Bulletin of the American Physical Society
63rd Annual Meeting of the APS Division of Fluid Dynamics
Volume 55, Number 16
Sunday–Tuesday, November 21–23, 2010; Long Beach, California
Session QP: Microfluidics: Mixing II |
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Chair: Hui Zhao, University of Nevada, Las Vegas Room: Long Beach Convention Center 203A |
Tuesday, November 23, 2010 12:50PM - 1:03PM |
QP.00001: Optimal advective mixing by two-dimensional chaotic Stokes flows David Saintillan, Qizheng Yan Numerous mixing strategies in microfluidic devices rely on chaotic advection by time-dependent body forces. The question of determining the required forcing function to achieve optimal mixing at a given kinetic energy or power input remains however open. Using finite-horizon optimal control theory, we numerically determine general optimal mixing flows in a two-dimensional periodic geometry as truncated sums of time-modulated Fourier modes. The time-averaged power spectra of these flows are calculated to investigate the effect of scale. We demonstrate that optimal mixing flows with fixed kinetic energy contain a wide range of spatial scales, whereas those with fixed power input are strongly dominated by large scales. We also determine the frequency spectra of the time-modulating functions and characterize the importance of non-harmonic forcing. [Preview Abstract] |
Tuesday, November 23, 2010 1:03PM - 1:16PM |
QP.00002: Analysis of Mixing in a 2D Drop with Time-Periodic Boundary Forcing Michael Davis, Amanda Clemm, Cecily Keppel, Dylan Marriner, Andrew Bernoff, Ali Nadim We carry out a detailed analysis on the model problem of Nadim \& Miraghaie [Bull.\ Am.\ Phys.\ Soc., {\bf 49}, 188 (2004)], which consists of a 2D circular drop driven by a tangential stress applied at its boundary giving rise to a pair of circulating flows in each half of the drop that are periodically reoriented. We characterize the resulting chaotic flow by computing the Lyapunov Exponents (LE) and their Finite-Time counterparts (FTLE) for all initial positions within the drop. We calculate the mean and variance of the FTLEs for a wide range of switching times, and identify the optimal switching time for efficient mixing. At some non-optimal switching times, the drop domain contains a mixing region and non-mixing islands which are associated with a bimodal distribution of FTLEs. For a certain switching time, we identify a group of 4 points (which form a square in the drop) that are permuted by the flow and return to their original positions after 4 switching periods. The space-time trajectories of these points, which can be regarded as virtual ``stirring rods,'' form braids when the flow is chaotically mixing. Calculation of braiding factors associated with different patterns of switching enables us to assess their mixing efficacy. [Supported by Fletcher Jones Fellowships/CCMS] [Preview Abstract] |
Tuesday, November 23, 2010 1:16PM - 1:29PM |
QP.00003: Low Reynolds number flow over slanted grooves in a micro-channel Sungchan Yun, Kwan Hyoung Kang A pressure driven flow over a micro-patterned geometry generates a transverse velocity component to the principal direction of flow. In the analysis of the flow inside a micro-channel, for simplicity of analysis, an effective slip velocity is applied to represent the transverse velocity developed by the slanted grooves. However, since the slip model is based on a periodically placed infinite length of linear grooves, the validity of model is limited only for shallow-depth grooves or thin channels. In this work, we investigated flow patterns near grooves in a closed channel based on three-dimensional numerical analysis, and the numerical results are verified experimentally through flow visualization. We found that the flow pattern becomes somewhat complicated, as the depth or width of the grooves is increased, which cannot be accounted for by the simple slip model. Based on the numerical results, we determined the range of depth and width of the grooves in which the effective slip model can be applied. [Preview Abstract] |
Tuesday, November 23, 2010 1:29PM - 1:42PM |
