Diffusioosmotic flow of electrolyte solutions in fibrous porous media at arbitrary zeta potential and double-layer thickness

The diffusioosmosis of electrolyte solutions in the fibrous medium constructed by a homogeneous assemblage of parallel, charged, circular cylinders caused by a uniform concentration gradient prescribed in their axial direction is studied theoretically. The electric double layers adjacent to the cylinders may have an arbitrary thickness. A unit cell model is used to account for the interaction effect among the cylinders. The electrostatic potential distribution in the fluid phase is determined with an analytical approximation to the solution of the Poisson–Boltzmann equation. By solving the fluid momentum equation with the constraint of no net electric current arising from the co-current diffusion, electric migration, and diffusioosmotic convection of the electrolyte ions, the macroscopic electric field and the fluid velocity in the axial direction induced by the applied electrolyte concentration gradient are obtained semi-analytically as functions of the radial position in a cell in a self-consistent manner. The magnitude and direction of the diffusioosmotic flow relative to the concentration gradient are determined by the combination of the porosity of the array of cylinders, the zeta potential of the cylinders, the properties of the electrolyte solution, and other relevant factors. The fluid velocity generally increases with increasing porosity of the array of cylinders, but there are exceptions. The effects of the radial distribution of the induced electric field and of the ionic convection in the double layers on the diffusioosmotic flow are significant.     

When MHD-based microfluidics is equivalent to pressure-driven flow

Magneto-hydrodynamics (MHD) provides a convenient, programmable means for propelling liquids and controlling fluid flow in microfluidic devices without a need for mechanical pumps and valves. When the magnetic field is uniform and the electric field in the electrolyte solution is confined to a plane that is perpendicular to the direction of the magnetic field, the Lorentz body force is irrotational and one can define a “Lorentz” potential. Since the MHD-induced flow field under these circumstances is identical to that of pressure-driven flow, one can utilize the large available body of knowledge about pressure-driven flows to predict MHD flows and infer MHD flow patterns. In this note, we prove the equivalence between MHD flows and pressure-driven flows under certain conditions other than flow in straight conduits with rectangular cross sections. We determine the velocity profile and the efficiency of MHD pumps, accounting for current transport in the electrolyte solutions. Then, we demonstrate how data available for pressure-driven flow can be utilized to study various MHD flows, in particular, in a conduit patterned with pillars such as may be useful for liquid chromatography and chemical reactors. In addition, we examine the effect of interior obstacles on the electric current flow in the conduit and show the existence of a particular pillar geometry that maximizes the current.     

Resonant Magnetic Field Sensor With Frequency Output

This paper presents a novel type of resonant magnetic field sensor exploiting the Lorentz force and providing a frequency output. The mechanical resonator, a cantilever structure, is embedded as the frequency-determining element in an electrical oscillator. By generating an electrical current proportional to the position of the cantilever, a Lorentz force acting like an additional equivalent spring is exerted on the cantilever in the presence of a magnetic field. Thus, the oscillation frequency of the system, which is a function of the resonator's equivalent spring constant, is modulated by the magnetic field to be measured. The resonant magnetic field sensor is fabricated using an industrial CMOS process, followed by a two-mask micromachining sequence to release the cantilever structure. The characterized devices show a sensitivity of 60 kHz/Tesla at their resonance frequency$f_0= 175~ kHz$and a short-term frequency stability of 0.025 Hz, which corresponds to a resolution below 1$~mu T$. The devices can thus be used for Earth magnetic field applications, such as an electronic compass. The novel resonant magnetic field sensor benefits from an efficient continuous offset cancellation technique, which consist in evaluating the frequency difference measured with and without excitation current as output signal. 1676     

Adhesion release and yield enhancement of microstructures usingpulsed Lorentz forces

