Bulletin of the American Physical Society
62nd Annual Meeting of the APS Division of Fluid Dynamics
Volume 54, Number 19
Sunday–Tuesday, November 22–24, 2009; Minneapolis, Minnesota
Session LN: Non-Newtonian Flows III |
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Chair: Gareth McKinley, Massachusetts Institute of Technology Room: 200C |
Monday, November 23, 2009 3:35PM - 3:48PM |
LN.00001: Blistering pattern and formation of nano-fibers in capillary thinning of polymer solutions Christian Wagner, Rainer Sattler, Stephan Gier, Jens Eggers When a dilute polymer solution experiences capillary thinning, it forms an almost uniformly cylindrical thread, which we study experimentally. In the last stages of thinning, when polymers have become fully stretched, the filament becomes prone to instabilities, of which we describe two: A ``breathing'' instability, originating from the edge of the filament, and a sinusoidal instability in the interior, which ultimately gives rise to a Rayleigh Plateau instability followed ``blistering'' pattern of beads on the filament. We describe the linear instability with a spatial resolution of 80 nm in the disturbance amplitude. Preliminary micro-PIV measurements indicate the existence of irregular flow fields. For sufficiently high polymer concentrations, the filament eventually separates out into a ``solid'' phase of entangled polymers, connected by fluid beads. A solid polymer fiber of about 100 nanometer thickness remains, which is essentially permanent. [Preview Abstract] |
Monday, November 23, 2009 3:48PM - 4:01PM |
LN.00002: Spatially-dependent elastic instabilities in flow around an array of cylinders Lichao Pan, Barry Scharfman, Paulo Arratia When flexible polymer molecules (in dilute solution) flow around a cylinder, they are strongly stretched due to the combination of both curved streamlines and extensional flow. Here, the flow of a viscoelastic fluid around an array of cylinders is investigated in a microchannel. As the strain- rate is varied at low Reynolds number ($<$10$^{-2}$), tracer and particle-tracking experiments show that molecular stretching produces two flow instabilities, one in which the velocity field becomes asymmetric, and a second in which it fluctuates non-periodically in time. These instabilities are spatially-dependent in the sense that the two instabilities may be present at a single values of strain-rate (or Wissenberg number) but at different locations in the microchannel. [Preview Abstract] |
Monday, November 23, 2009 4:01PM - 4:14PM |
LN.00003: Dynamical instability of viscoelastic fluids driven by steady roll-mills Bin Liu, Michael Shelley, Jun Zhang A layer of viscoelastic fluid, made of a polymeric solution, is driven from beneath by 16 rotating disks -- rollers -- on a square lattice. Each adjacent pair of rollers rotate in opposite directions at constant speed. We focus on the region near the free-surface of the fluid, where the dynamics is roughly two-dimensional. A set of stagnation points are thus created between the rollers, and divides the driven fluid into 16 cells. When the strain rate due to the local flow geometry is small compared to the relaxation time of the fluid, the fluid behaves like a Newtonian one, giving rise to fluid cells of equal size located above each individual roller. As the forcing increases, symmetries are broken, and the cells start differentiating in size. We observe experimentally that when the forcing is great enough, the asymmetric flow pattern becomes unsteady, and the stagnation points oscillate spontaneously. We show that the oscillatory frequency depends on the Weissenberg number $Wi$, characterizing the ratio of the forcing time scale to the relaxation time of the fluid. [Preview Abstract] |
Monday, November 23, 2009 4:14PM - 4:27PM |
LN.00004: A Transition to Mixing and Oscillations in a Stokesian Viscoelastic Flow Becca Thomases, Michael Shelley To understand observations of low Reynolds number mixing and flow transitions in viscoelastic fluids, we study numerically the dynamics of the Oldroyd-B viscoelastic fluid model. The fluid is driven by a simple time-independent forcing that creates a cellular flow with extensional stagnation points. We find that at O(1) Weissenberg number these flows lose their slaving to the forcing geometry of the background force, become oscillatory with multiple frequencies, and show continual formation and destruction of small-scale vortices. This drives flow mixing. These new flow states are dominated by a single large vortex, which may be stationary or move persistently from cell to cell. Increasing the number of degrees of freedom by increasing the number of driving cells broadens the temporal frequency spectrum and improves fluid mixing. [Preview Abstract] |
Monday, November 23, 2009 4:27PM - 4:40PM |
LN.00005: Thermal instabilities in melt spinning of viscoelastic fibers Chunfeng Zhou, Satish Kumar Nonisothermal melt spinning of viscoelastic fibers where the viscosity varies in a step-like manner with respect to temperature is studied in this work. A set of one-dimensional equations based on the slender-jet approximation and the upper-convected Maxwell model is used to describe the melt spinning process. The process is characterized by the force required to pull the fiber, the strength of external heating, and the draw ratio, the square of the ratio of the fiber diameter at the spinneret to that at the take-up roller. For low levels of elasticity and sufficiently strong external heating, there can be three pulling forces consistent with the same draw ratio, similar to the Newtonian case studied by Wylie et al. (J. Fluid Mech. 570 (2007) 1-16). For higher levels of elasticity, the process exhibits a draw ratio plateau where the draw ratio hardly changes with the pulling force, reflecting a competition between thermal and elastic effects. As in the Newtonian case, external heating introduces a new instability---termed thermal instability---that is absent in isothermal systems. Linear stability analysis reveals that external heating improves stability for low levels of elasticity, but can worsen stability for higher levels of elasticity, which is again a consequence of the interplay between thermal and elastic effects. The results of the present work demonstrate a possible mechanism through which external heating can stabilize the melt spinning of viscoelastic fibers. [Preview Abstract] |
Monday, November 23, 2009 4:40PM - 4:53PM |
