A new method for particle manipulation by combination of dielectrophoresis and field-modulated electroosmotic vortex

A field-modulated electroosmotic flow (FMEOF) in a microchannel can be obtained by applying modulating electric fields in a direction perpendicular to the channel wall. Micro-vortexes are generated around the electrodes along with an EOF due to the surface charge on the modulated wall. When polarizable particles are suspended near the electrodes, they experience dielectrophoretic forces due to a non-uniform electric field. In this paper, micro-vortexes and dielectrophoretic forces are combined to achieve separation and trap different sized particles in a continuous flow. Numerical results indicate that by adjusting the driving electric field parallel to the channel wall and the modulating electric field, the ratio of dielectrophoretic and hydrodynamic forces can be altered. One type of particles can be trapped by micro-vortexes (negative dielectrophoresis (DEP)), and the other particles are transported to the downstream so that the particles are separated. The influence of the electrode length and the channel height on the trapping rate is investigated.     

Viscoelasticity of a dielectric fluid in nonuniform electric fields generated by electrodes with flocked fabrics

The rheological behavior of a dielectric fluid is studied in nonuniform electric fields which are generated by an electrode covered with flocked fabrics. Although no electrorheological (ER) effects are observed in uniform fields between metal electrodes with smooth surfaces, striking increases in viscosity and elastic response are induced by the electrode with flocked fabrics. The presence of flocked fabrics does not have a significant effect on the fluid rheology without electric fields. The ER behavior and current density are influenced by the fiber length even at a constant field strength. When a very small amount of fine particles is introduced in the electrified fluid without shear, we can see the rapid and large-scale motion of particles between the tips of fibers and plate electrode. In high DC fields, the Coulomb force acting on a free charge often gives rise to the secondary motion of fluid. The local motion of fluid in high electric fields is refereed to as electrohydrodynamic (EHD) convection. The additional energy may be required to change the periodic patterns of EHD convection by forced shear. Therefore, the ER effect demonstrated by the modification of electrode with flocked fabrics can be attributed to a combined effect of EHD convection and external shear. Received: 10 March 1998 Accepted: 1 June 1998     

Manipulation of particles using dielectrophoresis

A numerical scheme based on the distributed Lagrange multiplier method (DLM) is used to study the motion of particles of electrorheological suspensions subjected to non-uniform electric fields. At small Reynolds number, the time taken by the particles to collect at the minimums or maximums of the electric field is primarily determined by a parameter defined to be the ratio of the dielectrophoretic and viscous forces. Simulations show that in non-uniform electric fields the collection time is also influenced by a parameter defined by the ratio of the electrostatic particle–particle interaction and dielectrophoretic forces. The collection time decreases as this parameter decreases because when this parameter is less than one, particles move to the regions of high or low electric field regions individually. However, when this parameter is greater than one, particles regroup into chains which then move toward the electric field maximums or minimums without breaking. It is also shown that when the real part of the Clausius–Mosotti factor (β) is negative the positions of the local minimums of the electric field, and thus also the locations where particles collect, can be modified by changing the electric potential boundary conditions.     

八电极静电陀螺支承系统的建模

八电极静电支承系统沿着四个非正交轴对转子施加静电力,这些作用力相互影响,因此需要对支承坐标进行垂直解耦。针对采用八电极方案的静电陀螺,给出了电极电容的计算公式和位移解算方法,推导了静电力计算公式,最后建立了八电极静电陀螺支承系统的模型并利用Simulink对系统进行仿真。仿真结果表明,在系统中加入解算矩阵和"3-4"变换矩阵后,可以使X、Y、Z三个轴向上对转子位移的控制相互独立,为转子的可靠支承奠定了基础。     

