Bulletin of the American Physical Society
63rd Annual Meeting of the APS Division of Fluid Dynamics
Volume 55, Number 16
Sunday–Tuesday, November 21–23, 2010; Long Beach, California
Session QF: Non-Newtonian Flows II |
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Chair: Pushpendra Singh, New Jersey Institute of Technology Room: Long Beach Convention Center 103A |
Tuesday, November 23, 2010 12:50PM - 1:03PM |
QF.00001: Peristalsis of a viscoelastic fluid in a cavity with closed ends Sarah Lukens, John Chrispell, Lisa Fauci Theoretical studies in microfluidics have examined a ``peristaltic mixer" - one that consists of a fluid filled cavity bounded above and below by flexible membranes which vibrate mechanically in a prescribed fashion. We use Lagrangian coherent structure (LCS) methods to identify geometric flow regions in a finite channel with closed ends due to low amplitude, high frequency peristaltically driven walls. The presence of sidewalls introduces a return flow in the system. We observe consistency with the asymptotic solutions in the Newtonian case. Cellular flow patterns are observed for Newtonian and Oldroyd-B fluids, and striking differences emerge when viscoelasticity is introduced. [Preview Abstract] |
Tuesday, November 23, 2010 1:03PM - 1:16PM |
QF.00002: Symmetric factorization of the conformation tensor in viscoelastic fluid models Becca Thomases, Nusret Balci, Michael Renardy, Charles Doering The positive definite symmetric polymer conformation tensor possesses a unique symmetric square root that satisfies a closed evolution equation in the Oldroyd-B and FENE-P models of viscoelastic fluid flow. When expressed in terms of the velocity field and the symmetric square root of the conformation tensor, these models' equations of motion formally constitute an evolution in a Hilbert space with a total energy functional that defines a norm. Moreover, this formulation is easily implemented in direct numerical simulations resulting in significant practical advantages in terms of both accuracy and stability. [Preview Abstract] |
Tuesday, November 23, 2010 1:16PM - 1:29PM |
QF.00003: Slow motion and deformation of a viscoplastic drop in a viscous fluid Olga Lavrenteva, Irina Smagin, Avinoam Nir The slow sedimentation of a deformable viscoplastic drop in a Newtonian fluid is studied making use of a variation of integral equation method. The Green function for the Stokes equation is used and the non-Newtonian stress is treated as a source term. The computations carried out for a range of physical parameters of the system revealed that increasing in the yield stress magnitude (the Bingham number, Bn) stabilizes both oblate and prolate drops. This is in contrast to the effect of the viscosity of Newtonian drop that is known to destabilize oblate drops. This strong stabilization effect can be explained by the presence of unyielded zones inside falling drops. An interesting observation is that the growth of the limiting viscosity of the Bingham fluid destabilize oblate deformations at low Bn and have stabilizing effect at higher Bn. [Preview Abstract] |
Tuesday, November 23, 2010 1:29PM - 1:42PM |
QF.00004: Steady State Visco-Elastic Rimming Flow Anton Mazurenko, Sergei Fomin, Brent Nelson, Jared Debrunner Using scale analysis and the method of perturbations, a theoretical description is obtained for the steady-state non-Newtonian flow on the inner wall of the rotating horizontal cylinder. The Maxwell upper-convective equation is chosen to model the visco-elastic properties of the fluid. In the general case, the derived governing equations can be solved only numerically. However, since the polymeric solutes used in roto-molding and coating technologies exhibit the relatively weak elastic properties, the Deborah number for such flows is rather small (De$<$1). Exploiting this fact, the perturbation method is applied for simplification of the model. As a result, the first order non-linear differential equation for the thickness of the fluid film is derived. An approximate analytical solution of this equation is found. The accuracy of analytical solution is verified by the direct numerical solution of the derived equation. The obtained equation is rather complex and contains several critical points. These points are classified by the analysis of the corresponding autonomous system. The type and location of these critical points are accounted for during numerical solution of the equation. Using the obtained solutions, the criteria which guarantee the stable steady-state flow of the liquid polymer and the uniform final thickness of the coating film are determined. The bounds for the different flow regimes and principal controlling parameters are identified. [Preview Abstract] |
Tuesday, November 23, 2010 1:42PM - 1:55PM |
QF.00005: Effect of Polymer Additives on Heat Transfer in a Laminar Boundary-Layer Flow Emily S.C. Ching, Roberto Benzi, Vivien W.S. Chu We have carried out a theoretical analysis of the effect of polymer additives on heat transfer in a laminar boundary-layer flow. We consider the simple Oldroyd-B model of polymers and show that the effect of the polymers can be understood as a position-dependent effective viscosity. We find that the presence of polymers leads to a reduction in the Nusselt number (Nu), the dimensionless number measuring heat transport. Moreover, the extent of reduction increases with the concentration of the polymers. We shall also discuss the relevance of our work to the recent experimental observation of a decrease in Nu in turbulent thermal convection upon the addition of polymers. [Preview Abstract] |
Tuesday, November 23, 2010 1:55PM - 2:08PM |
