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 FC: Microfluidics V: Numerical Studies-1 |
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Chair: Pushpendra Singh, New Jersey Institute of Technology Room: Tampa Marriott Waterside Hotel and Marina Grand Salon AB |
Monday, November 20, 2006 8:00AM - 8:13AM |
FC.00001: Direct Numerical Simulation (DNS) of Suspensions in Spatially Varying Electric Fields Nadine Aubry, Muhammad Janjua, Sai Nudurupati , Pushpendra Singh We have developed a numerical scheme to simulate the motion of dielectric particles suspended in a dielectric liquid in uniform and nonuniform electric fields. The particles are moved using a direct simulation scheme in which the fundamental equations of motion of fluid and solid particles are solved without the use of models. The motion of particles is tracked using a distributed Lagrange multiplier method. The electric force acting on a particle is calculated by integrating the Maxwell stress tensor over its surface. In our numerical scheme the Marchuk-Yanenko operator splitting technique is used to decouple the difficulties associated with the incompressibility constraint, the nonlinear convection term and the rigid body motion constraint. Simulations show that the accuracy of the point dipole approximation diminishes when the distance between the particles becomes smaller than the particles radius, the domain size is comparable to the particles size, and also as the dielectric mismatch between the fluid and particles increases. [Preview Abstract] |
Monday, November 20, 2006 8:13AM - 8:26AM |
FC.00002: Effect of frequency and electrode configuration on yeast cells subjected to traveling electric fields Sai Nudurupati , Pushpendra Singh, Nadine Aubry Biological particles, such as bacteria and viruses are the major cause for diseases and much of the current research has been devoted in identifying, and separating them. One way to trap these micro/nano sized particles is by conventional dielectrophoresis, which occurs due to varying electric fields. A much more efficient way is to combine this with the traveling wave dielectrophoresis force and torque, in which case the fluid is not required to be pumped into the channel. The particle electrodynamics is not only explained using these forces, but also with viscous drag associated with the fluid, and the electrostatic and hydrodynamic particle-particle interactions. The numerical scheme used for solving the equations of motion for the fluid and particles is based on Distributed Lagrange Multiplier (DLM) method. It is found that the motion of the yeast cells is determined primarily on the frequency dependent Clausius-Mossotti factor which is complex. Motion is also influenced by the specific configuration used, and hence two different MEMS devices, with electrodes at the bottom, are investigated. [Preview Abstract] |
Monday, November 20, 2006 8:26AM - 8:39AM |
FC.00003: Effect of Induced Charge Electroosmosis on the Dielectrophoretic Motion of Particles T. Swaminathan, Howard Hu Most suspensions involve the formation of ionic double layers next to the surface of particles due to the induced-charge on the surface. These double layers affect the motion of the particle even under AC electric fields. They modify the net dipole moment of the particle and at the same time produce slip velocities on the surfaces of these particles. A method to numerically evaluate the effect of the double layer on the dielectrophoretic motion of particles has been previously developed to study these two effects. The technique involves a matched asymptotic expansion of the electric field near the particle surface, where the double layer is formed, and is written as a jump-boundary-condition for the electric potential when the thickness of the double layer is small compared to the size of the particle. The developed jump-boundary-condition is then used to calculate an effective zeta potential on the particle surface. Unlike classical electroosmosis, this zeta potential is no longer constant on every part of the surface and is dependent on the applied electric field. The effect of the induced-charge electroosmotic slip velocity on the dielectrophoretic motion of particles has been observed using this technique. [Preview Abstract] |
Monday, November 20, 2006 8:39AM - 8:52AM |