Boundary layer viscosity of CNT-doped liquid crystals: effects of phase behavior

Carbon nanotube (CNT)-doped liquid crystals (LCs) have attracted intensive research studies as prospective materials in optic display devices, microfluidic sensors, and lubricants due to their unique molecular structures and properties. In this paper, the interaction between the doped CNTs and the hosting 4-cyano-4 $^{\prime }$ -pentylbiphenyl (5CB) molecules (in both nematic and isotropic phases) was investigated and we focused on the boundary layer rheological properties of the CNT-doped 5CB under external electric field. The experiments were performed by using a quartz crystal microbalance (for boundary layer viscosity investigation) and a rheometer (for bulk viscosity measurement). The results indicate that the bulk viscosity of the CNT-doped 5CB presents an obvious electroviscous effect in its nematic phase while no electroviscous effect in its isotropic phase. Additionally, we found that the boundary layer viscosity of the CNT-doped 5CB demonstrated significant electroviscous effects both in its nematic phase and isotropic phase. The enhanced electroviscous effects on the boundary layer viscosity of CNT-doped 5CB can be attributed to the highly ordered structures of LC molecules and CNTs on the substrate under external electric field. The unique properties of the boundary layer rheology of CNT-doped 5CB LC were further discussed in view of the ordering of LC molecules induced by the electric field, the polarity of CNTs, and the aligning interaction between CNTs and LC molecules.     

Forces acting on water droplets falling in oil under the influence of an electric field: numerical predictions versus experimental observations

The combination of an electric field and a moderate turbulent flow is a promising technique for separating stable water–oil emulsions. Field-induced charges on the water droplets will cause adjacent droplets to align with the field and attract each other. The present work describes the forces that influence the kinematics of droplets falling in oil when exposed to an electric field. Mathematical models for these forces are presented and discussed with respect to a possible implementation in a multi-droplet Lagrangian framework. The droplet motion is mainly due to buoyancy, drag, film-drainage, and dipole–dipole forces. Attention is paid to internal circulations, non-ideal dipoles, and the effects of surface tension gradients.Experiments are performed to observe the behavior of a droplet falling onto a stationary one. The droplet is exposed to an electric field parallel to the direction of the droplet motion. The behavior of two falling water droplets exposed to an electric field perpendicular to the direction of their motion is also investigated until droplet coalescence. The droplet motion is recorded with a high-speed CMOS camera. The optical observations are compared with the results from numerical simulations where the governing equations for the droplet motion are solved by the RK45 (Runge Kutta) Fehlberg method with step-size control and low tolerances. Results, using different models, are compared and discussed in detail. A framework is otlined to describe the kinematics of both a falling rigid spherical particle and a fluid droplet under the influence of an electric field.     

Non-local effects on the non-linear modes of vibration of carbon nanotubes under electrostatic actuation

Carbon nanotubes (CNTs) based NEMS with electrostatic sensing/actuation may be employed as sensors, in situations where it is fundamental to understand their dynamic behaviour. Due to displacements that are large in comparison with the thickness and to the non-linearity of the electrostatic force, these CNT based NEMS operate in the non-linear regime. The knowledge of the modes of vibration of a CNT provides a picture of what one may expect from its dynamic behaviour not only in free, but also in forced vibrations. In this paper, the non-linear modes of vibration of CNTs actuated by electrostatic forces are investigated. For that purpose, a p-version finite element type formulation is implemented, leading to ordinary differential equations of motion in the time domain. The formulation takes into account non-local effects, which influence the inertia and the stiffness of CNTs, as well as the electrostatic actuation. The ordinary differential equations of motion are transformed into algebraic equations of motion via the harmonic balance method (HBM) and then solved by an arc-length continuation method. Several harmonics are considered in the HBM. The importance of non-local effects, combined with the geometrical non-linearity and with the action of the electrostatic force, is analysed. It is found that different combinations of these effects can result in alterations of the natural frequencies, variations in the degrees of softening or hardening, changes in the frequency content of the free vibrations, and alterations in the mode shapes of vibration. It is furthermore found that the small scale, here represented by the non-local theory, has an effect on interactions between the first and higher order modes which are induced by the geometrical and material non-linearities of the system.     

