Edge Of Wedge Research Articles

Electric double-layer interactions in a wedge geometry: Change in contact angle for drops and bubbles

In this paper, we provide a theory to pinpoint the role of electric double layer (EDL) interactions in governing the contact angle of an electrolyte drop on a charged solid in air or a bubble on a charged surface within an electrolyte solution. The EDL interactions are analytically solved by representing the three phase contact line as a wedge edge, with the wedge being formed by the solid-liquid and the air-liquid interfaces, and calculating the corresponding Maxwell stresses. We demonstrate that the EDL effects induce an "electrowetting-like" behavior, resulting in a lowering of the contact angle. As a specific example, we use this model to analyze the effect of added salt on preformed surface nanobubbles, and find, in contrast to what has been reported earlier, that even for most moderate conditions, added salt may have remarkable effect in altering the contact angle in preformed surface nanobubbles.

Sicily’s fold–thrust belt and slab roll-back: the SI.RI.PRO. seismic crustal transect

Sicily is a thick orogenic wedge formed by (1) the foreland (African) and its Sicilian orogen and (2) the thick-skinned, Calabrian–Peloritani wedge. The crust under central Sicily, from the Tyrrhenian margin to the coastline of the Sicily Channel, has been investigated by the multidisciplinary (SI.RI.PRO.) research project. The project dealt with the nature and thickness of the crust and depth and geometry of the Moho, which is essential in formulating subduction models and improving the knowledge of African and Tyrrhenian–European lithospheres. The results resolve features such as (1) the main orogenic wedge, (2) the very steep, NW–SE-trending regional monocline suggesting inflection of the foreland crust, (3) the deep Caltanissetta synform imaged, for the first time, to about 25 km, and (4) the top of the crystalline basement and the inferred crust–mantle boundary. The SI.RI.PRO. transect confirmed that the NNW-dipping, autochthonous Iblean platform of SE Sicily and its basement extends all the way into central Sicily. Further NW, towards the NNW end of the transect, a large uplift involves the Iblean platform and its underlying basement. The associated gravity anomaly is interpreted as the southern wedge edge of the Tyrrhenian mantle that splits the subducting Iblean–Pelagian (African) continental slab from an overlying synformal stack of allochthonous thrust sheets. Supplementary materials: Additional data are available at www.geolsoc.org.uk/SUP18594 .

Stereo particle image velocimetry measurement of 3D soil deformation around laterally loaded pile in sand

A developed stereo particle image velocimetry (stereo-PIV) system was proposed to measure three-dimensional (3D) soil deformation around a laterally loaded pile in sand. The stereo-PIV technique extended 2D measurement to 3D based on a binocular vision model, where two cameras with a well geometrical setting were utilized to image the same object simultaneously. This system utilized two open software packages and some simple programs in MATLAB, which can easily be adjusted to meet user needs at a low cost. The failure planes form an angle with the horizontal line, which are measured at 27°–29°, approximately three-fourths of the frictional angle of soil. The edge of the strain wedge formed in front of the pile is an arc, which is slightly different from the straight line reported in the literature. The active and passive influence zones are about twice and six times of the diameter of the pile, respectively. The test demonstrates the good performance and feasibility of this stereo-PIV system for more advanced geotechnical testing.

Investigation of the laser action in a dye-doped cholesteric liquid crystal wedge cell

The wedge cell of cholesteric liquid crystal device is designed and fabricated, and doping PM580 (exciton) in the cholesteric liquid crystal, the laser emission action is studied. There appear a series of parallel wedge edges of dislocation lines and different shapes of domain in the wedge cell. The planar state of alignment is confirmed. A second harmonic Nd:YAG 532 nm laser is adopted as a pump light beam, and then one-dimensional tunable laser radiation is obtained and its wavelength interval is approximately 1 nm and tuning range is about 17 nm. In the processs of interaction between the torques of LC and the surface anchoring of direction film, the pitch elongation takes place. The positon of photonic band gap is changed, so the laser radiation wavelength can be tuned in the band edge.

Theoretical and experimental study of waves propagating along the edge of a wedge

The properties of a surface acoustic wave moving along the edge of an elastic wedge are studied. The equations defining the character of the wave motion under consideration are obtained. A method is proposed to determine field parameters that adequately describe the experimentally confirmed acoustic phenomena taking into account the characteristics of wave propagation in the wedge-shaped region. The results of the theoretical study are compared with experimental data obtained on an original device used to determine displacements in small surface areas.

