Bulletin of the American Physical Society
2005 58th Annual Meeting of the Division of Fluid Dynamics
Sunday–Tuesday, November 20–22, 2005; Chicago, IL
Session NC: Microfluidics: Electrophoresis and Electroosmosis II |
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Chair: Sandip Ghosal, Northwestern University Room: Hilton Chicago Grand Ballroom |
Tuesday, November 22, 2005 11:01AM - 11:14AM |
NC.00001: Controlling particle chaining in the manipulation of suspensions using dielectrophoresis Nadine Aubry, Pushpendra Singh In a non uniform electric field, the particles of a suspension experience both dielectrophoretic (DEP) and electrostatic particle-particle forces. In applications which require that the particles be manipulated individually, e.g., size separation of DNA molecules, the latter forces are not desirable since they induce particle chaining. On the other hand, such forces are crucial in applications where the particles must touch, e.g., electrofusion of biological cells, nanocircuit fabrication and electrorheological suspensions of increased viscosity. By using a numerical scheme based on the Maxwell stress tensor to compute electrostatic forces, we show how the ratio of the particle-particle and DEP forces varies with the particle size, the gap between the particles, and the Clausius-Mossotti factor. In AC dielectrophoresis, the particle chain formation can be controlled by operating in particular frequency regimes. Experiments manipulating viable yeast cells in a micro fluidic device have been performed, illustrating the various regimes. [Preview Abstract] |
Tuesday, November 22, 2005 11:14AM - 11:27AM |
NC.00002: Hydrodynamic interactions in induced-charge electrophoresis of colloidal rod dispersions David Saintillan, Eric S. G. Shaqfeh, Eric Darve The behavior of a dilute dispersion of ideally polarizable slender rods in an applied electric field is studied theoretically and numerically. The polarization of a rod results in the formation of a dipolar charge cloud around its surface, leading to a non-linear fluid slip, which causes particle alignment and creates a disturbance flow in the surrounding fluid. We derive a simple slender-body formulation for this phenomenon based on the thin double layer approximation and valid for high aspect ratio particles, and use it to study the hydrodynamic interactions between a pair of aligned rods. In particular, the pair probability density function in a dilute dispersion is calculated, and indicates that particle pairing can be expected. We also present results from large-scale numerical simulations that include both far-field and near-field hydrodynamic interactions as well as Brownian motion. Particle pairing is indeed observed to occur at high values of the Peclet number (weak Brownian motion), and results are reported for pair probabilities, orientation distributions and hydrodynamic diffusivities. [Preview Abstract] |
Tuesday, November 22, 2005 11:27AM - 11:40AM |
NC.00003: A high fidelity electrokinetic flow model for the prediction of electrophoregrams in on-chip electrophoresis applications Hao Lin, Rajiv Bharadwaj, Juan G. Stantiago, Bijan Mohammadi On-chip electrophoresis is a growing field with increasing chemical and bioanalytical applications such as genomics and proteomics. The use of multicomponent and heterogeneous electrolyte configurations can often lead to complex flow behavior. In this work, we present a high-fidelity, low computational cost electrokinetic flow model for the modeling and optimization of electrophoresis separations. The model adopts a depth-averaged approach that captures convective-dispersion processes, and includes important physical effects such as electrical body force and fully nonlinear multi-species electromigration. The corresponding numerical scheme is based on a finite volume approach using a monotonic upstream-centered construction (MUSCL). The numerical model can simulate arbitrary electrolyte and sample configurations, and capture the complex evolution of sharp, narrow sample peaks and high pre-concentration (stacking) ratios. Exemplary results showing both field amplified sample stacking and isotachophoresis processes are presented. The development of such models is critical to the efficient design and optimization of on-chip CE methods and devices. [Preview Abstract] |
Tuesday, November 22, 2005 11:40AM - 11:53AM |
NC.00004: A Mathematical Model Describing Gradient Focusing Methods for Trace Analytes Sandip Ghosal, Jon Horek The problem of Gradient Focusing for concentrating trace analytes is considered. Variation of buffer viscosity, conductivity and possibly also the zeta potential, results in a focusing point where the electrophoretic velocity is balanced by the electroosmotic flow (EOF) and where the sample concentrates. The axial inhomogeneity also results in an induced pressure gradient that alters the EOF profile and therefore causes Taylor dispersion. The coupled hydrodynamics and transport problem leading to the achievement of a steady state is studied in the context of the lubrication approximation: all variations in the axial direction take place over a length scale very much larger than the characteristic channel width. [Preview Abstract] |