温度场作用下输流悬臂碳纳米管的颤振失稳分析

以非局部弹性理论为基础,采用欧拉-伯努利梁模型,考虑碳纳米管的小尺度效应,应用哈密顿原理获得了温度场作用下的输流悬臂单层碳纳米管（SWCNT）的振动控制方程以及边界条件,依靠微分变换法（DTM法）对此高阶偏微分方程进行求解,通过数值计算研究了温度场中悬臂单层输流碳纳米管的振动与颤振失稳问题。结果表明：管内流体流速、温度场中温度变化情况与小尺度参数都会对系统振动频率以及颤振失稳临界流速产生影响。其中,小尺度效应将会降低悬臂输流系统的稳定性,使系统更为柔软;而高温场与低温场对系统动态失稳的影响不同,低温场中随温度变化值的增加,系统的稳定性提高;高温场这一作用效果恰好与之相反。     

Bifurcation mechanism of interfacial electrohydrodynamic gravity-capillary waves near the minimum phase speed under a horizontal electric field

We investigate the evolution of interfacial gravity-capillary waves propagating along the interface between two dielectric fluids under the action of a horizontal electric field. There is a uniform background flow in each layer, and the relative motion tends to induce Kelvin–Helmholtz(KH) instability. The combined effects of gravity, surface tension and electrically induced forces are all taken into account. Under the short-wave assumption, the expansion and truncation method of Dirichlet-Neumann(DN) operators is applied to derive a reduced dynamical model. When KH instability is suppressed linearly by a considerably large electric field, our numerical results reveal that in certain regions of parameter space, nonlinear symmetric traveling wave solutions can be found near the minimum phase speed. Additionally, the detailed bifurcation structures are presented together with typical wave profiles.     

Experimental analysis of particle and fluid motion in ac electrokinetics

An ac electric field is applied to induce particle and fluid motion in a wedge-shaped microchannel. Micron-resolution particle image velocimetry (-PIV) is used to determine spatially resolved particle velocity and fluid velocity fields. Under steady-state conditions, the particles experience a balance between dielectrophoretic forces induced by the nonuniform electric field and Stokes drag forces due to viscous interactions with the fluid. The particle velocity is therefore different from the fluid velocity because of dielectrophoresis. A variant of -PIV, two-color -PIV, is developed and used to uniquely determine the fluid velocity from the observation of particles without a priori knowledge of the electrical properties. This technique is used to explore ac electrokinetically generated fluid motion. A series of voltage levels at fixed frequency are applied to the wedge-shaped electrodes. The dependency of fluid velocity on applied voltage at different regions in the flow is obtained by fitting power-law curves. This is used to determine the underlying physical phenomena associated with ac electrokinetics. We found that both electrothermal effects and ac electroosmosis are important for the current experimental conditions. However, the electrothermal effect is dominant in the bulk fluid.     

Rotation of an elastic sphere about its mass center in the gravitational field of two attracting points

A planet model as a uniform elastic sphere in the gravitational field of two mass points whose mutual motion causes tidal deformations is considered. The sphere rotation about its mass center is studied with consideration of its deformations caused by the centrifugal force field and the gradient fields of gravitational forces. The sphere’s inertia tensor whose components are time dependent is found. The sphere’s angular velocity projections onto the axes associated with the sphere according to an integral law are determined. The results obtained are illustrated for the case of the Earth. For this case, the equivalent values of the elasticity modulus and Poisson’s ratio and the angular velocity disturbances are found.     