Adhesion of microstructures is an important failure mechanism in surface-micromachined devices. In this paper, a simple and effective method for releasing pinned microstructures is presented. The method uses the Lorentz force due to the interaction of a current with an external magnetic field to generate an upward force that frees the microstructures. The static and transient behavior of beams under the Lorentz force is examined. Critical values of current and pulse durations needed to release the microstructures are determined and verified with experimental data. Using this technique, previously pinned beams and rectangular plates have been released. The release technique is suitable for mass production environments since it is easily applied during the electrical testing of the device, thereby increasing the manufacturing yield     

Principles of nonlinear MEMS-resonators regarding magnetic-field detection and the interaction with a capacitive read-out system

This paper presents a magnetic field sensor with capacitive read-out, whose active element is a micromachined mechanical resonator. The MEMS magnetic field sensor exploits the Lorentz force to detect external magnetic flux density through the displacement of the resonant structure, which can be measured with optical and capacitive sensing techniques. The micromachined U-shaped cantilever features a length of 2 mm, a base width of 90 μm and a thickness of 20 μm, and is manufactured in SOI technology. The designed sensor has a measured resonant frequency of 4.359 kHz for the fundamental mode and a calculated mass of the flexible structure of 24.5 ng. A quality factor in the order of 10⁴ at an ambient pressure of 0.3 Pa has been measured where a magnetic field resolution of 15 nT can be achieved. Although these arrangements are well suited to capacitively sense the vibrations caused by the Lorentz force on the current lead on the silicon part, care has to be taken to avoid undesired mutual interferences. A serious interference was observed in case of a DC bias voltage at the readout capacitance and a significant voltage drop caused by the current needed for the generation of the Lorentz force. This work investigates in detail this phenomenon as well as the complete physical transduction chain and improves the understanding of such microelectromechanical systems significantly. An analytical model of the electrostatic system is established including all relevant components and their interactions as well as the motion of the MEMS part. The importance of electrostatic back-action for a feasible detection limit for magnetic fields was recognized for the first time.     

Diffusioosmosis of electrolyte solutions in fibrous porous media

An analytical study is presented for the diffusioosmotic flow of an electrolyte solution in the fibrous medium constructed by an ordered array of parallel charged circular cylinders at the steady state. The prescribed electrolyte concentration gradient is constant but can be oriented arbitrarily with respect to the axes of the cylinders. The electric double layer surrounding each cylinder may have an arbitrary thickness relative to the radius of the cylinder. A unit cell model which allows for the overlap of the double layers of adjacent cylinders is employed to account for the effect of fibers on each other. The electrostatic potential distribution in the fluid phase of a cell is obtained by solving the linearized Poisson–Boltzmann equation, which applies to the case of low surface potential of the cylinders. The macroscopic electric field induced by the imposed electrolyte concentration gradient through the fluid phase in a cell is determined as a function of the radial position. A closed-form formula for the fluid velocity profile of the electrolyte solution due to the combination of electroosmotic and chemiosmotic contributions as a function of the porosity of the array of cylinders correct to the second order of their surface charge density or zeta potential is derived as the solution of a modified Navier–Stokes equation. The diffusioosmotic velocity can have more than one reversal in direction over a small range of the zeta potential. For a given electrolyte concentration gradient in a cell, the fluid flow rate does not necessarily increase with an increase in the electrokinetic radius of the cylinder, which is the cylinder radius divided by the Debye screening length. The effect of the radial distribution of the induced axial electric field in the double layer on the diffusioosmotic flow is found to be of dominant significance in most practical situations.     

MHD flow in a rectangular duct with a perturbed boundary

The unsteady magnetohydrodynamic (MHD) flow of a viscous, incompressible and electrically conducting fluid in a rectangular duct with a perturbed boundary, is investigated. A small boundary perturbation $\epsilon$ is applied on the upper wall of the duct which is encountered in the visualization of the blood flow in constricted arteries. The MHD equations which are coupled in the velocity and the induced magnetic field are solved with no-slip velocity conditions and by taking the side walls as insulated and the Hartmann walls as perfectly conducting. Both the domain boundary element method (DBEM) and the dual reciprocity boundary element method (DRBEM) are used in spatial discretization with a backward finite difference scheme for the time integration. These MHD equations are decoupled first into two transient convection–diffusion equations, and then into two modified Helmholtz equations by using suitable transformations. Then, the DBEM or DRBEM is used to transform these equations into equivalent integral equations by employing the fundamental solution of either steady-state convection–diffusion or modified Helmholtz equations. The DBEM and DRBEM results are presented and compared by equi-velocity and current lines at steady-state for several values of Hartmann number and the boundary perturbation parameter.     

