Bulletin of the American Physical Society
65th Annual Meeting of the APS Division of Fluid Dynamics
Volume 57, Number 17
Sunday–Tuesday, November 18–20, 2012; San Diego, California
Session D11: Microfluidics: Mixing |
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Chair: Nadine Aubry, Carnegie Mellon University Room: 26A |
Sunday, November 18, 2012 2:15PM - 2:28PM |
D11.00001: A Mapping method for mixing with diffusion Conor P. Schlick, Ivan C. Christov, Paul B. Umbanhowar, Julio M. Ottino, Richard M. Lueptow We present an accurate and efficient computational method for solving the advection-diffusion equation in time-periodic chaotic flows. The method uses operator splitting which allows advection and diffusion steps to be treated independently. Taking advantage of flow periodicity, the advection step is solved with a mapping method, and diffusion is added discretely after each iteration of the advection map. This approach allows for a ``composite'' mapping matrix to be constructed for an entire period of a chaotic advection-diffusion process, which provides a natural approach to the spectral analysis of mixing. To test the approach, we consider the two-dimensional time-periodic sine flow. When compared to the exact solution for this simple velocity field, the operator splitting method exhibits qualitative agreement (overall concentration structure) for large time steps and is quantitatively accurate (average and maximum error) for small time steps. We extend the operator splitting approach to three-dimensional chaotic flows. Funded by NSF Grant CMMI-1000469. [Preview Abstract] |
Sunday, November 18, 2012 2:28PM - 2:41PM |
D11.00002: Advective-diffusive mixing in microchannels Oleksandr Gorodetskyi, Michel F.M. Speetjens, Patrick D. Anderson Laminar mixing is key to many processes in micro-devices and the mapping method is a proven and efficient approach to simulate and investigate mixing phenomena in realistic 3D geometries. However, the conventional mapping method is restricted to purely advective transport, while molecular diffusion is often significant, in particular in small-scale devices. A recent extension of the mapping method by Gorodetskyi et al. (Phys. Fluids, 2012, in press) allows inclusion of diffusion and thus greatly expands the application area of the technique. Diffusive mapping method enables in-depth analysis of the interplay between chaotic advection and diffusion in realistic systems by essentially the same procedure as successfully employed before for the purely convective approach. As a benchmark model for a realistic prototype system: the 3D staggered herringbone micro mixer is considered. Advective-diffusive mixing for various protocols of the mixer, that posses different dynamical properties, is investigated by means of the diffusive mapping method. [Preview Abstract] |
Sunday, November 18, 2012 2:41PM - 2:54PM |
D11.00003: Effect of viscosity contrast on mixing and dispersion in a capillary tube Amir A. Pahlavan, Birendra Jha, Luis Cueto-Felgueroso, Ruben Juanes, Gareth H. McKinley Microfluidic mixing has received a renewed attention during the past decade due to its ubiquitous presence in nature and novel industrial devices. Most microfluidic devices however operate in the Stokes flow regime, meaning that turbulence and inertia do not play any role in the mixing process. While many fundamental aspects of microfluidic mixing are now understood, and a variety of methods have been proposed to enhance mixing at low Reynolds number flows, the influence of viscosity contrast on the non-equilibrium physics of mixing remains to be explored. In this work we address this problem through numerical simulations and reduced-order modeling. We investigate the role of viscosity contrast on hydrodynamic instabilities that control the dispersion and mixing of miscible fluid flows in a capillary tube, and exploit this new understanding to propose strategies for enhancing mixing at the microscale. [Preview Abstract] |
Sunday, November 18, 2012 2:54PM - 3:07PM |
