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 AJ: Chaos and Fractals I |
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Chair: Mark Stremler, Virginia Tech Room: Salt Palace Convention Center 250 D |
Sunday, November 18, 2007 8:30AM - 8:43AM |
AJ.00001: Tailoring chaotic mixing within a translating droplet by oscillatory rotation. Rodolphe Chabreyrie, Dmitri Vainchtein, Cristel Chandre, Nadine Aubry, Pushpendra Singh The purpose of this talk is to show how to tailor chaotic mixing within an incompressible three dimensional droplet undergoing a steady translation as well as oscillatory rigid body rotation. We consider a Lagrangian flow which consist of an integrable Hill vortex perturbed by a time-periodic rigid body rotation. The latter is characterized by two parameters, the amplitude and the frequency of the rotation. By using a resonance condition between the frequencies of the integrable flow and the one of the perturbation, we are able to create a chaotic mixing region inside the droplet whose location and size can be tuned precisely. Our results can be viewed as a preliminary step toward the control of mixing for biochemical reactions within individual droplets, also referred to as ``digital microfluidics.'' [Preview Abstract] |
Sunday, November 18, 2007 8:43AM - 8:56AM |
AJ.00002: The Role of Walls in Chaotic Mixing: Experimental Results Jean-Luc Thiffeault, Emmanuelle Gouillart, Olivier Dauchot, Stephane Roux We report on experiments of chaotic mixing in a closed vessel, in which a highly viscous fluid is stirred by a moving rod. We analyze quantitatively how the concentration field of a low-diffusivity dye relaxes towards homogeneity, and observe a slow algebraic decay of the inhomogeneity, at odds with the exponential decay predicted by most previous studies. Visual observations reveal the dominant role of the vessel wall, which strongly influences the concentration field in the entire domain and causes the anomalous scaling. A simplified 1-D model supports our experimental results. Quantitative analysis of the concentration pattern leads to scalings for the distributions and the variance of the concentration field consistent with experimental and numerical results. (Physical Review Letters, in press. http://arxiv.org/abs/cond-mat/0612557) [Preview Abstract] |
Sunday, November 18, 2007 8:56AM - 9:09AM |
AJ.00003: Topological chaos and mixing in rectangular ducts Jie Chen, Mark Stremler, Vishwanath Somashekar, Michael Olsen Chaos and rapid mixing can be achieved in laminar duct flow when a strong secondary flow is induced at the duct boundary. This approach has been used previously for pressure-driven flow in microchannels with surface grooves and electro-osmotic flow in microchannels with variations in surface potential. For the proper choice of parameters, there exist streamtubes that `braid' the surrounding fluid as it moves through the duct. The ensuing mixing can be evaluated using the Thurston-Nielsen classification theorem, which predicts a lower bound on the stretching rate in the flow. This braiding motion suggests an approach for mixing fluid in rectangular ducts with very high aspect ratio. The discussion will include numerical modeling of `lid-driven' duct flows, analysis of topological chaos in these flows, and experimental characterization of mixing in pressure-driven flow through a high-aspect-ratio microchannel with surface grooves. [Preview Abstract] |
Sunday, November 18, 2007 9:09AM - 9:22AM |
AJ.00004: Chemical patterns in a two-dimensional vortex array with chaotic mixing Jeff Boehmer, Tom Solomon We present experimental studies of patterns formed by both the oscillatory and the excitable Belousov-Zhabotinsky (BZ) chemical reaction in a two-dimensional array of vortices. Two flows are used: a 14 x 14 array of 3/4" square vortices and a 40 x 40 array of 1/4" vortices. Two sets of plungers oscillate the fluid slowly back and forth across the system, resulting in chaotic mixing between the vortices. For both the excitable and oscillatory BZ reaction, chemical patterns form on small scales that mimic the stable and unstable manifolds that characterize chaotic mixing. On a larger scale, target and spiral patterns are observed, similar to those seen in the reaction-diffusion (no flow) limit. We explore the relation of these patterns to the size and strength of the vortices, as well as the frequency and amplitude of the oscillation of the vortex array. We also compare and contrast patterns formed by phase waves (oscillatory reaction) with those formed by trigger waves (excitable reaction). [Preview Abstract] |
Sunday, November 18, 2007 9:22AM - 9:35AM |
AJ.00005: Chaotic mixing in a helix-like pipe with a periodic modulation in curvature and torsion Bongkyun Jang, Mitsuaki Funakoshi The chaotic fluid mixing in a circular pipe with a periodic modulation in curvature and torsion caused by a steady viscous flow of small Reynolds number is examined. An approximate velocity field by an axial pressure gradient obtained under the assumption of small curvature and torsion is used in this study. The mixing properties are studied by using various methods in the theory of dynamical systems such as Poincare section. [Preview Abstract] |
Sunday, November 18, 2007 9:35AM - 9:48AM |
AJ.00006: Targeted mixing in an array of alternating vortices Xavier Leoncini, Romain Bachelard, Tousia Benzekri, Cristel Chandre, Michel Vittot Transport and mixing properties of passive particles advected by an array of vortices are investigated. Starting from the integrable case, it is shown that a special class of perturbations allows one to preserve separatrices which act as effective transport barriers, while triggering chaotic advection. In this setting, mixing within the two dynamical barriers is enhanced while long range transport is prevented. A numerical analysis of mixing properties depending on parameter values is performed; regions for which optimal mixing is achieved are proposed. Robustness of the targeted mixing properties regarding errors in the applied perturbation are considered, as well as slip/no-slip boundary conditions for the flow. [Preview Abstract] |
Sunday, November 18, 2007 9:48AM - 10:01AM |
AJ.00007: Chaotic advection in pulsed source-sink systems Pankaj Kumar, Mark Stremler Pulsed operation of a source and a sink is a classic approach to generating chaotic advection in the unbounded plane. This approach provides motivation for mixing laminar flows in high-aspect-ratio volumes using an arrangement of sources and sinks. In these bounded systems the sources and sinks must operate in pairs in order to conserve volume. When the sources and sinks are arranged on the boundary of a circular domain, particle motions are given explicitly by a discrete mapping. We use this mapping to explore the optimal operating parameters for producing chaos in pulsed source-sink systems. [Preview Abstract] |
Sunday, November 18, 2007 10:01AM - 10:14AM |
AJ.00008: Stirring fluid with ghost rods Mark Stremler, Jie Chen The existence and motion of periodic orbits play an important role in fluid mixing. In many cases, periodic orbits are associated with elliptic islands and are viewed as indicators of poor mixing. However, these orbits can serve as obstacles in the flow that assist in stirring the surrounding fluid. The discussion will focus on viscous flow in lid-driven cavities. For certain system parameters, a collection of four periodic orbits - two elliptic and two hyperbolic - generate a `ghost rod' structure that is similar to that of a physical rod. Analysis of the ghost rod motion can explain much of the fluid stirring. The existence, persistence, and influence of these ghost rods suggest they may play an important role in other fluid mixing systems. [Preview Abstract] |
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