Non-parallel Plates Research Articles

Liquid drop runs upward between two nonparallel plates.

We have recently observed an interesting phenomenon: even under gravity, a microliter-scaled silicone oil drop was still able to run upward between two nonparallel plates that were approximately vertically placed. We also saw the same phenomenon in the case of isopropyl alcohol (IPA) drops. In this work, we developed simple models to interpret this phenomenon, followed by experimental validation. We demonstrated that, by changing the locations of drops or tilt and opening angles of plates, the moving directions of silicone oil, IPA, and water drops could be controlled. In the cases of silicone oil and IPA, we also found that the speed of a drop had a linear relation with the square of the drop location when the drop was far away from the corner of two nonparallel plates and that the drop moved faster as it became closer to this corner.

Bioinspired plate-based fog collectors.

In a recent work, we explored the feeding mechanism of a shorebird to transport liquid drops by repeatedly opening and closing its beak. In this work, we apply the corresponding results to develop a new artificial fog collector. The collector includes two nonparallel plates. It has three advantages in comparison with existing artificial collectors: (i) easy fabrication, (ii) simple design to scale up, and (iii) active transport of condensed water drops. Two collectors have been built. A small one with dimensions of 4.2 × 2.1 × 0.05 cm(3) (length × width × thickness) was first built and tested to examine (i) the time evolution of condensed drop sizes and (ii) the collection processes and efficiencies on the glass, SiO2, and SU-8 plates. Under similar experimental conditions, the amount of water collected per unit area on the small collector is about 9.0, 4.7, and 3.7 times, respectively, as much as the ones reported for beetles, grasses, and metal wires, and the total amount of water collected is around 33, 18, and 15 times. On the basis of the understanding gained from the tests on the small collector, a large collector with dimensions of 26 × 10 × 0.2 cm(3) was further built and tested, which was capable of collecting 15.8 mL of water during a period of 36 min. The amount of water collected, when it is scaled from 36 to 120 min, is about 878, 479, or 405 times more than what was collected by individual beetles, grasses, or metal wires.

Separation of oil from a water/oil mixed drop using two nonparallel plates.

In this work, we have developed a simple approach to separate oil from a microliter-scaled water/oil mixture by squeezing the mixture using two nonparallel plates. Three pairs of plates with Teflon, SU-8, and SiO2 coatings, respectively, are used in the tests, and all of these plates are capable of separating the water/oil mixed drops. 95.5% silicone oil and 97.0% light mineral oil have been collected from their corresponding mixtures with water through the pair of Teflon plates. Furthermore, on the basis of pressure difference inside a liquid drop, theoretical models have been developed to interpret the corresponding mechanisms of the separation process, as well as the observed phenomena. To judge whether two immiscible liquids could be separated using the developed approach, a sufficient condition has also been derived, which includes three theoretical relations. The sufficient condition is subsequently validated by experiments. This condition also provides criteria for choosing a good plate coating. Such a coating should ensure (i) the oil wets the plate surface with a relatively large contact angle, and has small contact angle hysteresis, and (ii) the advancing contact angle that the water/oil interface forms on the plate surface is larger than 90°.

Behavior of a liquid drop between two nonparallel plates.

Liquid drops have shown interesting behaviors between two nonparallel plates. These plates may be fixed or movable relative to each other. In this work, we also explore these behaviors through a combination of theoretical and experimental investigations and obtain some new results. We show that when the two plates are fixed, different from the previous understanding, a lyophilic drop may not necessarily fill the corner of the two plates. We also demonstrate that it may fill the corner, when more liquid is added to the drop or when the top plate is lifted. Furthermore, we propose a physical model to interpret the shifting effect of a liquid drop. This effect appears when the drop is squeezed and relaxed between two nonparallel plates, and it has been used by some shorebirds to transport prey. On the basis of the proposed model, we have found three new phenomena related to the shifting effect.

