## Bau, Haim H.

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Publication Suppression of Rayleigh-Benard Convection with Proportional-Derivative Controller(2007-01-01) Remillieux, Marcel C; Zhao, Hui; Bau, Haim HWe study theoretically (linear stability) and experimentally the use of proportional and derivative controllers to postpone the transition from the no-motion state to the convective state in a circular cylinder heated from below and cooled from above. The heating is provided with an array of individually controlled actuators whose power is adjusted in proportion to temperatures measured in the cylinder's interior. As the proportional controller's gain increases, so does the critical Rayleigh number for the onset of convection. Relatively large proportional controller gains lead to oscillatory convection. The oscillatory convection can be suppressed with the application of a derivative controller, allowing further increases in the critical Rayleigh number. The experimental observations are compared with theoretical predictions.Publication Rendering a Subcritical Hopf Bifurcation Supercritical(1996-01-18) Yuen, Po Ki; Bau, Haim H.It is demonstrated experimentally and theoretically that through the use of a nonlinear feedback controller, one can render a subcritical Hopf bifurcation supercritical and thus dramatically modify the nature of the flow in a thermal convection loop heated from below and cooled from above. In particular, we show that the controller can replace the naturally occurring chaotic motion with a stable, periodic limit cycle. The control strategy consists of sensing the deviation of fluid temperatures from desired values at a number of locations inside the loop and then altering the wall heating to counteract such deviations.Publication Induction and measurement of minute flow rates through nanopipes(2007-01-01) Sinha, Shashank; Rossi, Maria Pia; Mattia, D.; Gogotsi, Yury; Bau, Haim HA simple technique to simultaneously induce fluid flow through an individual nanopipe and measure the flow rate and the pressure difference across the pipe is described. Two liquid drops of different sizes are positioned at the two ends of the nanopipe. Due to the higher capillary pressure of the smaller drop, flow is driven from the smaller drop to the bigger drop. The instantaneous pressures of the two drops are estimated from the drops' shapes and sizes. The flow rate is estimated by monitoring the sizes of the drops as functions of time with a microscope and a video camera. A theory that correlates the drops' sizes and the flow rate is derived. Measurements are carried out with an ionic salt and glycerin to estimate the effective tube radius of the nanopipes with diameters ranging from 200 to 300 nm. The tubes' diameters are independently measured with a scanning electron microscope. The method is also verified by tracking the motion of fluorescent particles through the nanopipe. The paper provides a simple technique for studying extremely low flow rates in nanofluidic systems. When working with low-evaporation fluids such as ionic salts, the measurements can be carried out with an electron microscope.Publication Feedback Control Stabilization of the No-Motion State of a Fluid Confined in a Horizontal Porous Layer Heated From Below(1993-06-24) Tang, Jie; Bau, Haim H.We consider a horizontal three-dimensional saturated porous layer, confined in an upright cubic box, heated from below and cooled from above. In the absence of a controller, the fluid maintains a no-motion state for subcritical Rayleigh numbers R < Rc, where Rc, depends on the boxâ€™s aspect ratio. Once this critical number is exceeded, fluid motion ensues. We demonstrate that, with the use of feedback control strategies which suppress flow instabilities, one can maintain a stable no-motion state for Rayleigh numbers far exceeding the classical critical one for the onset of convection. To preserve the equilibrium no-motion state of the classical problem, the controller alters the systemâ€™s dynamics so as to stabilize an otherwise non-stable state.Publication Gas Flow in Micr-Channels(1994-09-02) Harley, John C.; Bau, Haim H.; Huang, Yufend; Zemel, Jay N.An experimental and theoretical investigation of low Reynolds number, high subsonic Mach number, compressible gas flow in channels is presented. Nitrogen, helium, and argon gases were used. The channels were microfabricated on silicon wafers and were typically 100 Î¼m wide, 104 Î¼m long, and ranged in depth from 0.5 to 20 Î¼m. The Knudsen number ranged from 10-3 to 0.4. The measured friction factor was in good agreement with theoretical predictions assuming isothermal, locally fully developed, first-order, slip flow.Publication On the Stability and Flow Reversal of an Asymmetrically Heated Open Convection Loop(1981) Bau, Haim H.; Torrance, Kenneth E.Experimental results are reported for a U-shaped, free convection loop. The top of the loop is open to an isothermal reservoir. The horizontal leg and one vertical leg are heated at rates Q1 and Q2, respectively. The loop is filled either with water or a watersaturated porous medium. Symmetric heating and asymmetric heating favouring the ascending leg of the loop both yield stable flows. Asymmetric heating favouring