Electromagnetic fields near plasmonic wedges

The behavior of electromagnetic fields near the edge of a plasmonic wedge is investigated. We study the scattering properties, field divergence, and field enhancement near an Au wedge bounded by SiO2 upon illumination by TM-polarized light using hypersingular integral equations, as a function of wavelength, wedge angle, and angle of incidence. The transverse scattered field components show a convergent behavior at wavelengths approaching the surface plasmon energy asymptote (on the corresponding flat Au-SiO2 interface), and become strongly divergent at longer wavelengths. The computed divergence is compared with Meixner's theory and is found to be in good agreement over a restricted range of parameters.

Improvement of the sensitivity of measurements in the formation of holographic interferograms of wedge plates

We consider the method for improving the sensitivity of measurements in the formation of aberration-free interference images of wedge plates, which do not require a priori knowledge of the position of the wedge edge. It is shown that the sensitivity in the measurement of the wedge angle in real time interferometry is doubled in the case of recording on the reference hologram of the wedge plate followed by its reconstruction by the object light wave that has passed through the wedge plate rotated through 180° relative to the normal. It turns out that recording of a pair of holograms of the wedge plate, one of which is the image of the wedge plate turned through 180° relative to the normal to the plate, makes it possible to increase the sensitivity of measurements by more than an order of magnitude by eliminating the systematic components of measuring errors due to complete compensation of aberrations. The results of experimental testing of the method are considered.

THREE-DIMENSIONAL WEDGE DIFFRACTION CORRECTION DEDUCED BY THE STATIONARY PHASE METHOD ON THE MODIFIED EQUIVALENT CURRENT APPROXIMATION (MECA)

This paper presents a new method for computing fields diffracted by a wedge for the MECA formulation, which is valid not only for perfect electric conductors but also for lossy penetrable dielectrics. The method is based on the computation of a wedge correction matrix, which establishes a mapping function between fields incident at and diffracted by the wedge. The MECA method is based, in general, upon the oblique incidence of a plane wave at the interface between free space and lossy dielectric media. MECA reduces to the well-studied physical optics (PO) formulation in case of PEC (perfect electric conductor) scatterers. In this work, we consider a scenario involving diffraction caused by a plane wavefront incident on a wedge with flat faces and straight edge. The version of the stationary phase method for three-dimensional equivalent source distributions is employed to calculate the asymptotic contribution of the integration boundary along the edge of the diffraction wedge. This contribution of the critical boundary points is compared to the GTD (geometrical theory of diffraction) diffracted field in order to obtain the correction matrix by which the incident electric field vector is multiplied in MECA. As required to accomplish this comparison, the threedimensional incident electric field is previously resolved into an edgefixed coordinate system. Good agreement is demonstrated between full-wave method-of-moments (MoM) results and the results obtained by modifying MECA with our diffraction correction technique. Received 18 November 2011, Accepted 18 January 2012, Scheduled 17 February 2012 * Corresponding author: Hipolito Gomez-Sousa (hgomez@com.uvigo.es). 208 Gomez-Sousa, Martinez-Lorenzo, Rubinos-Lopez

Going upstairs: The decision review system – velvet revolution or thin edge of an ethical wedge?

The instant/slow-motion television replay may be seen as broadcasting's greatest gift to sport, by others as a symbol of unwanted change. This and further technological tools, such as super-slow-mo, HotSpot, HawkEye and, most recently, HD and 3D, were devised to bring the viewer closer to the action. Spurred, additionally, by the contradiction between what the viewer sees clearly at home and the paying spectator cannot even detect, sport has gingerly incorporated technology to aid the decision-making, modifying regulations and creating a new official: the video referee, video umpire, instant replay official, television match official or third umpire. No longer is the umpire's word final. Cricket, with the recent introduction of the Decision Review System, has been keener than most to open this Pandora's Box. Some maintain that the umpire's right to be wrong should be sacrosanct, that players should take rough with smooth; this chapter will contend that the greater incidence of correct decisions can only help the game's credibility, ensuring justice is more frequently done and even fostering a greater willingness to walk. It will also argue that the review system should be used in all major games, that it should be properly funded by the ICC in consort with its broadcasting partners, and that it should be revised to allow the third umpire to be proactive.