D11.00004: Chaotic fluid mixing by alternating microparticle topologies to enhance biochemical reactions Yang Gao, Alexander van Reenen, Martien Hulsen, Arthur de Jong, Menno Prins, Jaap den Toonder We report experimental results on chaotic mass transport induced by alternating topological changes of magnetic particle chains actuated by a rotating magnetic field. Results on the induced fluid flows, through particle tracing and mixing experiments, are obtained for (1) the regime of rigid chain rotation and (2) the regime wherein chains periodically fragment and reform. In the case of rigid rotating chains, the overall tracer particle trajectories are steady circles around the center of the microparticle chains. In the regime of periodic chain breaking and reformation, the tracer particle trajectories become chaotic. The level of mixing is measured utilizing a mixing index (M) in a water-dye system, i.e. in a perfectly mixed system M=0 while in an unmixed system M=1. When particle chains periodically break and reform, we observe that M decreases from 1 to 0.1 within 15 rotational cycles. We also report the effects of the different mixing regimes on a biological (streptavidin-biotin) binding reaction in the solution. We conclude that the alternating topological change of microparticle chains is an effective mechanism to achieve chaotic mixing and thereby promote and homogenize reactions in lab-on-a-chip systems. [Preview Abstract] |
Sunday, November 18, 2012 3:07PM - 3:20PM |
D11.00005: Mixing Diagnostics in Confined, High-Speed Droplet Collisions Brian Carroll, Carlos Hidrovo Fast mixing remains a major challenge in droplet-based microfluidics. The low Reynolds number operating regime of most mixing devices signifies orderly flows that are devoid of any inertial characteristics. To increase droplet mixing rates, a novel technique is under development that uses a high Reynolds number gaseous phase for droplet generation and transport and promotes mixing through binary droplet collisions at velocities near 1m/s. Limitations in existing mixing diagnostic methodologies has persuaded cultivation of a new technique for measuring droplet collision mixing in confined microchannels. The technique employs single fluorophore laser-induced fluorescence, custom image processing, and meaningful statistical analysis for monitoring and quantifying mixing in high-speed droplet collisions. Mixing progress is revealed through two statistics that separate the roles of convective rearrangement and molecular diffusion during the mixing process. The end result is a viewing window into the rich dynamics of droplet collisions with spatial and temporal resolutions of 1$\mu $m and 25$\mu $s, respectively. Experimental results obtained across a decade of Reynolds and Peclet numbers reveal a direct link between droplet mixing time and the collision convective timescale. This work provides valuable insight into the emerging field of two-phase gas-liquid microfluidics and opens the door to fundamental research possibilities not offered by traditional oil-based architectures. [Preview Abstract] |
Sunday, November 18, 2012 3:20PM - 3:33PM |
D11.00006: 3D mixing near the surface of actuated beads Neehar Moharana, Michel Speetjens, Ruben Trieling, Herman Clercx Mixing in microfluidic devices is often a challenge because of the absence of turbulence. Here we must instead resort to laminar mixing by chaotic advection. In order to achieve chaotic advection in such devices, we explore a promising future technology for active mixing by actuating microscopic magnetic beads with magnetic fields. The present study addresses the fundamental transport phenomena and associated mixing processes around a piecewise-steadily translating and/or rotating spherical bead. A detailed transport analysis revealed that perturbation of the Stokes flow around the sphere is essential to attain (locally) chaotic mixing. To this end we introduce a nonlinear perturbation that changes the flow in essentially the same way as fluid inertia or bead oscillations. The impact of this perturbation on the mixing properties has been explored for various actuation protocols via symmetry analysis and numerical simulation of three-dimensional (3D) fluid trajectories and computation of Poincar\'{e} maps (``stroboscopic maps'' of particle positions). We found evidence of intricate coherent structures which are key to 3D mixing in that they geometrically constrain and determine the tracer transport. Parallel to the above study, we have designed and manufactured a macro-scale experiment in order to validate the mixing properties around the sphere by 3D velocity and temperature measurements. Preliminary experimental results will be shown. [Preview Abstract] |
Sunday, November 18, 2012 3:33PM - 3:46PM |
D11.00007: An Experimental Study of Molecular Mixing Enhancement in a Small Shear Layer Facility Rohit Nehe, Manoochehr Koochesfahani An experimental investigation is carried out to characterize the mixing field in a very low Reynolds number forced shear flow where the flow velocity is so low that, without the imposed perturbation, there is little mixing due to the absence of turbulence. To enhance the mixing interfacial area, we provide flow perturbation over a range of frequencies and amplitudes. The chemically reacting LIF technique is used to quantify the level of mixedness, while single component MTV is employed to measure the amplitude of perturbation velocity. Results from streamwise LIF measurements show the existence of a limited range of perturbation frequencies that result in a high level of mixedness. The highest mixing cases also exhibit high levels of velocity fluctuation. The 3D nature of the mixing field is studied in more detail by performing spanwise LIF measurements. Results will be presented for the cross-stream structure of the mixing field over the cross section of the test facility. [Preview Abstract] |