Thermal and flow analysis of a magneto-hydrodynamic micropump

A study of transient fully developed laminar flow and temperature distribution in a magnetohydrodynamic (MHD) micropump is presented. The micropump is driven using the Lorentz force which is induced as a result of interaction between an applied electric field and a perpendicular magnetic field. The governing equations are solved analytically by an eigenfunction expansion method, and numerically by a finite-difference (ADI) method. The numerical and analytical results are found to be in good agreement with each other. The effect of different parameters on the transient velocity and temperature, such as aspect ratio, Hartman number, Prandtl number, and Eckert number is studied. The results obtained showed that controlling the flow and the temperature can be achieved by controlling the potential difference, the magnetic flux, and by a good choice of the electrical conductivity.     

Transport control in fusion plasmas by changing electric and magnetic field spatial profiles

For magnetically confined plasmas in tokamaks, we have numerically investigated how Lagrangian chaos at the plasma edge affects the plasma confinement. Initially, we have considered the chaotic motion of particles in an equilibrium electric field with a monotonic radial profile perturbed by drift waves. We have showed that an effective transport barrier may be created at the plasma edge by modifying the electric field radial profile. In the second place, we have obtained escape patterns and magnetic footprints of chaotic magnetic field lines in the region near a tokamak wall with resonant modes due to the action of an ergodic magnetic limiter. For monotonic plasma current density profiles we have obtained distributions of field line connections to the wall and line escape channels with the same spatial pattern as the magnetic footprints on the tokamak walls.     

Solution of magnetohydrodynamic flow in a rectangular duct by differential quadrature method

The polynomial based differential quadrature and the Fourier expansion based differential quadrature method are applied to solve magnetohydrodynamic (MHD) flow equations in a rectangular duct in the presence of a transverse external oblique magnetic field. Numerical solution for velocity and induced magnetic field is obtained for the steady-state, fully developed, incompressible flow of a conducting fluid inside of the duct. Equal and unequal grid point discretizations are both used in the domain and it is found that the polynomial based differential quadrature method with a reasonable number of unequally spaced grid points gives accurate numerical solution of the MHD flow problem. Some graphs are presented showing the behaviours of the velocity and the induced magnetic field for several values of Hartmann number, number of grid points and the direction of the applied magnetic field.     

Thermal and flow analysis of two-dimensional fully developed flow in an AC magneto-hydrodynamic micropump

The effect of fluctuating Lorentz force on the Ac magnetohydrodynamic micropump is studied. A two-dimensional transient fully developed laminar flow and temperature distribution are modeled. The governing Navier–Stokes and energy equations are solved numerically by a finite-difference (ADI) method. The effect of different parameters on the transient and steady flow velocity and temperature, such as aspect ratio, Hartman number, Prandtl number, and Eckert number is studied. The results obtained showed that controlling the flow and the temperature can be achieved by controlling the potential difference, the magnetic flux, and by a good choice of the electrical conductivity. The effect of Stanton number and phase angle is also included, and it is found that at high frequency, the pulsed volume is small which yield a continuous flow instead of pulsating flow, and the magnitude and direction of the flow can be controlled by the phase shift between the electrical and magnetic fields.     