LN.00006: Interfacial instability of turbulent two-phase stratified flow with non-Newtonian rheology Lennon O'Naraigh, Peter Spelt We study the stability of a stratified flow configuration where the bottom layer exhibits non-Newtonian rheology, and where the top layer is Newtonian, fully developed, and turbulent. We first derive a base-state model to describe the equilibrium flow in the flat-interface state, which takes into account the yield stress and power-law nature of the bottom fluid, while a closure model is used to constitute the Reynolds stresses in the upper fluid. Next, we develop a linear-stability analysis to predict when the base state is unstable, and pay particular attention to characterizing the influence of the non-Newtonian rheology on the instability. Increasing the yield stress (up to the point where unyielded regions form in the bottom layer) is destabilizing; increasing the flow index, while bringing a broader spectrum of modes into play, is stabilizing. In addition, a second mode of instability is found, which depends on conditions in the bottom layer. For shear-thinning fluids, this second mode becomes more unstable, and yet more bottom-layer modes can become unstable for a suitable reduction in the flow index. One further difference between the Newtonian and non-Newtonian cases is the development of unyielded regions in the bottom layer, as the linear wave on the interface grows in time. These unyielded regions form in the trough of the wave, and can be observed in the linear analysis for a suitable parameter choice. [Preview Abstract] |
Monday, November 23, 2009 4:53PM - 5:06PM |
LN.00007: Channel Flow of Wormlike Micellar Solutions Michael Cromer, Pam Cook, Gareth McKinley We examine the inhomogeneous response of the VCM model (Vasquez, Cook, McKinley 2006) in steady pressure-driven channel flow. The VCM model, a microstructural network model, was developed to describe concentrated solutions of wormlike micelles. The model comprises of a set of coupled partial differential equations, which incorporate breakage and reforming of two micellar species (a long species `A' and a shorter species `B') in addition to reptative and Rousian stress-relaxation mechanisms. We examine pressure-driven flow in microfluidic devices with rectangular cross-sections as well as with hyperbolic converging/diverging walls. The velocity profile predicted by the VCM model in Poiseuille flow deviates from the parabolic profile expected for a constant viscosity fluid and exhibits strong shear bands near channel walls. This shear-banding is analogous to that seen in circular Taylor-Couette flow and in good qualitative agreement with experimental observations in microfluidic channels. The hyperbolic planar contraction is of special interest due to the dominant contribution of extensional flow along the centerline and the proposed use of such flows as microfluidic extensional rheometers. The model predictions are compared with birefringence measurements of the evolution in the local microstructural orientation of CTAB and CPyCl-based micellar solutions. [Preview Abstract] |
Monday, November 23, 2009 5:06PM - 5:19PM |
LN.00008: Instability of the air cavity of a micellar solution in the wake of a submerged rod Thomas Ober, Gareth McKinley, Sunghwan Jung The behavior of flowing surfactant and polymeric solutions is of increasing importance as these materials are used more commonly as rheological modifiers. Here, we investigate the instability of the air cavity formed in the wake of a rod, which is submerged in the oncoming stream of a non-Newtonian fluid with a free surface exposed to air. Two fluid systems with different concentrations of cetylpyridinium chloride (CPyCl), sodium salicylate (NaSal) and NaCl are studied. Under certain conditions, the cavity exhibits a repeating tooth-like pattern, whose wavelength and amplitude vary with depth, rod diameter, oncoming velocity and fluid properties. We characterize experimentally the cavity closing dynamics, and the wavelength and amplitude along the profile of the cavity, probing the interplay between viscoelasticity, inertia and hydrostatic pressure in our experiments. Finally, we propose a simple model to capture the some of the key features of the dynamics of the air cavity. [Preview Abstract] |
Monday, November 23, 2009 5:19PM - 5:32PM |
LN.00009: Field-controlled adhesion in confined magnetorheological fluids Jose Miranda, Sergio Lira The study of reversible, functional, and controllable adhesives is a matter of considerable practical interest, and academic research. We report the adhesive response of a magnetorheological fluid confined between two parallel plates under a probe-tack test, when it is subjected to an applied magnetic field. Our analytical approach is based on a Darcy-like law formulation which considers a magnetic field-dependent yield stress behavior. The adhesion force is calculated in closed-form for two different configurations produced by a Helmholtz coils setup: uniform perpendicular, and nonuniform radial magnetic fields. In both cases, we verify that adhesion force is hugely increased as a result of the field-dependent nature of the yield stress. This provides a versatile way to obtain a shear resistant, tough structural adhesive through magnetic means. [Preview Abstract] |
Monday, November 23, 2009 5:32PM - 5:45PM |
LN.00010: Magnetohydrodynamic channel flow with Braginskii's anistropic viscosities Paul Dellar We study the channel flow of a fluid obeying Braginskii's magnetohydrodynamics, in which the viscosity parallel to the magnetic field lines greatly exceeds the viscosity in perpendicular directions. This reflects a weakly collisional regime where particles interact primarily through coupling to the magnetic field, rather than directly through inter-particle collisions. Contrary to the conclusion of a recent study, there is no well-defined limit as the ratio of perpendicular to parallel viscosities tends to zero. The maximum velocity grows as the minus one-quarter power of the (small) viscosity ratio $(\mu_\perp/\mu_\parallel)^{-1/4}$, due to large shears that develop across boundary layers at the walls. The width of these boundary layers scales as the three-quarters power of the viscosity ratio. They thus lie inside analogs of the usual Hartmann layers, and the Lorentz force does not enter their leading-order force balance. The long-time behavior of computations using lattice Boltzmann magnetohydrodynamics, which is readily adapted for anisotropic viscosities, is in excellent agreement with these asymptotic solutions. [Preview Abstract] |
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