Bulletin of the American Physical Society
2006 59th Annual Meeting of the APS Division of Fluid Dynamics
Sunday–Tuesday, November 19–21, 2006; Tampa Bay, Florida
Session GC: Microfluidics VI: Numerical Studies-2 |
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Chair: Jason Butler, University of Florida Room: Tampa Marriott Waterside Hotel and Marina Grand Salon AB |
Monday, November 20, 2006 10:30AM - 10:43AM |
GC.00001: Simulations of Magnetic Micro-swimmers Eric Keaveny, Martin Maxey, George Karniadakis Following a recent realization of artificial micro-swimming (Dreyfus et. al., \emph{Nature}, \textbf{437}, 862-865), we conduct simulations of a swimmer whose mechanism of propulsion is the magnetically driven undulation of a flagellum-like tail composed of chemically linked paramagnetic beads. In our model, the tail is treated as a series of spheres tied together by inextensible, bendable links. The spheres interact magnetically through mutual dipole interactions, and hydrodynamic interactions are achieved by the force-coupling method. We compare the swimming speeds determined by the simulations with those obtained experimentally and by previous theoretical modeling. In addition, we evaluate the performance of the micro-swimmer in external flow fields and explore the use of alternative applied magnetic fields. [Preview Abstract] |
Monday, November 20, 2006 10:43AM - 10:56AM |
GC.00002: Analytical and Numerical Investigations of the Influence of the Geometrical Parameters on the Flow Performance of Spiral Channel Viscous Micropump. A.T. Al-Halhouli, M.I. Kilani, A. Al-Salaymeh, S. B\"uttgenbach Spiral channel viscous micropump (Spiral CVMP) idea depends on dragging the fluid along a spiral channel either by rotating the spiral channel disk against a stationary flat disk or rotating the flat disk against the spiral channel. A net tangential viscous stress on the boundaries is built and produces a positive pressure gradient in the direction of flow. In this work, Analytical and numerical investigations for the effect of mean radius to channel width ratio ($R_m /w)$ on the flow performance of a newly introduced Spiral CVMP have been carried out. Drag and shape factors for the effect of $R_m /w$ were also generated. For this purpose computational fluid dynamics (CFD) simulations using finite volume method were performed, a number of 3D models for the pump geometry were built and analyzed at different boundary conditions. An analytical model estimating for the effect of mean radius to channel width ratio was also derived, and showed good agreement with the numerical simulations. It has been also found that the flow rate varies linearly with both the pressure difference and boundary velocity for a wide range of$R_m /w$, which supports the validity of the linear lubrication model for this problem for the full range of studied parameter. Further, it is found that resulting error from ignoring $R_m /w\ge 1.0$ is less than 10{\%}. [Preview Abstract] |
Monday, November 20, 2006 10:56AM - 11:09AM |
GC.00003: Linear Stability and Growth of Disturbances in Weakly-Rarefied Pulsatile Flows Francesco Fedele, Darren Hitt In this work we examine the response of pulsatile pipe flows to axisymmetric perturbations under weakly-rarefied flow conditions (‘slip regime’) roughly defined by Knudsen numbers $Kn \leq 0.1$. Such perturbations can arise, for example, due to surface roughnesses on the solid boundaries. An Orr-Sommerfeld equation is derived and solved by means of a Galerkin projection onto the approximate functional space spanned by a finite set of eigenfunctions derived in the longwave limit of the Orr-Sommerfeld operator. For first-order slip boundary conditions, the results from Floquet stability analyses show that pulsatile slip flow is slightly more stable than the steady slip-flow for longwave disturbance; further, the stability characteristics are found to be only weakly-dependent on the Knudsen number. The flow structures corresponding to the largest energy growth are toroidal vortex tubes that are transported diffusively and convectively by the mean flow. The transient energy growth is found to slightly increase with the Knudsen number, indicating that the Orr-Sommerfeld operator for slip flow is more non-normal when compared to continuum-based no-slip flows. The impact of higher-order slip conditions at $O(Kn^2)$ will also be discussed. [Preview Abstract] |
Monday, November 20, 2006 11:09AM - 11:22AM |