Sunday, November 18, 2012 3:46PM - 3:59PM |
D11.00008: Numerical study of elastic turbulence in a 3D curvilinear micro-channel Hongna Zhang, Tomoaki Kunugi, Fengchen Li Elastic turbulence is an intriguing phenomenon of viscoelastic fluid flow, and dominated by the strong nonlinear elasticity due to the existence of flexible microstructures. It implies the possibility to generate a turbulent state (so-called an elastic turbulence) in the micro-scale devices by introducing the viscoelastic fluids, which could significantly enhance the mixing efficiency therein. Several experiments have been carried out to study its characteristics and underlying physics. However, the difficulty in measuring the flow information and behaviors of the microstructures, especially in the cross section normal to the mean flow direction, limits our current understanding and controlling. In the present study, the nondimensionalization method in which the characteristic velocity is defined as the ratio of the solution viscosity to the width of the channel was adopted to simulate the elastic turbulence in the micro-scale devices. And the elastic turbulent flow was obtained numerically in the 3D curvilinear micro-channel. Therein, the characteristics of the velocity field and polymer's behavior are discussed. Moreover, the energy transfer between the kinetic energy and the polymer's elastic energy is also investigated to understand its physical mechanism. [Preview Abstract] |
Sunday, November 18, 2012 3:59PM - 4:12PM |
D11.00009: Electrothermal blinking vortices for chaotic mixing Sophie Loire, Paul Kauffmann, Paul Gimenez, Carl Meinhart, Igor Mezic We present an experimental and theoretical study of electrothermal chaotic mixing using blinking of asymmetric 2D electrothermal vortices. Electrothermal flows are modelled with 2D finite element method using COMSOL software based on an enhanced electrothermal model. Velocities in top-view and side-view devices are measured by micro particle image velocimetry ($\mu$PIV). The experimentally reconstructed velocity profile shows a dramatic asymmetry between the two vortices, in good agreement with the FEM model. The separation line between the two vortices is shifted and tilted making the blinking vortices overlap. We use the mix-variance coefficient (MVC) on experimental particle detection data and numerical trajectory simulations to evaluate mixing at different scales including the layering of fluid interfaces by the flow, a keypoint for efficient mixing. The blinking vortices method greatly improve mixing efficiency. Theoretical, experimental and simulation results of the mixing process will be presented. [Preview Abstract] |
Sunday, November 18, 2012 4:12PM - 4:25PM |
D11.00010: Experimental Study of Electrothermal 3D Mixing using 3D microPIV Paul Kauffmann, Sophie Loire, Carl Meinhart, Igor Mezic Mixing is a keystep which can greatly accelerate bio-reactions. For thirty years, dynamical system theory has predicted that chaotic mixing must involve at least 3 dimensions (either time dependent 2D flows or 3D flows). So far, 3D embedded chaotic mixing has been scarcely studied at microscale. In that regard, electrokinetics has emerged as an efficient embedded actuation to drive microflows. Physiological mediums can be driven by electrothermal flows generated by the interaction of an electric field with conductivity and permittivity gradients induced by Joule heating We present original electrothermal time dependant 3D (3D+1) mixing in microwells. The key point of our chaotic mixer is to generate overlapping asymmetric vortices, which switch periodically. When the two vortex configurations blink, flows stretch and fold, thereby generating chaotic advection. Each flow configuration is characterized by an original 3D PIV (3 Components / 3 Dimensions) based on the decomposition of the flows by Proper Orthogonal Decomposition. Velocity field distribution are then compared to COMSOL simulation and discussed. Mixing efficiency of low diffusive particles is studied using the mix-variance coefficient and shows a dramatic increase of mixing efficiency compared to steady flow. [Preview Abstract] |
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