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 KC: Microfluidics: Numerical Studies |
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Chair: Nicolas Hadjiconstantinou, Massachusetts Institute of Technology Room: Hilton Chicago Grand Ballroom |
Monday, November 21, 2005 4:10PM - 4:23PM |
KC.00001: Simulation of $\lambda$-phage DNA in microchannels using a coarse-grained MD method Vasileios Symeonidis, George Karniadakis, Bruce Caswell In this work we present Dissipative Particle Dynamics (\textsc{dpd}) simulations of polymers subject to the Marko-Siggia wormlike chain (\textsc{wlc}) spring law. We demonstrate the advantages of Lowe's \textsc{dpd} method, which simulates high Schmidt numbers for the solvent, and contrast it with the velocity-Verlet scheme. Shear flow results for the wormlike chain (\textsc{wlc}) simulating single \textsc{dna} molecules compare well with average extensions from experiments, irrespective of the number of beads. However, coarse-graining with more than a few beads degrades the agreement of the autocorrelation of the extension. [Preview Abstract] |
Monday, November 21, 2005 4:23PM - 4:36PM |
KC.00002: Ion Separation using a Y-Junction Carbon Nanotube Jae Hyun Park, Susan Sinnott, Narayana Aluru Using molecular dynamics simulations, we show that a Y-junction carbon nanotube can be used to separate potassium and chloride ions from a KCl solution. The system consists of a KCl solution chamber connected to an (8,8) carbon nanotube, which acts as the stem. Two carbon nanotube branches of sizes (5,5) and (6,6) are connected to the (8,8) nanotube forming the Y-junction. Uncharged (5,5) and (6,6) carbon nanotubes show close to zero occupancy for transport of potassium and chloride ions. By functionalizing a (5,5) carbon nanotube with a negative charge, we show that we can selectively transport potassium ions. Similarly, by functionalizing a (6,6) carbon nanotube with a positive charge, we can selectively transport chloride ions. By performing molecular dynamics simulations on the entire system comprising the two branches, stem and the KCl solution chamber, we show that perfect ion separation is observed when (5,5) and (6,6) nanotubes are charged with $\sigma_{w,(5,5)}=-0.181$ C/m$^2$ and $\sigma_{w,(6,6)}=+0.143$ C/m$^2$, respectively, whereas for the system with $\sigma_{w,(5,5)}=-0.168$ C/m$^2$ and $\sigma_{w,(6,6)}=+0.131$ C/m$^2$ the separation is not perfect because of the formation of ion pairs. We discuss the formation and control of ion pairing, which is a common phenomenon in confined nanochannels. [Preview Abstract] |
Monday, November 21, 2005 4:36PM - 4:49PM |
KC.00003: Efficient solutions of the nonlinear Boltzmann equation for low-speed applications Lowell Baker, Nicolas Hadjiconstantinou We show that efficient Monte Carlo solution methods for the nonlinear Boltzmann equation for low-speed applications can be constructed by expressing the single-particle distribution function as the sum of an equilibrium distribution and a deviational term. By considering the deviation from equilibrium when evaluating the collision integral, one can avoid simulating a large number of physically occuring collisions with no net effect and thus achieve a high degree of variance reduction. As the degree of deviation from equilibrium decreases, the degree of variance reduction increases, leading to a velocity signal to noise ratio that remains approximately constant and thus a computational cost which is essentially independent of the Mach number ($\textrm{Ma}$). These features are in sharp contrast to current particle-based simulation techniques (e.g. DSMC) in which statistical sampling leads to computational cost that is proportional to $\textrm{Ma}^{-2}$, making calculations at small Mach numbers very expensive. The present formulation can be incorporated into both direct numerical methods as well as particle-based methods. These approaches are validated by comparing results with analytical and direct simulation Monte Carlo (DSMC) solutions of the Boltzmann equation. [Preview Abstract] |
Monday, November 21, 2005 4:49PM - 5:02PM |
KC.00004: High-speed microfluidic differential manometer for cellular-scale hydrodynamics Magalie Faivre, Manouk Abkarian, Howard Stone We propose a broadly applicable high-speed microfluidic approach for measuring dynamical pressure drop variations along a micron size channel and illustrate the technique by presenting the first measurements of the additional pressure drop produced at the scale of individual flowing cells. The influence of drug-modified mechanical properties of the cell membrane is shown. Finally, single hemolysis events during flow are recorded simultaneously with the critical pressure drop for the rupture of the membrane. This scale-independent measurement approach can be applied to any dynamical process or event that changes the hydrodynamic resistance of micro- or nanochannels. [Preview Abstract] |
Monday, November 21, 2005 5:02PM - 5:15PM |