GC.00004: Mesoscale Fluctuation-Relaxation Model for Velocity Slip and Temperature Jump on Fluid-Solid Interface Justyna Czerwinska Many micro- and bio-engineering applications require correct prediction of fluid flow in complex geometries. Fluid-solid contact interface prominently influences flow behavior. Velocity slip and thermal jump on the fluid-solid boundary are the result of non-equilibrium intermolecular energy transport. For gases this phenomena is well described by Maxwell-Smoluchowski equation. For liquids, at present simulations are conducted by hybrid approach (Continuum- Molecular Dynamics; Lattice Boltzmann Method - Molecular Dynamics). Presented here Fluctuation-Relaxation model, which is consequence of non-equilibrium Fluctuation Theorem, provides coarse grained relation for intermolecular solid-fluid energy transport. The implementation and verification is obtained by using Voronoi Particle Dynamics. Consequently, velocity slip and thermal jump are the result of the relaxation to equilibrium of the near boundary fluid particles. The model predicts correctly other theoretical and computational results. Moreover it provides extension to understanding of fluid-solid interface behavior on the mesoscale. [Preview Abstract] |
Monday, November 20, 2006 11:22AM - 11:35AM |
GC.00005: Lateral migration of particles in a microchannel Alexander Leshansky, Avishay Bransky, Nataniel Korin, Uri Dinnar The use of microfabricated elements and microfluidics, offer a great promise in the field of clinical blood tests. An automated rheoscope has been developed, utilizing a microfabricated glass flow cell, high speed camera and advanced image-processing software. Red Blood Cells (RBCs) and rigid microspheres (1-8 $\mu$m) suspended in a high viscosity media were filmed flowing through a microchannel ($Re<<1$) and their spatial distributions and velocities were measured. Under these conditions, both the RBC and the microspheres showed an enhanced inward lateral migration. RBCs exhibit different orientations and deformations according to their location in the quadratic velocity profile. Therefore, the control over the spatial distribution of RBCs across the microchannel is a crucial issue. For RBCs, the inward lateral migration is usually attributed to their deformability. However, the symmetry of the Stokes equations rules out the possibility of lateral migration in a dilute suspension of rigid spheres. In the present work we demonstrate that {\it microelasticity} of the suspending fluid can be responsible for the particle lateral migration. Although, the suspending media was characterized as Newtonian, the small, but finite first normal stress difference can lead to the observed inward migration effect. The proposed theoretical model based on scaling arguments is in a very good agreement with the experimental results. [Preview Abstract] |
Monday, November 20, 2006 11:35AM - 11:48AM |
GC.00006: The role of Faradaic reactions in microchannel flows. David Boy, Brian Storey Microfluidic applications involving induced charge electroosmosis often rely upon having closely spaced electrodes inside the device. High electric fields are generated at relatively low voltage, which can drive significant flow. Even at low voltage, Faradaic reactions are known to occur and can impact device performance. This work considers the role of Faradaic reactions on microchannel flows, paying close attention to body forces on the bulk fluid. Binary electrolytes are modeled with the Poisson-Nernst-Planck equations with Butler-Volmer reaction kinetics. Two geometrical configurations are considered; an electrolyte between two parallel plate electrodes and an electrolyte over an alternating array of positive and negative electrodes. In the parallel plate configuration, body forces on the bulk fluid drive an instability in the system. Electro-convection sets in below the classical limiting current and impacts the predicted polarographic curves. In the alternating electrode configuration, we compare flow features and velocities from full numerical simulations to simpler models that assume electroneutrality in the bulk. [Preview Abstract] |
Monday, November 20, 2006 11:48AM - 12:01PM |