the descending leg leads to stable flows when the ratio Q1/Q2 is above a critical value. Below this critical value, the flow is observed to oscillate with increasing amplitude until the direction of flow in the loop undergoes a reversal. A steady flow follows the reversal. Analytical results include a stability analysis and time-dependent, one-dimensional numerical calculations, both of which compare favourably with experiment.Publication Thick Film Thermistors Printed on Low Temperature Co-fired Ceramic Tapes(2001-10-01) Zhong, Jihua; Bau, Haim HFocuses on the importance of ceramic tapes as a substrate material for hybrid microelectronic circuits. Fabrication of thermal reactor; Importance in monitoring temperature; Utilization of layered manufacturing and rapid prototyping processes.Publication Complex magnetohydrodynamic low-Reynolds-number flows(2003-07-01) Xiang, Yu; Bau, Haim HThe interaction between electric currents and a magnetic field is used to produce body (Lorentz) forces in electrolyte solutions. By appropriate patterning of the electrodes, one can conveniently control the direction and magnitude of the electric currents and induce spatially and temporally complicated flow patterns. This capability is useful, not only for fundamental flow studies, but also for inducing fluid flow and stirring in minute devices in which the incorporation of moving components may be difficult. This paper focuses on a theoretical and experimental study of magnetohydrodynamic flows in a conduit with a rectangular cross section. The conduit is equipped with individually controlled electrodes uniformly spaced at a pitch L. The electrodes are aligned transversely to the conduit's axis. The entire device is subjected to a uniform magnetic field. The electrodes are divided into two groups A and C in such a way that there is an electrode of group C between any two electrodes of group A. We denote the various A and C electrodes with subscripts, i.e., Ai and Ci , where i = 0, Â±1, Â±2, ... . When positive and negative potentials are, respectively, applied to the even and odd numbered A electrodes, opposing electric currents are induced on the right and left hand sides of each A electrode. These currents generate transverse forces that drive cellular convection in the conduit. We refer to the resulting flow pattern as A. When electrodes of group C are activated, a similar flow pattern results, albeit shifted in space. We refer to this flow pattern as C. By alternating periodically between patterns A and C, one induces Lagrangian chaos. Such chaotic advection may be beneficial for stirring fluids, particularly in microfluidic devices. Since the flow patterns A and C are shifted in space, they also provide a mechanism for Lagrangian drift that allows net migration of passive tracers along the conduit's length.Publication Magneto hydrodynamic (MHD) pump fabricated with ceramic tapes(2002-01-31) Zhong, Jihua; Yi, Mingqiang; Bau, Haim HThe use of Magneto Hydro Dynamics (MHD) to circulate fluids in conduits fabricated with low temperature co-fired ceramic tapes is described. Conduits shaped like toroidal and rectangular loops were fabricated. Electrodes printed on the ceramic substrate along the conduits' walls facilitated transmission of electric currents through the test fluids. When the devices were subjected to a magnetic field, the resulting Lorentz forces propelled the liquids. The paper details the fabrication process and describes experiments with mercury slugs, saline solution, and deionized water. The measured fluid velocities were compared with theoretical predictions.Publication Flow Patterns and Reaction Rate Estimation of RedOx Electrolyte in the Presence of Natural Convection(2006-10-01) Qian, Shizhi; Chen, Zongyuan; Wang, Jing; Bau, Haim HTransport processes in an upright, concentric, annular, electrochemical reactor filled with RedOx electrolyte solution are studied experimentally and theoretically. The electrodes form the two vertical surfaces of the reactor. The theoretical calculations consist of the solution of the Navier-Stokes and the Nernst-Planck equations accounting for species' diffusion, migration, convection, and electrochemical reactions on the electrodes' surfaces as a function of the difference in the electrodes' potentials and the average concentration of the electrolyte. Since the convection is driven by density gradients, the momentum and mass transport equations are strongly coupled. In spite of the small dimensions (mm-scale) of the reactor, the current transmitted through the electrolyte is significantly enhanced by natural convection. The current is measured as a function of the difference in the electrodes' potentials. To obtain the reaction rate constants, an inverse problem is solved and the reaction rate constants are determined by minimizing the discrepancy between theoretical predictions and experimental observations. As an example, we study the reversible electrochemical reaction Fe++++e- = Fe++ on platinum electrodes. The paper demonstrates that natural convection plays a significant role even when the reactorâ€™s dimensions are on the millimeter scale and that it is possible to predict reaction rate constants while accounting for significant mass transfer effects.