KC.00005: A hybrid continuum-atomistic simulation of heat transfer in micro flow Jin Liu, Shiyi Chen, Xiaobo Nie, Mark Robbins The heat transfer problem in a micro/nano flow is studied based on domain decomposition hybrid method. This method uses an atomistic description in one part of the domain and a continuum description in other place. Two solutions are matched in a coupling region which is necessary to ensure their consistency including the temperature and heat flux. In the coupling region, the statistical results from the atomistic simulation provides the boundary conditions for continuum energy equation, and the particle velocities are rescaled to account for the energy transfer from continuum domain to to particle domain. Simulation results for steady and unsteady heat transfer in a channel flow will be shown. The effect of rough wall on the heat transfer will also be discussed. [Preview Abstract] |
Monday, November 21, 2005 5:15PM - 5:28PM |
KC.00006: Molecular Dynamics Investigation of Ionic Flow and Separation by Carbon Nanotube Electrodes Soumik Banerjee, Sohail Murad, Ishwar Puri We report on molecular simulation studies of the ionic flow in the presence of charged carbon nanotubes. Our domain contains three species; viz. positively charged sodium ions, negatively charged chlorine ions and neutral water; and a pair of single-walled carbon nanotube electrodes. One of the nanotube is positively charged and the other is negatively charged. The system of 1024 atoms is initially allowed to equilibrate from an FCC crystal structure for the solution. The nanotubes are tethered and the carbon atoms are assumed to vibrate as in a One-Dimensional Harmonic Oscillator (ODHO) about their mean positions. The sodium ions travel towards the negatively charged carbon nanotube and the chlorine ions likewise flow towards the positively charged nanotube. The simulation uses a Lennard-Jones soft sphere potential model and coulombic potential for interaction between the charges. In addition to the ion transport mechanism, the hydrophobic character of carbon nanotubes is clearly evident from the simulated flow. [Preview Abstract] |
Monday, November 21, 2005 5:28PM - 5:41PM |
KC.00007: Temperature gradient driven transport of water inside a carbon nanotube Junichiro Shiomi, Shigeo Maruyama With growing need for micro-nanoscale manipulators and transporters, liquid systems confined in small geometries are of a great interest. An extreme case would be single walled carbon nanotubes (SWNTs), where the liquid motion is confined in quasi-one-dimensional geometry. In this work, by means of molecular dynamics simulations, we consider the transport of a water cluster which consists of a few hundred molecules in an SWNT with a diameter of about 1.4 nm. Especially, the influence of the non-equilibrium thermal boundary condition on the water cluster is investigated by imposing a longitudinal temperature gradient to the SWNT. Water molecules are modeled with the SPC/E model whereas the carbon-carbon and carbon-water interactions are expressed using the Brenner potential and a simple Lennard-Jones potential, respectively. It is demonstrated that the water cluster is transported with the temperature gradient at an average velocity that is proportional to the temperature gradient. The trend exhibits good correlation with the temperature dependence of the overall potential energy between water and carbon molecules. Together with the comparative case of a water cluster adsorbed on the outer-wall of an SWNT, the molecular dynamics of the transport phenomenon will be discussed. [Preview Abstract] |
Monday, November 21, 2005 5:41PM - 5:54PM |
KC.00008: Numerical Solutions and Structures of Double Quantum Jet Solving by an Upwind Scheme San-Yih Lin, Huei-Huang Chiu, Chin-Tien Lin The solutions of a double quantum jet are analyzed by solving the quantum fluid dynamical formulation (QFD) of the Schr\"{o}dinger equation. The QFD equations are obtained by expressing the Schr\"{o}dinger wave function as $\varphi =\rho ^{1/2}\exp (iS/\hbar )$and $\vec {u}=(u,v)$. In QFD, $Q=-\rho ^{-1/2}\Delta \rho ^{1/2}$ is called as quantum potential. An upwind method is developed to solve the QFD equations. The method use a third-order upwind method to discrete convection terms and the central finite difference method to discrete the quantum potential. A fourth-order Runge-Kutta method is used for time marching. Two cases, one-dimensional free particle with external potential and two-dimensional free particle with external potential, are presented to illustrate the accuracy of the QFD solver. The computational results are compared well with the results obtained by solving the Schr\"{o}dinger equation. Finally, the QFD solver is applied to solve the solutions of a double quantum jet and to investigate its structures. First, a mathematical formulation is derived to describe the double quantum jet. The jet has the probability density equals 2 and the velocity equals 2 at the inlet of the jet. Then, the solutions are computed by the QFD solver. The structures of the solutions are affected by the strength of the quantum potential. The interesting phenomena of quantum clustering are found. [Preview Abstract] |
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