Bulletin of the American Physical Society
61st Annual Meeting of the APS Division of Fluid Dynamics
Volume 53, Number 15
Sunday–Tuesday, November 23–25, 2008; San Antonio, Texas
Session GK: Micro Fluids: Mixing |
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Chair: Paulo E. Arratia, University of Pennsylvania Room: 102B |
Monday, November 24, 2008 8:00AM - 8:13AM |
GK.00001: ABSTRACT WITHDRAWN |
Monday, November 24, 2008 8:13AM - 8:26AM |
GK.00002: Analysis and numerical modeling of electrohydrodynamic instability in a three-layer stratified flow Venkat R.T. Narayanan, Jianbo Li, Jeffrey D. Zahn, Hao Lin Organic-aqueous liquid (phenol) extraction is one of many standard techniques to efficiently purify DNA directly from cells. Effective dispersion of one fluid phase in the other increases the surface area over which biological component partitioning may occur, and hence enhances DNA extraction efficiency. Electrohydrodynamic (EHD) instability can be harnessed to achieve this goal, and has been experimentally demonstrated by one of the co-authors (JDZ). In this work, analysis and simulation are combined to investigate EHD instability in a three-layer, stratified, and immiscible microchannel flow. Such instability induces droplet formation, thereby increasing the interfacial area available for partitioning. A linear analysis is carried out with a Chebyshev pseudo-spectral method, whereas a fully nonlinear simulation is implemented using a finite volume, immersed boundary method. The results from both models compare favorably with each other. The linear analysis reveals basic instability characteristics such as kink and sausage modes, while the nonlinear simulation predicts surface deformation in the strongly nonlinear regime pertinent to droplet formation. The eventual objective is to utilize these numerical tools to determine relevant parameters for maximizing interfacial surface area for optimized DNA extraction. [Preview Abstract] |
Monday, November 24, 2008 8:26AM - 8:39AM |
GK.00003: Scattering analysis of streaming flow in a microfluidic channel J.-C. Tsai, David Hansen, Sascha Hilgenfeldt We study the effect of a localized streaming source on the viscous flow in a thin microfluidic channel. A mean flow is established through a global applied pressure gradient, while the local streaming is superimposed by means of a microbubble oscillating at small amplitude. The character of the resulting flow changes qualitatively with the relative strengths of these flow components. Our experiments and simulations show a well- defined lateral range of influence of the bubble streaming. Using a narrow beam of tracer particles passing by the oscillating bubble, analogous to conventional fixed-target scattering experiments, we investigate microscopic details of the flow, such as the sensitive dependence of the final transverse distance and time of flight on a slight variation of initial position, useful for describing micromixing. Further investigations show that active variation of the bubble oscillation amplitude significantly enhances mixing compared to the passive superposition of the two steady viscous flows, but only when the modulation frequency is comparable to the inverse mean flow passage time. [Preview Abstract] |
Monday, November 24, 2008 8:39AM - 8:52AM |
GK.00004: Mixing in a translating drop in the presence of modulated electric field Dmitri Vainchtein, Thomas Ward We study chaotic advection and mixing in a drop translating in the presence of an electric field. The flow is a combination of a Hadamard-Rybczynski and a Taylor circulation due to the steady translation and periodically modulated electric field. We consider small perturbations in time and space to what is otherwise an integrable flow. Using a technique introduced by Neishtadt we find an adiabatic invariant for the system by averaging the equations of motion. The chaotic advection is due to quasi-random jumps of the AI after crossing the separatrix of the unperturbed flow. We derive analytical expressions to quantify the change in the AI during a single crossing and compare the results with numerical simulations. [Preview Abstract] |
Monday, November 24, 2008 8:52AM - 9:05AM |
GK.00005: Efficient methods for optimal feedback control of mixing in a Stokes fluid flow Ian Couchman, Eric Kerrigan, John Christos Vassilicos Many microfluidic applications require the mixing of fluids but the laminar nature of the flow can make this difficult. The advent of laboratory techniques, such as magnetohydrodynamics, make it possible to generate time-varying velocity fields and provide a mechanism by which a flow can be controlled. As such, research into the optimal control of mixing in advection-dominated flows is a highly relevant problem. This work considers the optimal control of a system comprising of a scalar field being advected by a velocity field, which is influenced by a control variable. The cost by which performance is judged is the `mix-norm' defined in Mathew et al. (2005). The approach involves solving a dynamic optimization problem based on a low-order model with diffusivity several orders of magnitude larger than that of the actual system. This significantly reduces the complexity of the optimization problem. By solving recursively, feeding back the current system state as the initial model state, this work demonstrates that a controller based on a low-order model can provide satisfactory performance. A key benefit of this approach is the explicit incorporation of state and input constraints representative of some physical properties of the system or source. [Preview Abstract] |
