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 GG: Microfluidics: Mixing |
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Chair: Luca Cortelezzi, McGill University Room: 101G |
Monday, November 23, 2009 8:00AM - 8:13AM |
GG.00001: Formation of coherent structures in 3D laminar mixing flows Michel Speetjens, Herman Clercx Mixing under laminar flow conditions is key to a wide variety of industrial systems of size extending from microns to meters. Examples range from the traditional (and still very relevant) mixing of viscous fluids via compact processing equipment down to emerging micro-fluidics applications. Profound insight into laminar mixing mechanisms is imperative for further advancement of mixing technology (particularly for complex micro-fluidics systems) yet remains limited to date. The present study concentrates on a fundamental transport phenomenon of potential relevance to laminar mixing: the formation of coherent structures in the web of 3D fluid trajectories due to fluid inertia. Such coherent structures geometrically determine the transport properties of the flow and better understanding of their formation and characteristics may offer ways to control and manipulate the mixing properties of laminar flows. The formation of coherent structures and its impact upon 3D transport properties is demonstrated by way of examples. [Preview Abstract] |
Monday, November 23, 2009 8:13AM - 8:26AM |
GG.00002: Streamlines and mixing patterns for drops in capillaries Francois Blanchette We present a theoretical and numerical investigation of streamlines and mixing patterns within drops flowing in capillaries. We study theoretically the limit case of purely viscous flow around a small drop, and find that recirculating regions are always present at the front and back of such drops. Using two-dimensional simulations, we visualize streamlines for larger drops, showing that the extent of these recirculating torii increases with drop size and decreases with Reynolds number. We study the mixing within drops as they are subjected to time-dependent shear, thus modeling a sinusoidal channel, and find that while cross-stream mixing is efficient, streamwise mixing is hindered by the front and back recirculating regions. [Preview Abstract] |
Monday, November 23, 2009 8:26AM - 8:39AM |
GG.00003: Chaotic mixing in a plane channel with rotating arc walls Kamal El Omari, Adil Achhoud, Yves Le Guer The effect of chaotic advection on the advection-diffusion of passive species is investigated for a new type of open flow mixer. This mixer is of active type with a perturbation of the flow imposed by three rotating circular arc walls (RAW) in a two-dimensional plane channel flow. Different steady flow topologies can be obtained depending on the respective directions of the RAW. Efficient stirring protocols were designed by the combination of some steady streamline patterns giving rise to chaotic mixing. The dynamical behavior of the mixing induced by these protocols were compared and discussed for different control parameters. [Preview Abstract] |
Monday, November 23, 2009 8:39AM - 8:52AM |
GG.00004: The Ranz Stretch model and its extensions applied to mixing and reversibility Pavithra Sundararajan, Joseph Kirtland, Donald Koch, Abraham Stroock Mixing and separation are central to several chemical systems and are often carried out using microfluidics. Flow in a microfluidic device is usually in the laminar or Stokes regime. So mixing - a combination of stirring and diffusion - is often performed using chaotic flows which stir much faster than non chaotic flows. For separation of solutes of different diffusivities, Heller proposed the principle of Separation by Diffusive Irreversibility (SDI) which combines the reversibility of stirring and irreversibility of diffusion. Fundamental to both mixing and SDI is the interplay of convection and diffusion which is difficult to understand because of the challenging nature of convective coupling of solute concentration and the flow in the governing convective diffusion equation. Our approach is to use the Ranz model which observes the evolution of a single strand of concentration in the local linear flow. While this model captures the qualitative behavior of the chaotic and non chaotic flows, it fails to quantitatively predict the scaling of mixing and separation characteristics. Our goal is to identify a set of parameters that quantify the effects of stretch history and distribution and the presence of islands on mixing and separation. I will present a study of these effects, and the extensions of Ranz model incorporating these effects. I will compare the results from the model to the numerical simulation. The model will improve our understanding of mixing and irreversibility in Stokes flows. [Preview Abstract] |
Monday, November 23, 2009 8:52AM - 9:05AM |
GG.00005: Long-term description of chaotic mixing induced by resonance phenomena Dmitri Vainchtein, Sahand Hariri Akbari, Roman Grigoriev We present a quantitative long-term theory of resonant mixing in 3-D near-integrable flows. We illustrate that such resonance phenomena as resonance and separatrix crossings accelerate mixing by causing the jumps of adiabatic invariants. The resulting mixing can be described in terms of a single diffusion-type equation. We show what modifications must be made to accommodate the effects of the boundaries of the domain and possible correlations between the successive jumps. [Preview Abstract] |