Magmatic and solid state structures of the Abu Ziran pluton: Deciphering transition from thrusting to extension in the Eastern Desert of Egypt

The 606Ma old Abu Ziran granite of the Eastern Desert of Egypt intruded the southern margin of the Meatiq dome in a sinistral shear extensional setting. Its emplacement was enabled by a system of NW-trending sinistral shears, related Riedel shears and N–S extensional shear zones and faults. Magmatic flow was east-directed and controlled by Riedel shears that progressively rotated to an orientation favourable for extension. Strain markers that document magmatic flow show eastward decreasing strain together with strain increase from pluton centre to margins. This is explained by Newtonian flow between non-parallel plates and differences in flow velocities across the pluton. Solid state fabrics including shear fabrics, orientation of late magmatic dykes and quartz tension gashes, together with quartz C-axes distributions, document southward extensional shear within the solidified pluton and adjacent host rocks. Extensional shear is correlated with exhumation of the Meatiq dome coeval and soon after pluton solidification (585Ma). Pressure temperature evolutionary paths, derived from fluid inclusions, show a clockwise path with exhumation by isothermal decompression in the Meatiq dome. By contrast, the overlying volcanosedimentary nappes experienced an anti-clockwise path released by temperature rise due to pluton emplacement followed by isobaric cooling. Quartz fabrics indicate high-temperature coaxial N–S flow in the northern Meatiq dome and lower-temperature, non-coaxial southward flow within the overlaying superficial nappe. This is explained by the exhumation process itself that progressively localised into simple shear domains when rocks approached higher crustal levels. Late extension at ca. 580Ma was pure shear dominated and resulted in reversal of shear, now dextral, in the western Meatiq shear zone.

Drop transport between two non-parallel plates via AC electrowetting-driven oscillation

We propose a simple transport method of drops inside a pair of non-parallel electrode plates with a small wedge angle by using AC electrowetting. We observe different drop transport behaviors depending on the frequency. At low frequency (10Hz), a drop bounded by the plates moves quickly toward the narrower gap by the repeated wetting and de-wetting process. At high frequency (10kHz), however, drops initially move slowly in the same direction with a small-amplitude of oscillation and then quickly penetrate the space at the narrower gap. Even if the drop does not touch the top plate, an electrostatic force can deform the drop to make a bridge, resulting in a similar drop motion. We also demonstrate the similar transport behavior of drops between a pair of parylene-coated plates with a smaller contact angle and a higher contact angle hysteresis than the Teflon and parylene-coated surface. We assert that the proposed method can control the transport of drops by using a simple geometric configuration and a simple electrical signal control.

Retraction Note: Effects of boundary slippage on thin-film lubrication between two nonparallel plane plates

Hydrodynamic lubrications between two plane plates with an intersection angle θ have been investigated using the boundary slippage theory, and relations are obtained between dimensionless pressures and coordinate x, between bearing capacity, friction force, friction coefficient and dimensionless slipping size factor. The results show that bearing capacity of two plane plates without boundary slippage significantly increases with increasing intersection angle θ when 0 1°. The results also show that negative pressure occurs in fluid entrance region and bearing capacity decreases, and friction force and friction coefficient increase with the increase of dimensionless slipping size factor.

RETRACTED ARTICLE: Effects of boundary slippage on thin-film lubrication between two nonparallel plane plates

Hydrodynamic lubrications between two plane plates with an intersection angle θ have been investigated using the boundary slippage theory, and relations are obtained between dimensionless pressures and coordinate x, between bearing capacity, friction force, friction coefficient and dimensionless slipping size factor. The results show that bearing capacity of two plane plates without boundary slippage significantly increases with increasing intersection angle θ when 0 1°. The results also show that negative pressure occurs in fluid entrance region and bearing capacity decreases, and friction force and friction coefficient increase with the increase of dimensionless slipping size factor.

Are Casimir Forces Conservative?

