished. The ``quasi-Newtonian'' evolution of the streaks in the polymeric flow matches the Newtonian equivalent at the same total (solvent) Reynolds number when polymer relaxation is very fast (slow). The ``elastic'' response is significant, when the polymer relaxation time is long, and leads to significant streak amplification even with very weak inertia. When the diffusion and polymer relaxation timescales are commensurate, the streaks are re-energised in a periodic cycle. This behaviour is enhanced in the instantaneously elastic limit where the governing equation reduces to a wave equation with harmonic forcing. The streak re-energisation is demonstrated to be a superposition of trapped inertio-elastic shear waves. [Preview Abstract] |
Monday, November 25, 2013 5:32PM - 5:45PM |
L11.00010: Intermittent Flow In Yield Stress Fluids Slows Down Chaotic Mixing Jalila Boujlel, Dawn Wendell, Emmanuelle Gouillart, Franck Pigeonneau, Pierre Jop Many mixing situations involve fluids with non-Newtonian properties: mixing of building materials such as concrete or mortar are based on fluids that have shear- thinning rheological properties. Lack of correct mixing can waste time and money, or lead to products with defects. When fluids are stirred and mixed together at low Reynolds number, the fluid particles should undergo chaotic trajectories to be well mixed by the so-called chaotic advection resulting from the flow. Previous work to characterize chaotic mixing in many different geometries has primarily focused on Newtonian fluids. First studies into non-Newtonian chaotic advection often utilize idealized mixing geometries such as cavity flows or journal bearing flows for numerical studies. Here, we present experimental results of chaotic mixing of yield stress fluids with non-Newtonian fluids using rod-stirring protocol with rotating vessel. We describe the various steps of the mixing and determine their dependence on the fluid rheology and speeds of rotation of the rods and the vessel. We show how the mixing of yield-stress fluids by chaotic advection is reduced compared to the mixing of Newtonian fluids and explain our results, bringing to light the relevant mechanisms: the presence of fluid that only flows intermittently, a phenomenon enhanced by the yield stress, and the importance of the peripheral region. This result is confirmed via numerical simulations. [Preview Abstract] |
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