Monday, November 23, 2009 9:05AM - 9:18AM |
GG.00006: Development of an optimal mixer: a conceptual study Oleg Gubanov, Luca Cortelezzi We define as an optimal mixer a mixing device able to deliver a uniformly optimal mixing performance over a wide range of operating and initial conditions. We consider the conceptual problem of designing an optimal mixer starting from a reference mixing device, the sine flow. We show that the time-periodic sine flow performs poorly and erratically over most operating and initial conditions. In steps we modify the design of the reference mixer to obtain a mixing device whose performance, over the entire operating range, is as good as or better than the best performance of the sine flow. First, we optimize the time-sequence of the stirring velocity fields. The resulting mixer performs substantially better than the sine flow, but it is still suboptimal because the actuating system cannot control all the states. Second, we equip the sine flow with a new actuating system that allows optimized shifts of the stirring velocity fields in the cross-flow direction. This new actuating system is able to control all states. The resulting mixer delivers a suboptimal performance only at low operating conditions due to the use of a time-periodic stirring protocol. Finally, we obtain an optimal mixer by coupling the time and shift optimizations. We show that the resulting optimal mixer is able to deliver a nearly uniform optimal performance, insensitive to the geometry of the initial conditions, over the entire operating range. [Preview Abstract] |
Monday, November 23, 2009 9:18AM - 9:31AM |
GG.00007: Effects of herringbone groove geometry on flow kinematics in a high aspect-ratio microchannel Vishwanath Somashekar, Michael Olsen, Mark Stremler Passive mixing is often achieved in laminar microscale flows by driving fluid through microchannels with geometries that produce secondary flows and/or by splitting and recombining the fluid multiple times. One very successful microscale mixer design is the staggered herringbone mixer introduced by Stroock et al. (Science 2002) In the presented work, we consider very high aspect ratio (62:1) microchannels with a repeated staggered herringbone pattern spanning the entire width of the microchannel. Herringbone geometries with three different interior angles of the herringbone pattern (45, 90, and 135 degrees) were investigated. The flowfields within the herringbone mixers were determined using microscopic particle image velocimetry (microPIV). Velocity fields were measured at the midplane of the microchannel and at the groove-channel interface for Reynolds numbers based on microchannel hydraulic diameter of 0.08, 0.8, and 8. These wide microchannels produce secondary flow patterns that effectively split the fluid into parallel streams without having to fabricate physically separate channels. [Preview Abstract] |
Monday, November 23, 2009 9:31AM - 9:44AM |
GG.00008: Breaking Regular Islands for Improved Mixing in an Electro-osmotic Device Rodolphe Chabreyrie, Cristel Chandre, Pushpendra Singh, Nadine Aubry Two-dimensional electro-osmotic flow with strong spatial and weak temporal variations of the zeta potential is investigated theoretically for the purpose of enhancing mixing in a microchannel. The flow is a superposition of a primary component and a perturbation. The primary flow, generated by the spatially periodic zeta potential, consists of recirculating rolls, while the perturbation arises due to a small time periodic variation of the zeta potential distribution. In this work, we propose a method that allows us to identify the values of the parameters which produce complete mixing. The method is based on tracking the linear stability of the main periodic orbits corresponding to the recirculating rolls of the primary flow. Poincar\'{e} maps, Lyapunov exponents and a box counting measure are computed to corroborate our results. [Preview Abstract] |
Monday, November 23, 2009 9:44AM - 9:57AM |
GG.00009: Experimental study of mixing in low gravity by vibrations Aliaksandr Mialdun, Yurii Gaponenko, Denis Melnikov, Valentina Shevtsova In the absence of external forces, the diffusion process leads to the mixing of species on long time scale. The application of vibrations to a fluid system with density gradient causes relative flows inside the fluid. The aim of this study is to analyze the physical mechanism, by which vibrations affect the mixing process of two stratified miscible fluids. The rectangular cavity (10mm x5 mm x 3mm) filled half-by-half with the two different miscible liquids is subjected to translational vibration. The direction of translational periodic vibrations with a constant frequency and amplitude is parallel to the interface between the two fluids. The system is kept at constant temperature. There is strong interplay between gravity and vibrational impact. To elucidate the vibrational mechanism the experiments were performed in parabolic flights organized by the European Space Agency. Parabolic flights provide repeated periods of approximately 20 seconds of reduced gravity preceded and followed by 20 seconds of hypergravity. The transient evolution of concentration field during microgravity time is investigated by optical digital interferometry. The analysis of the results shows that mixing and flow pattern in liquids depends not only on vibration stimuli but on the sharpness of the interface as well. [Preview Abstract] |
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