FC.00004: ``Superfast'' and ``Hyperfast'' Electrophoresis in DC and AC Electric Fields Evgeny Demekhin, Alex Korovyakovsky Movement of a small conducting spherical granule in an electrolyte solution under force of DC and AC fields is considered. The problem is described by strongly coupled nonlinear PDE system. The fact that it has two small parameters, the ratio of the ion double layer to the diffusion layer and the ratio of the diffusion layer to the granule's diameter, makes the problem unique and extremely difficult to solve. This is the reason why only solutions for some particular cases have been known. In this work for the first time, combining asymptotic and numerical methods, a complete theory of electrophoresis in DC and AC fields is developed. By special decomposition method the system is transformed to new variables. Analytical solution in the inner region results in the nonlinear Smoluchowski slip velocity. In the intermediate region convection-diffusion equation is solved numerically. In tern, the intermediate solution is matched with the outer solution of Laplace equation to complete the statement. For a strong DC field (``superfast'' electrophoresis) the theory predicts, in agreement with experiments, the granule's velocity to be proportional to the granule's size and squared external field; there is a large elongated vortex behind the granule and a small one near its equator. There is an excellent agreement with available experimental data. Granule's velocity for AC field becomes even larger than for DC, it has a maximum with respect to the field's frequency (``hyperfast'' electrophoresis). [Preview Abstract] |
Monday, November 20, 2006 8:52AM - 9:05AM |
FC.00005: Direct numerical simulations of three-dimensional electrokinetic flows Keng-Hwee Chiam We discuss direct numerical simulations of three-dimensional electrokinetic flows in microfluidic devices. In particular, we focus on the study of the electrokinetic instability that develops when two solutions with different electrical conductivities are coupled to an external electric field. We characterize this ``mixing'' instability as a function of the parameters of the model, namely the Reynolds number of the flow, the electric Peclet number of the electrolyte solution, and the ratio of the electroosmotic to the electroviscous time scales. Finally, we describe how this model breaks down when the length scale of the device approaches the nanoscale, where the width of the electric Debye layer is comparable to the width of the channel, and discuss solutions to overcome this. [Preview Abstract] |
Monday, November 20, 2006 9:05AM - 9:18AM |
FC.00006: 3-D Numerical Simulation of Slug Flow in Micro-channel Chen Fang, Carlos Hidrovo, Fu-Min Wang, Julie Steinbrenner, Eon-soo Lee, John Eaton, Kenneth Goodson Water management that ensures the effective removal of produced water in the microchannel at cathode is critical for the performance of Micro PEM fuel cells. The small dimension and the confined space of the channel leads to the importance of the surface force in determining the dynamics of liquid slugs inside it. The present study focuses on the simulation of the slug detachment process in the micro-channel, using a contact angle hysteresis model within the framework of VOF approach. Based on solving the nonlinear equations accounting for the relationship among volume fraction, interface position, and contact angle, a special model is developed to replicate the hysteresis effect. In addition, a special algorithm is introduced to simulate the thin liquid/gas films. A systematic comparison between experiment and simulation has been conducted and the quantitative match in terms of slug dimensions is achieved for a wide range of flow conditions. The simulation reveals that the contact angle distribution along the slug profile could be approximated using piecewise linear function. The calculation also shows that the contact angle hysteresis might be responsible for several phenomena observed in experiment, including slug instability and pre -detachment liquid film. [Preview Abstract] |
Monday, November 20, 2006 9:18AM - 9:31AM |
FC.00007: Fully Coupled 1D Model for the Response of a Membrane in a Thin Air-Filled Cavity. Max Roman, Arnaud Goullet, Nadine Aubry A fully coupled 1D model based on a spring-mass system is derived for the response of a membrane subject to a time varying electrostatic charge in a thin air filled cavity. The elasticity of the membrane, the time dependent electric field, and the fluid flow are included in the model. The fluid film of air in the gap between the fixed electrode and deformable membrane is modeled using the linearized compressible Reynolds gas film equation, modified to account for the membrane deformation. From this, a fluid damping and spring coefficient are computed, which are used to calculate the fluid force on the membrane. A stiffness coefficient accounts for both linear and nonlinear membrane deformation. A capacitance-based generalized equation is used for the electrostatic field. Frequency and voltage are the only required inputs. It is found that there are distinct overdamped regimes consistent with spring-mass systems. The response computed from the model is compared to that obtained with a fully coupled 3D finite element solver. Excellent agreement is seen between the model and FEM results, with the model having a great advantage in the time necessary to obtain a solution for the response. The model is deemed a powerful tool in the design of microsystems with moving structures in which fluid damping plays a critical role in the structure's response. [Preview Abstract] |