A theory of plasticity for carbon nanotube reinforced composites

Carbon nanotubes (CNTs) possess exceptional mechanical properties, and when introduced into a metal matrix, it could significantly improve the elastic stiffness and plastic strength of the nanocomposite. But current processing techniques often lead to an agglomerated state for the CNTs, and the pristine CNT surface may not be able to fully transfer the load at the interface. These two conditions could have a significant impact on its strengthening capability. In this article we develop a two-scale micromechanical model to analyze the effect of CNT agglomeration and interface condition on the plastic strength of CNT/metal composites. The large scale involves the CNT-free matrix and the clustered CNT/matrix inclusions, and the small scale addresses the property of these clustered inclusions, each containing the randomly oriented, transversely isotropic CNTs and the matrix. In this development the concept of secant moduli and a field fluctuation technique have been adopted. The outcome is an explicit set of formulae that allows one to calculate the overall stress-strain relations of the CNT nanocomposite. It is shown that CNTs are indeed a very effective strengthening agent, but CNT agglomeration and imperfect interface condition can seriously reduce the effective stiffness and elastoplastic strength. The developed theory has also been applied to examine the size (diameter) effect of CNTs on the elastic and elastoplastic response of the composites, and it was found that, with a perfect interface contact, decreasing the CNT radius would enhance the overall stiffness and plastic strength, but with an imperfect interface the size effect is reversed. A comparison of the theory with some experiments on the CNT/Cu nanocomposite serves to verify the applicability of the theory, and it also points to the urgent need of eliminating all CNT agglomeration and improving the interface condition if the full potential of CNT reinforcement is to be realized.     

Natural Frequency and Stability Tuning of Cantilevered CNTs Conveying Fluid in Magnetic Field

This paper investigates the dynamics of cantilevered CNTs conveying fluid in longitudinal magnetic field and presents the possibility of controlling/tuning the stability of the CNT system with the aid of magnetic field. The slender CNT is treated as an Euler-Bernoulli beam. Based on nonlocal elasticity theory, the equation of motion with consideration of magnetic field effect is developed. This partial differential equation is then discretized using the differential quadrature method(DQM). Numerical results show that the nonlocal small-scale parameter makes the fluid-conveying CNT more flexible and can shift the unstable mode in which flutter instability occurs first at sufficiently high flow velocity from one to another. More importantly,the addition of a longitudinal magnetic field leads to much richer dynamical behaviors of the CNT system. Indeed, the presence of longitudinal magnetic field can significantly affect the evolution of natural frequency of the dynamical system when the flow velocity is successively increased.With increasing magnetic field parameter, it is shown that the CNT system behaves stiffer and hence the critical flow velocity becomes higher. It is of particular interest that when the magnetic field parameter is equal to or larger than the flow velocity, the cantilevered CNT conveying fluid becomes unconditionally stable, indicating that the dynamic stability of the system can be controlled due to the presence of a longitudinal magnetic field.     

Frequency response of primary resonance of electrostatically actuated CNT cantilevers

This paper deals with electrostatically actuated carbon nanotube (CNT) cantilever over a parallel ground plate. Three forces act on the CNTs cantilever, namely electrostatic, van der Waals, and damping. The van der Waals force is significant for values of 50 nm or less of the gap between the CNT and the ground plate. As both forces electrostatic and van der Waals are nonlinear, and the CNTs electrostatic actuation is given by AC voltage, the CNT undergoes nonlinear parametric dynamics. The methods of multiple scales and reduced order model (ROM) are used to investigate the system under soft AC near half natural frequency of the CNT and weak nonlinearities. The frequency–amplitude response and damping, voltage, and van der Waals effects on the response are reported. It is showed that only five terms ROM predicts and accurately predicts the pull-in instability and the saddle-node bifurcation, respectively.     

