Browsing by Subject "spectral element method"
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Item Numerical simulation of electrokinetically driven micro flows(Texas A&M University, 2005-11-01) Hahm, JungyoonSpectral element based numerical solvers are developed to simulate electrokinetically driven flows for micro-fluidic applications. Based on these numerical solvers, basic phenomena and devices for electrokinetic applications in micro and nano flows are systematically studied. As a first application, flow and species transport control in a grooved micro-channel using local electrokinetic forces are studied. Locally applied electric fields, zeta potential patterned grooved surfaces, and geometry are manipulated to control mixed electroosmotic/pressure driven flow in the grooved micro-channel. The controlled flow pattern enables entrapment and release of prescribed amounts of scalar species in the grooves. As another application, hydrodynamic/ electrokinetic focusing in a micro-channel is studied. External electric field, flow rate of pressure driven flow, and geometry in the micro-channel are manipulated to obtain the focusing point, which led to determination of the electrophoretic mobility and (relative) concentration of dilute mixtures. This technique can be used to identify and detect species in dilute mixtures.Item Theoretical and numerical studies of chaotic mixing(Texas A&M University, 2008-10-10) Kim, Ho JunTheoretical and numerical studies of chaotic mixing are performed to circumvent the difficulties of efficient mixing, which come from the lack of turbulence in microfluidic devices. In order to carry out efficient and accurate parametric studies and to identify a fully chaotic state, a spectral element algorithm for solution of the incompressible Navier-Stokes and species transport equations is developed. Using Taylor series expansions in time marching, the new algorithm employs an algebraic factorization scheme on multi-dimensional staggered spectral element grids, and extends classical conforming Galerkin formulations to nonconforming spectral elements. Lagrangian particle tracking methods are utilized to study particle dispersion in the mixing device using spectral element and fourth order Runge-Kutta discretizations in space and time, respectively. Comparative studies of five different techniques commonly employed to identify the chaotic strength and mixing efficiency in microfluidic systems are presented to demonstrate the competitive advantages and shortcomings of each method. These are the stirring index based on the box counting method, Poincare sections, finite time Lyapunov exponents, the probability density function of the stretching field, and mixing index inverse, based on the standard deviation of scalar species distribution. Series of numerical simulations are performed by varying the Peclet number (Pe) at fixed kinematic conditions. The mixing length (lm) is characterized as function of the Pe number, and lm ? ln(Pe) scaling is demonstrated for fully chaotic cases. Employing the aforementioned techniques, optimum kinematic conditions and the actuation frequency of the stirrer that result in the highest mixing/stirring efficiency are identified in a zeta potential patterned straight micro channel, where a continuous flow is generated by superposition of a steady pressure driven flow and time periodic electroosmotic flow induced by a stream-wise AC electric field. Finally, it is shown that the invariant manifold of hyperbolic periodic point determines the geometry of fast mixing zones in oscillatory flows in two-dimensional cavity.