QP.00004: Designing a Robust Micromixer Based on Fluid Stretching David Mott, Dipesh Gautam, Greg Voth, Elaine Oran A metric for measuring fluid stretching based on finite-time Lyapunov exponents is described, and the use of this metric for optimizing mixing in microfluidic components is explored. The metric is implemented within an automated design approach called the Computational Toolbox (CTB). The CTB designs components by adding geometric features, such a grooves of various shapes, to a microchannel. The transport produced by each of these features in isolation was pre-computed and stored as an ``advection map'' for that feature, and the flow through a composite geometry that combines these features is calculated rapidly by applying the corresponding maps in sequence. A genetic algorithm search then chooses the feature combination that optimizes a user-specified metric. Metrics based on the variance of concentration generally require the user to specify the fluid distributions at inflow, which leads to different mixer designs for different inflow arrangements. The stretching metric is independent of the fluid arrangement at inflow. Mixers designed using the stretching metric are compared to those designed using a variance of concentration metric and show excellent performance across a variety of inflow distributions and diffusivities. [Preview Abstract] |
Tuesday, November 23, 2010 1:42PM - 1:55PM |
QP.00005: A Two-Equation Model For Mixing in Viscous-Fingering Displacements Birendra Jha, Luis Cueto-Felgueroso, Ruben Juanes We study, by means of numerical simulation, the mixing of two fluids of different viscosities in advection-dominated flows in a porous medium. It is well known that when a less viscous fluid displaces a more viscous fluid, the displacement front is unstable and leads to the formation of a pattern known as viscous fingering. We present a high-resolution simulation approach that is stable for arbitrary viscosity ratios, and study mixing under different configurations with viscosity contrasts up to M = 400. We observe, in agreement with lab experiments, that for high-M displacements, the growth of new fingers follows the trace of previous ones. This channeling effect, which is a result of the nonlocal coupling through the pressure field, greatly reduces mixing. A two-equation mixing model using the scalar variance and its dissipation rate is derived from the advection-diffusion equation. It provides a measure of effective diffusivity due to convective and diffusive mixing processes. Our analysis predicts the optimum range of viscosity contrast and Peclet number that maximizes the interfacial area by balancing the number of fingers with their length before diffusive mixing across the sharp interface takes over. Interesting fingering patterns such as channeling and tip-splitting play an important role in this balancing act which makes degree of mixing a non-monotonic function of the viscosity contrast and the Peclet number. [Preview Abstract] |
Tuesday, November 23, 2010 1:55PM - 2:08PM |
QP.00006: Lubrication Analysis of Flow and Mixing in a 3D Translating Sessile Drop Cecily Keppel, Amanda Clemm, Michael Davis, Dylan Marriner, Andrew Bernoff, Ali Nadim We consider the flow within a sessile drop that translates along a surface. The drop height is taken to be small compared to the radius of its wetted base allowing a lubrication approximation. The drop is also assumed to maintain its static shape (i.e., spherical cap approximated by a paraboloid) during translation, which requires vanishingly small capillary and Bond numbers. The 3D flow and pressure field in the drop are obtained and the form of the singularity in pressure and stress at the contact line is determined. The closed streamlines of the flow are seen to correspond to the intersection between a family of axisymmetric shell-like surfaces and another family of sheets that are flat in the direction of translation but curved in the plane perpendicular to that direction. Mixing within the drop is investigated when the direction of translation is periodically switched by 90$^\circ$. With such switching, a passive scalar is found to become well mixed on the 2D surfaces of the axisymmetric shells identified in the steady flow, but no mixing occurs across the shells. Addition of small diffusion, however, enables the passive scalars to cross to neighboring shells and get well mixed within the drop volume. [Supported by Fletcher Jones Fellowships/CCMS] [Preview Abstract] |
Tuesday, November 23, 2010 2:08PM - 2:21PM |
