Bulletin of the American Physical Society
60th Annual Meeting of the Divison of Fluid Dynamics
Volume 52, Number 12
Sunday–Tuesday, November 18–20, 2007; Salt Lake City, Utah
Session AB: Non-Newtonian Flows I |
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Chair: Dennis Siginer, Wichita State University Room: Salt Palace Convention Center 150 D-F |
Sunday, November 18, 2007 8:30AM - 8:43AM |
AB.00001: Experiments using a viscoelastic fluid to beat the Scallop Theorem Tony S. Yu, May Gicquel, Eric Lauga, A.E. Hosoi At vanishingly-small Reynolds number, the Scallop Theorem states that a time-reversible or ``reciprocal'' motion in a Newtonian fluid produces no net force. In principal, a viscoelastic fluid, combined with a reciprocal motion driven at an appropriate frequency---e.g. one that is comparable to the inverse of the intrinsic time scale of the fluid---could break symmetry in the flow and generate propulsion. Here, we present experimental evidence of net flow driven by a low Reynolds number, two-link (one-degree-of-freedom) flapper in a viscoelastic fluid. Particle image velocimetry (PIV) experiments reveal that propulsion has a strong dependence on the Deborah numbers of the flow. [Preview Abstract] |
Sunday, November 18, 2007 8:43AM - 8:56AM |
AB.00002: A mechanism for oscillatory instability in viscoelastic cross-slot flow Li Xi, Michael Graham Interior stagnation point flows of viscoelastic liquids arise in a wide variety of applications including extensional viscometry, polymer processing and microfluidics. Experimentally, these flows have long been known to exhibit instabilities, but the mechanisms underlying them have not previously been elucidated. We computationally demonstrate the existence of a supercritical oscillatory instability of low- Reynolds number viscoelastic flow in a two-dimensional cross- slot geometry. The fluctuations are closely associated with the ``birefringent strand'' of highly stretched polymer chains associated with the outflow from the stagnation point at high Weissenberg number. Additionally, we describe the mechanism of instability, which arises from the coupling of flow with extensional stresses and their steep gradients in the stagnation point region. [Preview Abstract] |
Sunday, November 18, 2007 8:56AM - 9:09AM |
AB.00003: Particle-particle and particle-wall interactions in a second-order fluid Arezoo M. Ardekani, Roger H. Rangel, Daniel D. Joseph The motion of a sphere normal to a wall is investigated. The normal stress at the surface of the sphere is calculated and the viscoelastic effects on the normal stress for different separation distances are analyzed. The contribution of the second-order fluid to the overall force applied to the particle is an attractive force towards the wall. Results are obtained using Stokes equations when $\alpha _1 +\alpha _2 =0$. In addition, a perturbation method utilized for a sphere very close to a wall and the effect of non-zero $\alpha _1 +\alpha _2$ is considered. Moreover, viscoelastic potential-flow theory is used and the results are compared with the other methods. Similarly, the forces acting on two fixed spheres in a second-order uniform flow are investigated. For flow along the line of centers or perpendicular to it, the net force is in the direction that tends to decrease the particle separation distance. For the case of flow at arbitrary angle, unequal forces are applied to the spheres perpendicularly to the line of centers. These forces result in a change of orientation of the sedimenting spheres until the line of centers aligns with the flow direction. These results are in agreement with experimental studies on the motion of two settling spheres in a viscoelastic fluid which show that particles line and chain up in the direction of flow. [Preview Abstract] |
Sunday, November 18, 2007 9:09AM - 9:22AM |
AB.00004: Flow induced by a sphere settling in an aging yield-stress fluid Blandine Gueslin, Laurence Talini, Benjamin Herzhaft, Yannick Peysson, Catherine Allain The settling of non-Bownian spheres in a laponite suspension has been studied experimentally. A specific preparation of the fluid has been set up and the fluid's rheology has been characterized. A suspension of laponite constitutes a yield stress, shear thinning and viscoelastic fluid that exhibits aging, i.e. in particular an evolution with time of its rhelogical properties. The settling of single spheres has been studied in the case of low Reynolds numbers. The velocity of a sphere slows down exponentially with aging time. Two flow field patterns around the sphere have been observed according to the stress exerted by the sphere on the fluid: the flow exhibits either a negative wake (an upward motion in the wake of the sphere) for large stresses or not for smaller stresses. A link between the presence of the negative wake and the viscoelastic properties of the fluid has been established. [Preview Abstract] |
Sunday, November 18, 2007 9:22AM - 9:35AM |