The belief among investigators of the Casimir effect is that it is conservative and that the two interpretations as to the source of energy behind the Casimir effect are equivalent. In the first, the energy source is considered to be the zeropoint fields in the vacuum of space between the plates. In the second, the source is considered to come from the potential energy of atoms in the bulk matter making up the plates. The bulk matter interpretation will be trivially conservative because the plates comprise a closed system. The vacuum energy interpretation is not as clear. If the zero-point fields between the plates are static, the system will be closed and the forces will be conservative. However the fields may be a dynamic steady state in which case the system could be open and the forces not conservative. This paper examines a plausible but speculative extension of the vacuum centric proximity force approximation that incorporates the local geometry of non-parallel plates. This inclusion eliminates problems of local scale nonsensical distances between plates as well as some absurd results but introduces non-conservative forces. While only an experiment or more fundamental analytic approach can determine whether Casimir forces are conservative, the purpose of this paper is to merely raise the question.

Squeeze flow of a power-law fluid between non-parallel plates

Abstract Squeeze flow in the gap between non-parallel circular plates of radius R is discussed. The test material is assumed to be a power-law fluid, with a no-slip boundary condition at the plates. If the mean separation between the plates is h, and the angle of inclination between the plates is ϕ ≪ h/ R, the force on the plates is perturbed only at O( ϕ 2) and is increased by less than 10% if ϕ < 0.35 h/ R. A torque O( ϕ) tends to return the plates to a parallel configuration.

Narrow-Flow-Channel-Driven EHD Gas Pump for an Advanced Thermal Management of Microelectronics

In order to study the feasibility of applying electrohydrodynamic (EHD) gas pumps for advanced thermal management of microelectronics, an experimental investigation was conducted to drive gas flow through a narrow flow channel by an EHD gas pump. The net gas flow induced by corona discharge was generated by a push-fan (PF)-type EHD gas pump with and without a partially covered corona wire and nonparallel ground plate electrodes to transfer gas through millimeter-order circular channels. Therefore, it is important to know the effect of a narrow channel on the characteristics of the EHD gas pump with the corona wire electrode covered. The results show that the effects of narrow circular flow channels significantly influence the flow characteristics of the PF-type EHD gas pump and that the use of an insulator on the corona wire electrode can significantly enhance the current flux density and the pump performance under dc positive applied voltage.

Particle image velocimetry measurements of wire-nonparallel plates type electrohydrodynamic gas pump

2D particle image velocimetry (PIV) measurements were performed in a wire nonparallel plates type electrohydrodynamic (EHD) gas pump. Using simultaneously two CCD cameras allowed obtaining high resolution vector maps which illustrate the flow patterns generated inside the EHD gas pump.

A novel capacitive micro-accelerometer with grid strip capacitances and sensing gap alterable capacitances

The comb capacitances fabricated by deep reactive ion etching (RIE) process have high aspect ratio which is usually smaller than 30: 1 for the complicated process factors, and the combs are usually not parallel due to the well-known micro-loading effect and other process factors, which restricts the increase of the seismic mass by increasing the thickness of comb to reduce the thermal mechanical noise and the decrease of the gap of the comb capacitances for increasing the sensitive capacitance to reduce the electrical noise. Aiming at the disadvantage of the deep RIE, a novel capacitive micro-accelerometer with grid strip capacitances and sensing gap alterable capacitances is developed. One part of sensing of inertial signal of the micro-accelerometer is by the grid strip capacitances whose overlapping area is variable and which do not have the non-parallel plate's effect caused by the deep RIE process. Another part is by the sensing gap alterable capacitances whose gap between combs can be reduced by the actuators. The designed initial gap of the alterable comb capacitances is relatively large to depress the effect of the maximum aspect ratio (30 : 1) of deep RIE process. The initial gap of the capacitance of the actuator is smaller than the one of the comb capacitances. The difference between the two gaps is the initial gap of the sensitive capacitor. The designed structure depresses greatly the requirement of deep RIE process. The effects of non-parallel combs on the accelerometer are also analyzed. The characteristics of the micro-accelerometer are discussed by field emission microscopy (FEM) tool ANSYS. The tested devices based on slide-film damping effect are fabricated, and the tested quality factor is 514, which shows that grid strip capacitance design can partly improve the resolution and also prove the feasibility of the designed silicon-glass anodically bonding process.