Electric effects on the rheology of insulating oils in electrodes with flocked fabric

The rheological behavior of insulating oils is studied in nonuniform electric fields which are generated by an electrode covered with flocked fabric. Although the oils show no electrorheological effects in uniform fields between metal electrodes with smooth surfaces, the flocked fabric leads to a striking increase of viscosity in steady shear. The viscosity enhancement increases with decreasing zero-field viscosity and decreasing conductivity of oils. In the limit of zero shear rate, the oils with low conductivity behave as solids with yield stress. When a very small quantity of fine particles is introduced into electrified oils without shear, a rapid and large-scale motion of particles is observed between the tips of fibers and the plate electrode. The local motion of fluids in high electric fields is referred to as electrohydrodynamic (EHD) convection. Periodic patterns of circulation flow are formed in static oils. The electric energy which is dissipated during the circulation motion contributes to holding the periodic flow in static oils. When the stress is very low, the periodic patterns are not broken down. The yield stress corresponds to the force required to rupture the domain structures of EHD convection. In shear fields, the additional energy may be required to change the periodic patterns of EHD convection. The striking increase of viscosity in steady shear can be attributed to the interactions between EHD convection and external shear. Received: 31 August 1998 Accepted: 17 February 1999     

Rheological characterization of carbon nanotubes/poly(ethylene oxide) composites

Rheological properties of poly(ethylene oxide) nanocomposites embedded with carbon nanotubes (CNTs) were investigated in the present study. It was found that the CNT nanocomposites had a higher effective filler volume fraction than the real filler volume fraction, which yielded a drastic enhancement of shear viscosity. As the CNT loading in the nancomposites increases, non-Newtonian behavior was observed at the low-shear-rate region in the steady shear experiments. Oscillatory dynamic shear experiments showed that more addition of the CNTs led to stronger solidlike and nonterminal behaviors. To identify a dispersion state of the CNTs, field emission scanning electron spectroscopy and transmission electron microscopy were adopted and thermal analysis was also performed by using differential scanning calorimetry. The existence of percolated network structures of the CNTs even at a low CNT loading was verified by rheological properties and electrical conductivities.     

Two-fold enhancement in tensile strength of carbon nanotube–carbon fiber hybrid epoxy composites through combination of electrophoretic deposition and alternating electric field

A new carbon nanotube (CNT)–hybridized carbon fiber (CF) was introduced in an attempt to improve interfacial strength between CF and polymeric matrix. Amine-functionalized CNTs was radially deposited on the CF surface through a combination of alternating electric field with electrophoretic deposition process. Radial deposition of CNTs on CF formed a unique porous structure around CF that could significantly increase the interfacial adhesion through interlocking of polymeric matrix. Tensile properties and fatigue life of the reinforced composites were investigated in order to study the effect of interfacial adhesion on mechanical properties of reinforced composites. Results indicate that the radial deposition of CNT on CF can remarkably enhance the compatibility of polymeric matrix with CF. This improvement in compatibility of polymeric matrix with CNT–hybridized CF resulted in considerable enhancement in mechanical properties of composites. The interfacial reinforcing mechanism was explored through fractography of reinforced composites and possible failure modes have been precisely discussed.     

Particle velocimetry in high-gradient/high-curvature flows

Particle-velocimetry techniques typically rely on the assumption that particle velocities match fluid velocities. However, this assumption may be invalid if external forces or inertia cause the particle motion to differ from that of the flow. In this paper, particle motion through premixed stagnation flames is modeled, including Stokes-drag and thermophoretic forces. The finite time interval employed in particle-tracking techniques can act as a low-pass filter in flow regions with large curvature in the velocity field. To account for this effect, the modeled-particle-tracking profile for a specified time interval is estimated from the predicted particle position in time and compared to measurements. The implementation presented here is applicable to other simulated flow fields and allows direct comparisons with particle-velocimetry measurements. Expressions are also derived that allow particle-tracking data to be corrected for these effects.     

Concentration of electric field near electrodes on piezoelectric layer

This paper aims at the study of electric field concentration near the edge of the electrodes for a piezoelectric layer. For simplicity, attention is focussed on a piezoelectric layer that is bonded to a rigid, conductive substrate and then covered by a pair of conductive electrodes on the surface. The analysis is performed within the scope of linear piezoelectricity. Fourier transform technique is applied to reduce the boundary value problem to a pair of dual integral equations. An analytical solution to the integral equations is obtained by using an iteration method. Numerical results for distributions of stresses and electric fields are displayed and discussed.