Conical refraction of elastic waves in absorbing crystals

The absorption-induced acoustic-axis splitting in a viscoelastic crystal with an arbitrary anisotropy is considered. It is shown that after “switching on” absorption, the linear vector polarization field in the vicinity of the initial degeneracy point having an orientation singularity with the Poincare index n = ±1/2, transforms to a planar distribution of ellipses with two singularities n = ±1/4 corresponding to new axes. The local geometry of the slowness surface of elastic waves is studied in the vicinity of new degeneracy points and a self-intersection line connecting them. The absorption-induced transformation of the classical picture of conical refraction is studied. The ellipticity of waves at the edge of the self-intersection wedge in a narrow interval of propagation directions drastically changes from circular at the wedge ends to linear in the middle of the wedge. For the wave normal directed to an arbitrary point of this wedge, during movement of the displacement vector over the corresponding polarization ellipse, the wave ray velocity s runs over the same cone describing refraction in a crystal without absorption. In this case, the end of the vector moves along a universal ellipse whose plane is orthogonal to the acoustic axis for zero absorption. The areal velocity of this movement differs from the angular velocity of the displacement vector on the polarization ellipse only by a constant factor, being delayed by π/2 in phase. When the wave normal is localized at the edge of the wedge in its central region, the movement of vector s along the universal ellipse becomes drastically nonuniform and the refraction transforms from conical to wedge-like.

Eat, Swim, Pray

Eat, Swim, Pray

On elastic waves in a wedge

The existence of waves propagating along the edge of an elastic wedge has been established by many authors by physically rigorous arguments on the base of numerical computations. A mathematically rigorous proof for a wedge with aperture angle less than π/2 was presented by I. Kamotskii. We supplement the I. Kamotskii result and prove the existence of fundamental modes for some range of aperture angles greater than π/2. Bibliography: 7 titles.

Dispersion analysis and measurement of circular cylindrical wedge acoustic waveguides

This study investigates the propagation of flexural waves along the outer edge of a circular cylindrical wedge, as well as phase velocities and corresponding mode displacement. Due to the complexity of boundary-value problems, only approximate solutions to these problems have been derived so far. Here, the dispersion curves are determined using a bi-dimensional finite element method (Bi-d FEM), as derived through the separation of variables and Hamilton’s principle. According to calculation of modal displacement, the maximum deformations appear at the outer edge of the wedge tip. Numerical examples also reveal how distinct thin-film materials deposited on the outer surface of the circular cylindrical wedge influence the dispersion curves. Additionally, the dispersion curves are measured via a laser-induced guided wave experiment, in which a knife-edge measurement scheme and the 2-dimensional fast Fourier transform (2D-FFT) method are used. Both numerical and experimental results correlate well with each other, demonstrating the validity of the numerical solution. A prototype ultrasonic motor is also developed based on the circular cylindrical wedge-like acoustic waveguide.

1211 溝付き面板を用いた樹脂材の突切り加工における曲げ効果が切断抵抗へ及ぼす影響(OS12-3高精度・高機能化加工技術)

1211 溝付き面板を用いた樹脂材の突切り加工における曲げ効果が切断抵抗へ及ぼす影響(OS12-3高精度・高機能化加工技術)

Effect of centrifugal rotational speed on wedge castability of titanium

This study examined the effects of the speed and force in centrifugal casting on the wedge castability of Ti–5 mass%Cu (Ti–5Cu) alloy and commercially pure titanium (CP-Ti). The Ti–5Cu alloy was prepared by argon-arc melting. Whole wedge-shaped acrylic patterns were prepared with either 15° or 30° angles and invested with a MgO-based material. The wedge specimens were cast using a centrifugal casting machine at rotational speeds of 600, 1000, 1250, 1500 and 3000 rpm. Mold filling, an index for a measure of castability, was determined as the missing length between the edge of the cast wedge and the theoretical acute tip of the triangle. CP-Ti was used as a control. An analytical model was developed to relate the mold-filling index to the surface energy and rotational speed. The experimental results indicate that the means of the mold-filling index of the 30° wedge angle were lower than those of the 15° wedge angle when compared for each corresponding metal and rotational speed. In each angle for CP-Ti, the means tended to reduce with increase in the rotational speed. The mold-filling index of 5% Cu titanium was found to be similar to that of CP-Ti, even for 15° wedge when the rotational speed was higher than 1250 rpm. The results suggest that dental prosthesis, which has narrow cross sections containing very narrow regions (for example, clasps of a denture), can be cast successfully by utilizing high rotational speed during centrifugal casting. The complex dependence of mold-filling index on wedge angle and rotational speed is explained on the basis of the analytical model and the dependence of the apparent surface energy on rotation speed.