Revised electrostatic model of the LISA Pathfinder inertial sensor

A comprehensive electrostatic finite-element (FE) analysis of the LISA Pathfinder Inertial Sensor (IS) has been carried out at Astrium GmbH. Starting with a detailed geometrical model of the IS housing and test mass (TM) flight units, FE results were derived from multiple analyses runs applying the Maxwell 3D field simulation software. The electrostatic forces and torques on the TM in 6DoF, as well as all non-negligible capacitances between the TM, the 18 electrodes, and the housing, have been extracted for different TM translations and rotations. The results of the FE analyses were expected to confirm the existing IS electrostatic model predictions used for performance analysis, simulations, and on-board algorithms. Major discrepancies were found, however, between the results and the model used so far. In general, FE results give considerably larger capacitance values than the equivalent infinite non-parallel plate estimates. In contrast, the FE derived forces and torques are in general significantly lower compared to the analytic IS electrostatic model predictions. In this paper, these results are discussed in detail and the reasons for the deviations are elaborated. Based on these results, an adapted analytic IS electrostatic model is proposed that reflects the electrostatic forces, torques, and stiffness values in the LISA Pathfinder IS significantly more accurate.

Mechanism of electrohydrodynamically induced flow in a wire-non-parallel plate electrode type gas pump

An experimental investigation and one-dimensional modeling have been conducted to study the mechanism of net flow direction induced by electrohydrodynamic (EHD) forces in a wire-non-parallel plate electrode type EHD gas pump. The experiments were conducted with various different locations of corona wire electrode for negative and positive applied voltage from 0 to 14 kV at atmospheric pressure and room temperature, where air was used as the working fluid. A one-dimensional cross-sectional averaged model based on mass and momentum conservation as well as Poisson electric field and ion transport equations was also developed. The results show that the net flow direction of electrohydrodynamically induced gas flow in a wire-non-parallel plate electrode system significantly depends on the location of the corona wire electrode relative to the grounded electrode position. The effect of conversion angle of non-parallel plate electrode on the net flow direction and pressure drop also was investigated and discussed in detail.

THE CASIMIR EFFECT BETWEEN NON-PARALLEL PLATES BY GEOMETRIC OPTICS

The first two authors have developed a technique which uses the complex geometry of the space of oriented affine lines in ℝ3 to describe the reflection of rays off a surface. This can be viewed as a parametric approach to geometric optics which has many possible applications. Recently, Jaffe and Scardicchio have developed a geometric optics approximation to the Casimir effect and the main purpose of this paper is to show that the quantities involved can be easily computed by this complex formalism. To illustrate this, we determine explicitly and in closed form the geometric optics approximation of the Casimir force between two non-parallel plates. By making one of the plates finite, we regularize the divergence that is caused by the intersection of the planes. In the parallel plate limit, we prove that our expression reduces to Casimir's original result.

Effects of non-parallel combs on reliable operation conditions of capacitive inertial sensor for step and shock signals

The combs of the comb capacitive inertial sensors fabricated by a deep reactive ion etching are usually not parallel. This non-ideal feature is greater in high aspect ratio structure and significantly affects the capacitance and electrostatic force. In this paper, the effects of non-parallel combs on the reliable operation range for step and pulse signals in three capacitive configurations are investigated when alternative electronic testing signals are applied on the sensors for detecting the variation of capacitance. Analytical expressions of the critical step acceleration and the critical time duration of pulse acceleration of the capacitive sensor whose comb electrodes have little angle of the decline are obtained. Results show that for a step inertial signal, even the angle of the decline is 0.5°, the reliable operation ranges of the sensor with single-sided structure, double-sided structure and double-sided structure with feedback voltage are diminished to 0.34, 0.44 and 0.54 of the ones whose comb electrodes are parallel, respectively, for pulse inertial signal, the reliable operation ranges with single-sided structure and double-sided structure are diminished to 0.45 and 0.56, respectively, and the ones of double-sided capacitive sensor with feedback voltage are diminished to 0.95 as the angle is changed from 0.1° to 0.15°, which show that the effects of the non-parallel can not also been ignored. Results also show that the reliable dynamic operation ranges of the sensor with double-sided comb capacitive structure are least affected by the effects of non-parallel plates and its merit is more evident as the angle of the decline of the comb electrodes increases. Compared to the effects of non-parallel comb electrodes on the reliable operation range for step inertial signal, the effects for pulse inertial signal are smaller.