A Novel Coilless Scanning Mirror Using Eddy Current Lorentz Force and Magnetostatic Force

This paper reports on novel coilless microscanning mirrors driven by the magnetostatic force that resulted from a magnetic interaction as well as the Lorentz force that is induced by an eddy current. This eliminates complicated coil routing and insulation layer deposition and simplifies fabrication allowing easy integration with micromachining and complementary metal-oxide-semiconductor processes. Bulk micromachined one-axis and two-axis scanning mirrors are demonstrated, displaying 1-D and 2-D scanning patterns. Two-dimensional scanning patterns are easily tuned by varying the combination of driving frequencies. The results show that the diamagnetic (Cu) mirror is mainly driven by the eddy-current-induced Lorentz force, whereas the ferromagnetic (Ni) mirror is mainly driven by the magnetostatic force.     

Flow-induced forces on two circular cylinders in proximity

Flow-induced forces on two nearby circular cylinders of equal diameter immersed in the cross flow at Re = 100 were numerically studied. We consider all possible arrangements of the two circular cylinders in terms of the distance between the two cylinders and the inclination angle of the line connecting the cylinder centers with respect to the direction of the main flow. It turns out that significant changes in the characteristics of flow-induced forces are noticed depending on how the two circular cylinders are positioned, resulting in quantitative changes of force coefficients on both cylinders. Collecting all the numerical results obtained, we propose contour diagrams for mean force coefficients and rms values of force coefficient fluctuations for each of the two cylinders. The perfect geometrical symmetry implied in the flow configuration allows one to use those diagrams to estimate flow-induced forces on two circular cylinders of equal diameter arbitrarily positioned in physical space with respect to the main flow direction.     

Electromagnetic and Thermomechanical Effect Produced by an Electronic Beam on a Solid Barrier

The developed mathematical model simulates the thermomechanical effects which accompany electron scattering in a barrier. The generation of a space charge and an electromagnetic field is taken into account. For the ionized substance of the barrier and an electromagnetic field, Euler equations with the Lorentz force and Joule heating and Maxwell equations with a convective current are considered. Equations are constructed for the density of the Lorentz force acting on the ionized substance and for its Joule heating in the electromagnetic field. Conservative difference analogs of the quantities responsible for the interaction of the electromagnetic field with the ionized substance are developed.     

梯度向量流的各向异性扩散分析

为了解决梯度向量流力场(gradient vector flow,简称GVF)难以进入目标凹部的问题,提出了一种新的主动轮廓模型外力场——各向异性梯度向量流.GVF的扩散项是各向同性且光滑性强的拉普拉斯算子,它在各个方向的扩散速度相同.拉普拉斯算子根据图像的局部结构可分为沿边界法线和切线方向的扩散,沿切线方向的扩散具有增强边界的作用,而法线方向扩散具有去除噪音、扩散力场的作用.基于分析二者在扩散过程中的作用,提出了一种各向异性梯度向量流扩散方法,切线和法线方向的扩散速度可以根据图像的局部结构自适应地选择.实验结果表明,与GVF相比,所提出的方法考虑了扩散过程中法线和切线方向的不同作用,能够进入细长的凹部,并改进了分割结果.     

Dynamic motion analysis of magnetic particles in microfluidic systems under an external gradient magnetic field

To gain an insightful understanding of motion behavior of paramagnetic particles suspended in a nonmagnetic fluid under a gradient magnetic field, a coupled fluid–structure model based on a direct numerical scheme is developed in this work. The governing equations of magnetic field, fluid flow field and particle motion are simultaneously solved using an Arbitrary Lagrangian–Eulerian method, taking into account magnetic and hydrodynamic interactions between particles in a fully coupled manner. The accuracy of the proposed method is validated using the magnetic particulate flows of two particles under a uniform magnetic field as the test problem and is then applied to investigate effects of magnetic and hydrodynamic interactions between particles on the particle motion behavior. Results show that neighboring magnetic particles are easy to form chain-like clusters along field direction due to magnetic interactions between particles and then move together toward the surface of magnetic source under the action of gradient magnetic force. More importantly, it has been found that both magnetic and hydrodynamic interactions between particles are conducive to the acceleration of particles and the chain formation of particles. The present method and results could help in understanding the basic mechanism underlying the low-gradient magnetophoretic separation process and designing magnetic aggregate-based microfluidic devices.     