Tuesday, November 22, 2005 11:53AM - 12:06PM |
NC.00005: Electroosmotic flow in rectangular microchannels: numerical simulation and asymptotic theory Subhra Datta, Sandip Ghosal, Neelesh Patankar The problem of fluid flow in a microfluidic channel of rectangular cross- section is solved numerically when the zeta potential is not uniform. Variations in the axial direction as well as along the perimeter of the channel cross-section is considered. Excellent agreement is found with a previously published (Ghosal, 2002 JFM vol.459 pg. 103) asymptotic theory based on the lubrication approximation, even when the length scale of axial variations is of the same order as the characteristic channel width. [Preview Abstract] |
Tuesday, November 22, 2005 12:06PM - 12:19PM |
NC.00006: Countering capillary pressure with electroosmotic pressure at small scales Paul Steen, Michael Vogel, Peter Ehrhard Electroosmosis, originating in the double-layer of a small liquid-filled pore (size $R$) and driven by a voltage $V$, is shown to be effective in pumping liquid against the capillary pressure of a larger liquid droplet (size $B$) provided the dimensionless parameter $R^2 \sigma /\varepsilon | \zeta | V B$ is small enough. Here $\sigma$ is surface tension of the droplet liquid/gas interface, $\varepsilon$ the liquid dielectric constant, and $\zeta$ the zeta potential of the solid/liquid pair. As droplet size diminishes, the voltage required to pump eletroosmotically scales as $V \sim R^2/B$. Accordingly, the voltage needed to pump against smaller higher-pressure droplets can actually {\em decrease} provided the pump pore-size scales down with droplet size appropriately. In this talk, we shall focus on the electroosmotic droplet-switch, two droplets coupled by an electroosmotic pump. For millimeter-size droplets and micron-size pores, 5 volts yields switching times under 5 seconds in experiment. The down-scaling of this voltage and switching-time are of interest. [Preview Abstract] |
Tuesday, November 22, 2005 12:19PM - 12:32PM |
NC.00007: Electrophoresis in strong electric fields: The role of Maxwell stresses Yariv Ehud Electrophoresis, the motion of a charged colloidal particle under the action of an externally-applied electric field, is common in miniaturized systems. This motion is usually described by a linear model, based upon the smallness of the applied field relative to the equilibrium field in the screening Debye layer surrounding the particle. This model, in turn, leads to the Smoluchowskiâ€™s slip condition and eventually results in mobility relations. The mobility concept, however, is only valid provided the quadratic Maxwell stresses are neglected. In the literature, this neglect is implicitly supported by two arguments: (i) consistency with the linearization process leading to the slip condition; and (ii) the net electric neutrality of the combined particle-layer system. It will be shown that these arguments are incorrect. Accordingly, a consistent scheme is formulated for analyzing the motion of a particle in an applied field. The quadratic interactions with the field are represented by two tensorial coefficients, which describe the resulting particle translation and rotation. These nonlinear interactions are illustrated in two contexts: rotation of non-spherical particles, and drift of a spherical particle towards a planar wall. These effects are absent in the standard electrophoretic description. [Preview Abstract] |
Tuesday, November 22, 2005 12:32PM - 12:45PM |
NC.00008: Effect of Divalent Electrolytes on Electroosmotic Flow Haifeng Li, Minami Yoda, Pradeep Gnanaprakasam, A. Terry Conlisk Electroosmotic flow (EOF) is of importance in micro- and nanofluidic applications. Recent numerical results [Zheng \textit{et al.} (2003) \textit{Electrophoresis} \textbf{24}, 3006] suggest that the addition of even trace amounts of divalent counterions can greatly affect the velocity and electric potential distribution for EOF of a nominally monovalent electrolyte solution, nearly halving the flow rate in 20 nm channels. Scaled experiments were therefore carried out for steady and fully-developed EOF of buffered aqueous mono- and divalent electrolyte mixtures through fused silica microchannels. Nano-particle image velocimetry (nPIV), based upon evanescent-wave illumination of colloidal tracers, was used to obtain velocity data within about 300 nm of the wall. In all cases, the thickness of the electric double layer, defined as the distance from the wall where the velocity and electric potential recover to 99{\%} of their freestream values, is of $O$(10 nm), or much less than the channel dimension of $O$(10 $\mu $m). The nPIV results are compared with predictions from an asymptotic perturbation analysis. [Preview Abstract] |
Tuesday, November 22, 2005 12:45PM - 12:58PM |