Scattering of a plane electromagnetic wave by an infinite wedge with a truncated circular cylinder coated coaxially with a magnetodielectric layer

We formulate and solve the problem of scattering of a plane electromagnetic wave by an infinite, perfectly conducting wedge with a truncated, perfectly conducting circular cylinder which is coated coaxially with a magnetodielectric layer and located along the wedge edge. The rigorous solution is obtained and reduced to a system of linear algebraic equations of the second kind for unknown coefficients of Fourier expansions of the scattered field. The results of calculating the scattered field in the far zone with a specified accuracy are presented for the case of an H-polarized wave. It is shown that for certain values of the electric radius of the cylinder, the backscattering cross section of such a structure has pronounced maxima.

The interaction of punches on the face of an elastic wedge

The interaction of two punches, which are elliptic in plan, on the face of an elastic wedge is investigated in a three-dimensional formulation for different types of boundary conditions on the other face. The wedge material is assumed to be incompressible. An asymptotic solution is obtained for punches which are relatively distant from one another and from the edge of the wedge. For the case when the punches are arranged relatively close to the edge of the wedge (or reach the edge, the contact area is unknown) the numerical method of boundary integral equations is used. The mutual effect of the punches is estimated by means of calculations. The asymptotic solution of the generalized Galin problem, concerning the effect of a concentrated force applied on the edge of the three-dimensional wedge on the contact pressure distribution under a circular punch relatively far from the edge, is obtained.

Numerical computations of the flow in a finite diverging channel

The flow in a finite diverging channel opening into a large space and resembling the experimental prototype of Putkaradze and Vorobieff (2006) was numerically investigated. The effects of the Reynolds number, initial condition, intersection angle, length of the wedge edges, and the outer boundary condition were examined. The numerical results showed that the flow in the wedge undergoes a change from symmetrical flow to unsymmetrical flow with a weak backflow, then a vortical (circulation) flow and finally an unsteady jet flow as the Reynolds number is increased for an intersection angle of 32° and a wedge edge of length 30 times the width of the inlet slit. For the unsteady flow, the jet attached to one side of the wedge constantly loses stability and rolls up into a mushroom-shaped vortex-pair near the outlet of the wedge. As the intersection angle is increased to 50°, a stable jet flow is observed as a new regime between the vortex and unsteady regimes. Both the intersection angle and the wedge length have negative effects on the stability of the flow, although the effect of the wedge length on the critical Reynolds number for the symmetry-breaking instability is not pronounced. The outer boundary condition was found not to affect the flow patterns inside the wedge significantly. At a certain Re regime above the onset of symmetry-breaking instability, the flows evolve into steady state very slowly except for the initial stage in the case of decreasing flow flux. Two different solutions can be observed within the normal observation time for the experiment, providing a possible explanation for the hysteresis phenomenon in the experiment.

Leaky waveguide modes along the edge of a dielectric wedge

It is shown experimentally that a Gaussian beam focused from within a finite wedge onto its edge at an angle of total reflection excites a leaky waveguide mode propagating along the edge. This newly described phenomenon is interpreted in terms of waveguide modes of a tapered dielectric slab of a mode index, which is known to decrease with slab thickness. This decrease in the refractive index leads to a gradual refraction of the incident beam parallel to the edge. A numerical simulation of a focused Gaussian beam incident on a finite dielectric wedge gives a full account of this phenomenon.

Contact problems for a two-layer elastic wedge

We obtain integral equations for plane contact problems for a two-layer wedge (composite) under three types of boundary conditions on one of its sides (absence of stresses, sliding, or rigid fixation). The composite consists of two wedges completely linked with each other, which have different opening angles and elasticity parameters. Using the symbols (Mellin transforms) of the kernels of integral equations for the two-layer wedge, one can derive the symbols of the kernels of integral equations for symmetric problems about a crack in a three-layer wedge or a three-layer strip and for contact problems for a two-layer strip (by passing to the limit in a special way). The complex zeros of the Mellin transform determine the asymptotics of the normal contact pressure at the corner point of the composite as the contact region approaches this point. It is important that this asymptotics is also preserved in three-dimensional contact problems as the die enters the edge of a two-layer wedge (outside the corner points of the die itself). Taking into account this asymptotics, we obtain solutions of the contact problems as the die enters the vertex of the composite. We show that by appropriately choosing the materials and the internal angle of the two-layer wedge one can avoid contact pressure oscillations at the vertex, which occur in the case of a homogeneous wedge and result in loss of contact. The contact pressure at the wedge vertex can be made zero for a composite, while for a homogeneous wedge with the same opening angle it increases unboundedly. We construct asymptotic solutions of the contact problems for a plane die located relatively close or to the vertex of a two-layer wedge or relatively far from the vertex.