Inplane vibration analysis of polar orthotropic annular plates with linearly varying thickness

The natural frequencies of inplane vibrations of polar orthotropic annular plates with linearly varying thickness have been analysed. A semi-analytical method of analysis has been used where the radial and tangential displacements are expanded in the circumferential direction as Fourier series and the radial behaviour is solved using the finite element method. For the sake of comparison, results have been obtained starting with two different kinds of displacement functions. The frequencies have been studied with respect to various boundary conditions. aspect ratios, thickness ratios, ratios of moduli, and two fibre directions.     

Magnetohydrodynamic state estimation with boundary sensors

We present a PDE observer that estimates the velocity, pressure, electric potential and current fields in a magnetohydrodynamic (MHD) channel flow, also known as Hartmann flow. This flow is characterized by an electrically conducting fluid moving between parallel plates in the presence of an externally imposed transverse magnetic field. The system is described by the inductionless MHD equations, a combination of the Navier-Stokes equations and a Poisson equation for the electric potential under the so-called inductionless MHD approximation in a low magnetic Reynolds number regime. We identify physical quantities (measurable on the wall of the channel) that are sufficient to generate convergent estimates of the velocity, pressure, and electric potential field away from the walls. Our observer consists of a copy of the linearized MHD equations, combined with linear injection of output estimation error, with observer gains designed using backstepping. Pressure, skin friction and current measurements from one of the walls are used for output injection. For zero magnetic field or nonconducting fluid, the design reduces to an observer for the Navier-Stokes Poiseuille flow, a benchmark for flow control and turbulence estimation. We show that for the linearized MHD model the estimation error converges to zero in the L² norm. Despite being a subject of practical interest, the problem of observer design for nondiscretized 3-D MHD or Navier-Stokes channel flow has so far been an open problem.     

不同错开位置锯齿翅片热力特性的三维仿真

对通道壁面沿流动方向周期性地错开而在横向上通道壁面有几组不同错开位置的强化换热翅片的层流流动和传热情况进行了三维仿真分析。这类翅片经常被应用在汽车和电子设备的冷却系统中。三维有限元方法用来模拟Re数在100-1500范围时翅片的速度场和温度场，考虑了通道壁面的不同错开位置(SSP)对翅片传热性能的影响。仿真结果与以前的试验数据也进行了比较研究。     

Analytical model of microfluidic transport of non-magnetic particles in ferrofluids under the influence of a permanent magnet

This study describes an analytical model and experimental verifications of transport of non-magnetic spherical microparticles in ferrofluids in a microfluidic system that consists of a microchannel and a permanent magnet. The permanent magnet produces a spatially non-uniform magnetic field that gives rise to a magnetic buoyancy force on particles within ferrofluid-filled microchannel. We obtained trajectories of particles in the microchannel by (1) calculating magnetic buoyancy force through the use of an analytical expression of magnetic field distributions and a nonlinear magnetization model of ferrofluids, (2) deriving governing equations of motion for particles through the use of analytical expressions of dominant magnetic buoyancy and hydrodynamic viscous drag forces, (3) solving equations of motion for particles in laminar flow conditions. We studied effects of particle size and flow rate in the microchannel on the trajectories of particles. The analysis indicated that particles were increasingly deflected in the direction that was perpendicular to the flow when size of particles increased, or when flow rate in the microchannel decreased. We also studied ??wall effect?? on the trajectories of particles in the microchannel when surfaces of particles were in contact with channel wall. Experimentally obtained trajectories of particles were used to confirm the validity of our analytical results. We believe this study forms the theoretical foundation for size-based particle (both synthetic and biological) separation in ferrofluids in a microfluidic device. The simplicity and versatility of our analytical model make it useful for quick optimizations of future separation devices as the model takes into account important design parameters including particle size, property of ferrofluids, magnetic field distribution, dimension of microchannel, and fluid flow rate.