Monday, November 20, 2006 9:31AM - 9:44AM |
FC.00008: Atomistic Simulation of the Stochastic Dynamics of Thin Liquid Films Adam Willis, John Freund For interface flows (e.g.\ unstable thin films or spreading drops), it has been proposed that at small enough scales classic hydrodynamic continuum equations should be augmented with stochastic terms that model the effect of, for example, thermal noise on the instantaneous geometry of liquid-vapor interface. Since the regions where such effects are thought to be important are challengingly small for experimental diagnostics and sensitive to potential contamination, atomistic simulation provides a clean means of evaluating and testing these theories. We use simulations with a Lennard-Jones potential to investigate the spreading rate of small liquid drops and find deviations potentially consistent with the stochastic model of Davidovitch et al. [Phy. Rev. Let, \textbf{95}:244505, 2005] Most Lennard-Jones simulations truncate the interaction potential at a finite radius. This has the effect of also cutting off the disjoining pressure, which is often modeled in continuum expressions as a $1/h^3$ term, $h$ being the film thickness. To properly investigate continuum equations which retain non-local interactions, we have designed a special un-truncated implementation of the Lennard-Jones potential that has an acceptable $O(N \log N)$ computation expense scale with number of atoms $N$. This will also be discussed in the context of these investigations. [Preview Abstract] |
Monday, November 20, 2006 9:44AM - 9:57AM |
FC.00009: Towards a Theory of Disjoining Pressure in Statics and Dynamics of Liquid Nanofilms Iskander Akhatov, Svyatoslav Chugunov, Artur Lutfurakhmanov, Sergey Gavrilyuk Van der Waals attractive forces drastically change the material properties of thin liquid layers several nanometers when in contact with a solid. At this scale, the fluid is no longer homogeneous. Moreover, it has properties which analogous to those of solids. In particular, in equilibrium the stress tensor is no longer spherical. We calculate the stress tensor components and discuss the concept of ``disjoining pressure'' for such fluids. We use a long-wave approximation to derive the evolution of a liquid nanofilm on a substrate. Finally, we derive the equation for nanofilm dynamics by using mass conservation formulation. As an example, some characteristic parameters for statics and dynamics of liquid argon film on a pure silicon substrate are calculated according to the proposed model. [Preview Abstract] |
Monday, November 20, 2006 9:57AM - 10:10AM |
FC.00010: Modeling Thermal Transport in Two-dimensional Nanocomposites Arvind Pattamatta, Cyrus Madnia The Boltzmann transport equation (BTE) for phonon intensity is numerically solved to study the thermal properties of nanocomposites. To establish the phonon particle model it is assumed that the phonon wave effect can be neglected and the frequency-dependent scattering rate in the bulk medium is approximated by the average phonon mean free path. Both Euler with first order Upwind and MacCormack with fourth order compact finite difference schemes are used to solve the BTE. The material considered in this study is composed of silicon (Si) nanowires embedded in the host semiconductor material of germanium (Ge). Due to the two-dimensionality of the nanocomposite the heat flow along the silicon wire is excluded, and therefore only the heat flow perpendicular to the wire is considered. In order to model the cell-cell interaction in the Si-Ge matrix, periodic boundary conditions are applied along the direction of heat flow. The interfaces between the host and nanowires are modeled as diffusely scattering. It is found that the thermal characteristics in the nanoscale composites are different from the macroscale composites. The resulting temperature profiles and effective thermal conductivity of the nanocomposites cannot be predicted accurately using the Fourier’s heat conduction model. The dependence of thermal conductivity on the nanocomposite size has also been studied. The results of this study can be used to improve the efficiency of thermoelectric energy conversion materials. [Preview Abstract] |
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