QF.00006: Purely elastic instabilities in parallel shear flows Lichao Pan, Paulo Arratia In this talk, the stability of viscoelastic fluids in parallel shear flow at low Reynolds number (\textit{Re}$<$0.01) is experimentally investigated using dye advection visualization and particle tracking velocimetry. The fluid of interest is a dilute polymeric fluid with nearly constant shear-viscosity. The experimental setup is a micro channel that is 3 cm long and 100 um wide. The channel consists of two regions. The first region contains a linear array of cylinders designed to introduce perturbations to the viscoelastic flow. The second region is a long (2.7 cm) and straight channel devoid of cylinders in which the spatial-and temporal behavior of the initial perturbation is monitored. This second region is the parallel shear geometry. Preliminary results based on velocity measurements shows that the initial disturbance is sustained far downstream in the parallel shear geometry above certain Wissenberg number (\textit{Wi}), and increase non-linearly with \textit{Wi} even at vanishing small \textit{Re}. For the viscoelastic fluid, curved streamlines are observed in the parallel shear geometry region of the channel. No velocity fluctuations or curved streamlines are found for the Newtonian fluid under the same conditions. [Preview Abstract] |
Tuesday, November 23, 2010 2:08PM - 2:21PM |
QF.00007: Rinsing Flows of Non-Newtonian Fluids Gerald Fuller, Travis Walker, Tienyi Hsu, Patrick Anderson The rinsing flow of a jet of water impinging onto both Newtonian and non-Newtonian viscous fluids has been considered to qualitatively and quantitatively understand the flow structure of the resulting hydraulic jump. This study seeks to investigate the interactions of the two fluid system during the transient growth of the flow profile. This growth is seen to vary drastically in magnitude, velocity, and topology, while undergoing varying instabilities, depending on the properties of the coating fluid. Currently, four classes of test fluids, all having approximately equal viscosities at low shear, have been chosen for this study: a Newtonian solution, a viscoelastic polymer solution, a Boger fluid, and a worm-like micelle solution. Each fluid experiences Saffman-Taylor instabilities, and the experiments show that the elasticity of the samples will influence the pattern of the instabilities. The elasticity is also seen to dampen the disturbances of the hydraulic jump, influence the overall jump height, and vary the radial growth of the jump. In addition, the shear-thinning nature of the samples seems to influence the overall velocity of the radial growth, while determining the geometry of the driving front. Finite element simulations are also presented in an attempt to understand these complex flow kinematics. [Preview Abstract] |
Tuesday, November 23, 2010 2:21PM - 2:34PM |
QF.00008: Impact of a cylindrical rod on a concentrated particle suspension: dynamics, crack growth and relaxation Eglind Myftiu, Matthieu Roche, Pilnam Kim, Howard A. Stone Many highly concentrated particle suspensions are shear thickening; the viscosity increases with shear rate. The physics underlying shear thickening is still under discussion. In recent years, it was pointed out that shear thickening may be connected with a liquid-to-solid phase transition of the suspension. We provide direct evidence of this transition by studying the behavior of aqueous cornstarch suspensions of various concentration and layer thicknesses after impact of a free-falling cylindrical rod, which induces high strain rates and stresses. We observe patterns of regularly distributed radial cracks growing outwards from the impact region. Just after impact, a wave propagates on the surface of the layer and in the neighborhood of the impact a cavity expands. During this expansion, the cavity boundary is torn, and cracks start to grow. These cracks have rough boundaries, as is seen in solids. Once the cracks have reached their maximal extension, the suspension relaxes. The solvent slowly fills the cracks, until the layer returns to its initial shape. We discuss the influence of the layer thickness, starch concentration and impact energy on the dynamics of these cracks. We also discuss some properties of the solid phase of these suspensions as well as their relaxation dynamics. [Preview Abstract] |
Tuesday, November 23, 2010 2:34PM - 2:47PM |
QF.00009: Pinch-off Dynamics of Non-Newtonian Fluids F.M. Huisman, S.R. Gutman, P. Taborek The pinch-off dynamics of a variety of shear-thinning fluids (foams, concentrated emulsions, and slurries) were studied using high speed videography. The pinch was characterized by the variation of the minimum neck radius rmin as a function of the time to pinch t, with rmin prop to $t^{\alpha}$. The rheology of shear thinning fluids can be characterized by an exponent $\tau$ = $k \dot{\gamma}^{n}$, with n $<$ 1. We found that for a variety of shear-thinning fluids including mayonnaise and acrylic paint, rmin scales with t to a power $\alpha$ equal to the flow index for the particular fluid. The flow index was measured using a TA instruments AR-G2 rheometer. The flow index for acrylic paint was 0.440 +/- 0.014 and rmin scales with t to the 0.41 +/- 0.03; for mayonnaise the flow index was 0.355 +/- 0.014; and rmin scales with t to the 0.35+/- 0.02. To study the transition from conventional Newtonian pinch, we systematically varied the concentration of a water-Xanthan gum mixture. [Preview Abstract] |
Tuesday, November 23, 2010 2:47PM - 3:00PM |
QF.00010: Buckling of cornstarch solutions after pinch-off: evidence for a jamming transition at high extensional rates Matthieu Roche, Oyku M. Akkaya, Hamid Kellay, Howard A. Stone We studied the behavior of density-matched cornstarch solutions during and after pinch-off from a needle. We observed an exponential slowing down in the thinning dynamics of the bridge connecting the droplet to the needle during which the bridge adopts a cylindrical shape. At this stage, the flow is mainly extensional allowing us to explore the behavior of starch solutions at extension rates greater than 10 s$^{-1}$. The bridge continues to thin and then destabilizes leading to break-up in multiple parts. These parts retract on themselves and buckle. We show that this buckling behavior can be understood as a consequence of a liquid-to-solid transition of starch solutions during thinning. Using microscopy, we demonstrate that the neck is inhomogeneous during the last stages of pinch-off: the thinner sections of the neck are fluid while the thicker regions are jammed. We explain buckling by showing that the bridge deforms around its fluid sections, making this system analogous to a chain of solid links connected by fluid bridges. [Preview Abstract] |
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