AB.00005: Interplay of Inertia and Elasticity, Enhanced Heat Transfer and Change of Type of Vorticity in Tube Flow of Nonlinear Viscoelastic Fluids Dennis Siginer The effect of the interplay of elasticity and inertia on heat transfer enhancement in pressure gradient driven laminar flow of nonlinear viscoelastic fluids in straight tubes of non-circular cross-section at constant wall temperature is discussed. The coupling between viscoelasticity and inertia is crucial to enhancement. Heat transfer enhancements of an order of magnitude larger as compared to their Newtonian counterparts are predicted. Enhancement is a convex function of the second normal stresses. The rate of enhancement decreases with increasing second normal stresses and asymptotically tends to an upper limit. The implications on the enhancement of the change of type of the vorticity equation are discussed. There is a supercritical region away from the wall where the vorticity is hyperbolic with the viscoelastic Mach number $M$ exceeding one. $M $becomes larger and the radius of the hyperbolic region becomes smaller with growing \textit{Re} as the elasticity number $E $stays smaller than one. Vorticity in this hyperbolic region is rapidly damped, the larger the Weissenberg number \textit{Wi} the smaller the rate of damping. There is a cause and effect relationship between the leveling off of the enhancement with increasing \textit{Wi} and the gradual shrinking of the hyperbolic region together with the damping of the vorticity with increasing \textit{Wi} and $M.$ [Preview Abstract] |
Sunday, November 18, 2007 9:35AM - 9:48AM |
AB.00006: Viscoelastic secondary flows in homogeneous and stratified pipe flows Pengtao Yue, Chunfeng Zhou, Joseph Dooley, James Feng The second normal stress difference $N_2$ experienced by non- Newtonian fluids flowing in a pipe amounts to an extra body force that may give rise to secondary flows in the transverse direction. In polymer extrusion, such secondary motion may distort the interface in two-component coextrusion and affect layer uniformity. In this paper, we perform numerical and theoretical studies on the secondary flow in both one-component homogenous and two-component stratified viscoelastic fluids. The simulations are performed based on a phase-field method using finite elements with adaptive meshing. For homogenous systems, we propose a general criterion for the direction of the secondary flow based on the second normal stress coefficient $\Psi_2$ and the shear viscosity $\eta_s$: if $\Psi_2(\dot{\gamma})/\eta_s (\dot{\gamma})$ is an increasing function of the strain rate $\dot{\gamma}$, the fluid flows from high shear region to low shear region along the walls, and vice versa. For two-component flow in circular pipes, the fluid with the larger magnitude of $\Psi_2$ tends to protrude into the other component in the center of the pipe. If the cross section is non-circular, the secondary flow is a superposition of two effects: one caused by the geometry as in a homogenous fluid, and the other due to elasticity stratification as in a circular pipe. The outcome is determined by the competition of these two factors. [Preview Abstract] |
Sunday, November 18, 2007 9:48AM - 10:01AM |
AB.00007: Turbulence of Dilute Polymer Solutions: Lagrangian Particle Tracking Haitao Xu, Nicholas Ouellette, Eberhard Bodenschatz We report measurements from particle tracking experiments of intense turbulence of a dilute polymer-water solution far away from the boundaries at Taylor microscale Reynolds numbers between 200 to 500. The turbulent water flows were created by inertial forcing using baffled disks or propellers in a Von K\'{a}rm\'{a}n swirling flow. For this forcing the effect of polymers on energy injection was observed to be negligible. For small polymer concentration, only the small-scale properties of turbulence were affected, whereas the inertial energy cascade was unchanged -- the presence of polymers seems to introduce an additional energy dissipation mechanism. When the polymer concentration exceeded a threshold value, the large scales were affected as well, and the whole cascade was altered. The energy transfer rate decreased, and the Lagrangian acceleration correlations decayed oscillatorily. [Preview Abstract] |
Sunday, November 18, 2007 10:01AM - 10:14AM |
AB.00008: Experimental study of Multi-Particle Lagrangian Dynamics in Intense Turbulent Flows Eberhard Bodenschatz, Haitao Xu, Nicholas T. Ouellette We report experimental measurements of Lagrangian dynamics following multiple particles in intense turbulent flows with Taylor microscale Reynolds number up to 800. We focus on the course grained-velocity gradient measured from 4 fluid particles -- the tetrads. We present data obtained from tetrads with sizes in a wide range of the inertial range. For any size of tetrads in the inertial range, the probability distribution of the coarse-grained velocity gradient is skewed towards the bi-axial extensional flows. We also measured the evolution of the coarse-grained velocity gradients following the Lagrangian tetrads, which reveals the importance of pressure in this problem. Finally, we report the effect of polymer additives on the coarse-grained velocity gradients and the comparison with theoretical and numerical work. [Preview Abstract] |
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