NC.00009: Mathematical Modeling of Electroosmotic Flow in Micro/Nanonozzles Pradeep Gnanaprakasam, A.T. Conlisk, Xin Hu, L.J. Lee Electroosmotic flow in micro/nano nozzles is important in many applications for example in patch clamps for studying ion channel currents. Nanonozzles are also manufactured from micronozzles by a process in which a solution is pumped into a micro-nozzle electroosmotically to deposit a material from the solution on the inner walls of the channel, thus reducing the dimension of the channel to the nano-scale ranges. A mathematical model is developed for electroosmotic flow in a micro/nano nozzle. The flow through the nanonozzle is calculated first using the lubrication approximation and those results are compared with a full two dimensional steady simulation. The velocity field is composed of an electroosmotic component and a pressure driven component. The pressure gradient is set up by the electroosmotic driving force coupled with the converging/diverging channel profile. Results for the concentration distribution, velocity and potential distribution in the nanonozzle are presented. [Preview Abstract] |
Tuesday, November 22, 2005 12:58PM - 1:11PM |
NC.00010: Electroosmotic Flow in Rectangular Nanochannels with Variable Wall potential: Generation of Multiple Nano-Vortices Lei Chen, A.T. Conlisk Electroosmotic flow in nanochannels is characterized by a very small Reynolds number so that mixing is difficult. While several researchers have presented results for the case of periodic wall potential, and for a sudden change in potential there has been no systematic study of the effect of the variation of wall potential on the flow structure. We have calculated the flow and mass transport in a two-dimensional nanochannel having discontinuities in wall potential. Multiple nano-vortices are generated within the bulk flow due to the overpotential at the surface. The distributions of potential, velocity and mole fractions are calculated numerically and the structure of the flow within the ``nano-vortices'' resembles that of the classical Lamb vortex. The parameters that affect the circulation are investigated as well. The long electrode limit (the aspect ratio much less than one ) is investigated for small channels (EDLs are overlapped) and wide (thin EDL) channels as well. It is found that the flow is two-dimensional only near the corners of the electrode and is fully-developed elsewhere. The flow can be thus decomposed into one-dimensional electroosmotic flow and Poiseuille flow. For a wide channel, a singular perturbation analysis is performed for the electroosmotic component. The results are compared with recently generated experimental data. *This work is supported by the Air Force Office of Scientific Research through its Multi-University Research Initiative(MURI) program. [Preview Abstract] |
Tuesday, November 22, 2005 1:11PM - 1:24PM |
NC.00011: Unsteady Transport of Bio-molecular Species in Nanochannels Ankan Kumar, Prashanth Ramesh, Christa Baker, A.T. Conlisk Unsteady simulation of species transport in Electroosmotic Flow (EOF) has been carried out for a three component system in a nanochannel. The third species is present in very small concentration compared to the main buffer which essentially causes the bulk velocity. The flux of any species is caused by Fick's diffusion, electrophoresis and bulk convection. The mutual balance between these driving forces determines the direction of the movement of the species as well as its transit time. For EOF in a channel with negatively charged walls, a negatively charged species may move in a direction opposite to the direction of bulk fluid flow. A positive species is transported in the direction of fluid flow and there is a significant decrease in transit time as compared to an uncharged or negatively charged species. The diffusion coefficient of large biomolecules is significantly reduced inside nanochannels. The unsteady transport problem then has multiple diffusive time scales. Results for concentration and species flux are presented for both charged and uncharged species. [Preview Abstract] |
Tuesday, November 22, 2005 1:24PM - 1:37PM |
NC.00012: Molecular simulations of electro-osmotic flows in nano-channels: from molecules to continuum Moran Wang, Jin Liu, Shiyi Chen Most previous molecular dynamics simulations of electro-osmotic flows claimed that the continuum-based Poisson-Boltzmann theory is failed at nanoscale. Here we present our MD results of electroosmotic flows in nanochannels, and compare our results with predictions from continuum theory. Our results show that: 1) the MD results are strongly dependent on the bin size, in which the macroscopic characteristics are sampled. When the bin size is larger than one molecular diameter size, the MD results are comparable with the continuum theoretical solutions. 2) the MD results agree well with the Poisson-Boltzmann theory in the diffusion layer as long as the ion-density is not too high. Furthremore, our MD results are not dependent on the channel size as reported previously by others. [Preview Abstract] |
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