GC.00007: Induced-charge electro-osmosis over non-ideally polarizable surfaces Gilad Yossifon, Itzchak Frankel, Touvia Miloh Appearance of vortices in electro-kinetic flows around corners in micro-channel junctions have recently been documented in the literature. Their occurrence is related to the non-linear mechanism of induced-charge electroosmosis (ICEO). This is associated with the small yet finite dielectric constant of the channel walls allowing for electric-field leakage through them. This leakage localized at the corner polarizes it bringing opposite excess ion concentrations across the corner, thus modifying the electric body force acting on the fluid within the Debye layer. This, in turn, has a global effect on the hydrodynamics of the fluid outside the Debye layer and, under certain conditions, may induce vortices. We study theoretically the onset of such vortices in channel junctions and provide a physically and mathematically consistent description of the general ICEO phenomena over non-ideally polarizable (dielectric) surfaces. An effective channel-wall boundary condition is obtained which `integrates out' the thin electric double layer domain, thus, allowing a purely macro-scale calculation of the ICEO flow. Finally, encouraged by our success of modeling the occurrence of vortices in the micro-scale regime we extend our theory to the nano-scale regime. [Preview Abstract] |
Monday, November 20, 2006 12:01PM - 12:14PM |
GC.00008: A concept of concentration choice for electrical double layer overlapped K.-D. Huang, R.-J. Yang The electrokinetic phenomena under electrical double layer (EDL) overlapped condition present different results estimated by Gouy-Chapman model, especially the conductance and streaming current. In this study, we use the concept of concentration choice to estimate the streaming current, potential, and the electroviscous effect for the EDL from non-overlapped to overlapped condition. Analytical scaling and numerical simulations are used to investigate the problem. The results reveal that the concentration of net charge dominates the system under the EDL overlapped condition, which shows the streaming current is independent on the concentration of electrolyte. The maximum elctroviscous effect occurs at a specific concentration. The present results reveal that under double layer overlapped, noticeable variations in the ionic transport phenomena occur when comparing to that for the double layer non-overlapped. [Preview Abstract] |
Monday, November 20, 2006 12:14PM - 12:27PM |
GC.00009: Transport of densities in position-orientation space for the study of orientable particles in microchannels Thomas John, Igor Mezic We consider the dynamics of orientable particles in low Reynolds number flows. We use Langrangian methods to analyze transport of densities in the extended phase space that we have shown is appropriate for the analysis of reaction between these oriented particles. We prove the equivalence of the advection equation in the extended space with the infinitesimal generator of the semi-group of Perron-Frobenius operators associated with the dynamics of the particles and use this equivalence to compute the density at downstream locations in micro-devices given the inlet densities. In the case that includes diffusion, we develop an efficient backward Monte Carlo method to study the transport of density. We compare with the PDE solution and show that in cases where the solution is desired on a lower dimensional subset of the domain, substantial gains can be made by these methods. We apply the method to the study of a shear superposition micro-mixer. [Preview Abstract] |
Monday, November 20, 2006 12:27PM - 12:40PM |
GC.00010: Migration in confined polymer solutions induced by flow and external forces Berk Usta, Jason Butler, Tony Ladd We investigate the effects of hydrodynamic flow and external body forces on the dynamics of dilute polymer solutions in microchannels using an algorithm which combines the fluctuating lattice-Boltzmann method with micromechanical models of the polymer molecules. We examine different combinations of concurrent and countercurrent applications of the flow and external forces. We specifically address the importance of hydrodynamic interactions, the extent of hydrodynamic dispersion compared to molecular diffusion, and the lateral migration of polymers across the channel. The lateral migration, which results from both the hydrodynamic flow and external forces, exhibits non-trivial behavior depending upon the specific combination of the flow and body forces. We explain the results by comparing to an analysis of a simple dumbbell model and also discuss the possibility of performing separations of different chain sizes. [Preview Abstract] |
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