QP.00007: Optimizing Chaotic Mixing in a Two-Inlet Microfluidic Channel by Out-of-Phase Pulsing. David Chang, Rodolphe Chabreyrie, Nadine Aubry While mixing is often a necessary step in microfluidic applications, it has proven to be difficult at small scale. Our focus has been on the generation of chaotic mixing by using out-of-phase pulsing in two-inlet channels, such as T or Y channels. Cases ranging from in-phase to anti-phase inlet pulsing have been simulated to optimize the size of the chaotic mixing region. Poincar\'{e} analysis was performed for each of the cases and the area of chaotic mixing was measured to determine the value of the parameters leading to the best mixing results. In addition, Lagrangian Coherent Structures (LCS) were be identified from the Finite-Time Lyapunov Exponent Maps (FTLE) for certain parameter values. [Preview Abstract] |
Tuesday, November 23, 2010 2:21PM - 2:34PM |
QP.00008: Passive scalar separation using chaotic advection Andrew Duggleby, Pradeep Rao, Pankaj Kumar, Mark Stremler Separation of two substances with slightly different diffusivities using chaotic advection is explored for finite Reynolds numbers (up to Re$\sim10$) and high average Schmidt numbers ( $\overline{\mathrm{Sc}}=(\mathrm{Sc}_1 + \mathrm{Sc}_2)/2 = 10^6$)) for a modified lid-driven cavity. In this approach, exponential stretching of material interfaces enhances diffusion and accelerates separation of concentrated molecules having slightly different diffusivities. At low Re the flow can be reversed and the separated molecules extracted. Using the exponential convergence afforded by the use of a 2D Fourier-Chebyshev spectral algorithm for streamfunction-vorticity formulation with passive scalar transport enables accurate tracking of exponential stretching of material lines in the flow and capturing of the sharp concentration gradients associated with large $\overline{\mathrm{Sc}}$. The two substances separate significantly faster than for simple diffusion. Performance based on topological entropy and almost-invariant sets, as well as application to real separation systems, will be discussed. [Preview Abstract] |
Tuesday, November 23, 2010 2:34PM - 2:47PM |
QP.00009: Evidence of streaming-related irreversibility and mixing in low Reynolds number acinar flows Haribalan Kumar, Ching-Long Lin, Merryn H. Tawhai, Eric A. Hoffman Understanding kinematic irreversibility and mixing deep in the lung helps improve particle retention estimates and hence provide better drug delivery strategies. The time-periodic low-Reynolds number flow in the tiny alveolar units can be computed using an open cavity configuration. Steady streaming is found to hold the key to the origin of irreversibility and dispersion in the duct, cavity mouth and within the cavity. The mechanism of steady streaming is hydrodynamic in nature. The results of tracer advection and mixing rates are used to quantify the irreversibility and mixing resulting from this streaming. The effect of varying Strouhal numbers, Reynolds numbers and geometrical parameters on the resulting mixing are also investigated. This streaming mechanism may provide a route to explaining dispersion observed in bolus experiments deep in the lung. [Preview Abstract] |
Tuesday, November 23, 2010 2:47PM - 3:00PM |
QP.00010: Experimental study on biological mixing by micro-organism Jihoon Kim, Yonghee Jang, Doyoung Byun, Sungwon Nam, Sungsu Park, Minjun Kim Recently, the most challenge in a microfluidic device remains in acting on the device without external source such as syringe pump, magnetic driven force, and electrohydrodynamic force. Instead of the artificial external force, biological propelled mechanism has been paid much attention. Most of micro-organisms have shown to generate straight motion, vibration, and rolling motion. Those motions can be applied to numerous part of micro-actuator or biological robot. In this paper, we investigated the flow field induced by swimming Tetrahymena and suggest this for mixing mechanism. Using micro-particle image velocimetry system, we visualized dynamic motions by DC, AC, and AC+DC galvanotaxis. Due to the periodic signal of AC voltage, Tetrahymena swimming is easily controlled on any desired direction. AC galvanotaxis also allows it to stop at a position only by changing the applied frequency and voltage. Therefore, this galvanotactic motion control can be applied to biological micro-mixer in the microfluidic device. [Preview Abstract] |
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