Monday, November 24, 2008 9:05AM - 9:18AM |
GK.00006: Separation by diffusive irreversibility in a chaotic Stokes flow in a microchannel Pavithra Sundararajan, Joseph Kirtland, Donald Koch, Abraham Stroock Taylor famously demonstrated that a fluid could be reversibly stirred and unstirred at low Reynolds numbers. Heller further suggested that stirring and unstirring of a mixture of diffusive solutes into a diluent could lead to partial purification of the mixture of solutes of low diffusivity. Finally, Jones and Aref showed in a numerical study that this separation process could be more efficient if the stirring flow was chaotic. This process, separation of particles by diffusive irreversibility (SDI), could be an extremely simple method of chemical separation that would not require external fields or membranes. We have investigated the reversibility of convection-diffusion in laminar chaotic flows in a microchannel patterned with staggered herring-bone shaped grooves. We will discuss a model that predicts the extent of reversibility of the flow and compare it with experimental and numerical results. We demonstrate the generality of the finding of Jones and Aref: chaotic flows allow for more efficient SDI by providing a clean separation of the time-scales of stirring and diffusive mixing. We will present the design of a micro-fluidic device that implements the principle of SDI effectively. The experiments and the model together could improve our understanding of the fundamental aspects of reversibility in chaotic Stokes flows. [Preview Abstract] |
Monday, November 24, 2008 9:18AM - 9:31AM |
GK.00007: On the optimization of mixing for shear-sensitive materials Oleg Gubanov, Luca Cortelezzi Microfluidic mixing could have a major impact on medical applications involving the treatment of biological fluids. In these applications, high shear stresses induced by mixing can damage shear-sensitive components such as red blood cells, DNA or microbial cultivations. Further damages can be produced by mixing over long periods of time or by turbulence. Hence, these applications require a mixing device able to induce a desired level of homogeneity in the shortest time possible for a given value of energy while maintaining shear stresses below a given threshold. In this study, we address the conceptual challenge of designing such a device by studying the optimization of mixing in an idealized advective-diffusive model derived from the sine flow. In our model, a concentration field is stirred iteratively by blinking orthogonal velocity fields whose profiles, represented by a truncated Fourier series, are optimized at each blinking time. These velocity profiles are the solution of a constrained optimization problem which maximizes the efficiency of the mixer for a given value of the operating kinetic energy while satisfying a shear stress constraint. We establish the domain of operability of the mixer and quantify its mixing efficiency for a range of values of the operating kinetic energy and shear stress. We show that for a given kinetic energy the optimized flow can be substantially more mixing efficient than the periodic sine flow while satisfying the shear stress constraint. [Preview Abstract] |
Monday, November 24, 2008 9:31AM - 9:44AM |
GK.00008: Micro-fluidic Mixing using Artificial Cilia Michiel Baltussen, Jaap den Toonder, Femke Bos, Patrick Anderson The unexpectedly high mixing efficiency of our previously developed micro-mixer [1] is investigated. This mixer uses polymer actuators mimicking cilia which move periodically. A model containing fluid inertia, which is often negligible in micro-fluidics, is solved with a finite element method. The obtained velocity field is used as an input for tracking passive particles during multiple actuation cycles. It is found that fluid inertia causes a net flow opposite to that found in Stokes flow, and results in better distributive mixing than Stokes flow. Next the simulations are compared with optical coherence tomography experimental data and the simulations which contain fluid inertia are in close agreement with the experiments. Therefore inertia is the cause for the exceptionally good mixing in these devices. [1] J.M.J. den Toonder, F.M. Bos, D.J. Broer, L. Filippini, M. Gillies, J. de Goede, G.N. Mol, W. Talen, J.T.A. Wilderbeek, V. Khatavkar and P.D. Anderson, Artificial cilia for active micro-fluidic mixing, Lab Chip, 8, 533-541, 2008 [Preview Abstract] |
Monday, November 24, 2008 9:44AM - 9:57AM |
GK.00009: 3D Shrinky-Dink Vortex Micromixer: Efficient Mixing at Low Reynolds Numbers Michael Sprague, Chi-Shuo Chen, Maureen Long, Anthony Grimes, Fran\c{c}ois Blanchette, Michelle Khine Rapid and effective mixing of macromolecular solutions remains a persistent challenge when studying biochemical reactions. We show here that rapid and enhanced micromixing can be achieved in an easily fabricated (requiring no lithography), topologically simple 3D microvortex mixer at low Reynolds numbers. Experiments indicate dramatically improved mixing performance when compared with the traditional 2D serpentine design. Direct numerical simulation is used to examine vortex formation and to offer mechanistic understanding of our experimental data. [Preview Abstract] |
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