Equilibrium conditions and symmetries for foams in contact with solid surfaces

The patterns formed by liquid foams in contact with solid surfaces resemble 2D foams. We derive the equilibrium equations for such 2D foams when the solid surface is curved and smooth, generalising the standard case for flat Hele–Shaw cells. The equilibrium conditions at the vertices in 2D are invariant under conformal transformations. We establish the transformation rules for films under conformal maps. Even if conformal invariance does not hold in general, by considering foams confined between two closely spaced non-parallel plates, we show that an exponential profile gives a pattern that resembles the image of a regular hexagonal foam under a complex logarithm map, to lowest order.

Two-dimensional evaluation of an ion plasma produced by pulsed lasers extracted by non-parallel collectors

Two-dimensional hydrodynamics of ion extraction from quasi-neutral plasmas has been calculated numerically for non-parallel ion extractors, and the results compared with those for the parallel case. The ions were assumed to be initially uniform with a very steep density profile at the boundaries, and held between two non-parallel metal plates as cathode and anode with fixed potentials. Experimentally, tunable pulsed lasers through stepwise photo-excitation and photo-ionization or multi-photo-ionization processes can produce such plasma. Poisson's equation was solved simultaneously with the equations of mass and momentum, assuming the Maxwell–Boltzmann distribution for electrons. Ordinary Cartesian co-ordinates are not suitable for the rotated extractor geometry; therefore using the `algebraic method' a transformation from the physical domain into the computational rectangular plane is applied for analysing the irregular boundaries. Such a technique provides adequate resolution for the boundary layer. Using a first-order explicit upwind differencing in an appropriate transformed Cartesian co-ordinate system, the hydrodynamics of the plasma ions between the two non-parallel electrodes was evaluated. In these calculations electric potential, ion density between the two electrodes, and the extraction time were assessed, considering three separate regions for the plasma, i.e. the ion sheath where (ni≫ne≈0), the transition region (pre-sheath) (ni = ne), and the quasi-neutral plasma (ni−ne≪ni). The results were compared with those for parallel electrodes. A significant discrepancy was found between the two results. From the calculation, the non-uniform asymmetric potential contour, and the ion density contour across the plasma, were obtained for the non-parallel electrodes. For comparison with the parallel extractors, we have also obtained almost the same extraction time for the non-parallel extractors.

Porous structure of waste fly ashes and their chemical modifications

Changes in the porous structure of fly ashes ZS-13 subjected to chemical treatment with solutions of NaOH, NaOH/NH 4HCO 3, EDTA, and HCl are examined. The initial material with 3 m 2/g surface area and 0.01 cm 3/g pore volume after modification revealed an increased surface area and pore volume. The greatest increase in the surface area equal to 105 m 2/g was noted for the sample treated with HCl, while the greatest increase in pore volume equal to 0.18 cm 3/g was obtained for the sample treated with EDTA. In the modified products, meso- and macropores prevail, although in the sample treated with HCl, the presence of a small contribution of micropores was detected. All the modifications, except that treated with HCl, were found to contain slit-shaped macropores. In the sample treated with HCl, the pores were in the shape of nonparallel plates. A study by scanning electron microscopy (SEM) allowed a detailed determination of the shape of the isles and agglomerates. Chemical treatment of the initial fly ashes resulted in a transformation of the ball-shaped agglomerations into different products characterised by specific size and shape of particles.