Free Lateral Surface Research Articles

Thermal and Concentrational Maragoni Convection at Liquid∕Air Bubble Interface

The paper presents the experimental study of thermo- and solutocapillary Marangoni convection around a gas bubble in an inhomogeneous fluid with a vertical thermal or surfactant concentration gradient. The stationary bubble in the form of a short horizontal cylinder with a free lateral surface was placed into a vertically oriented thin liquid layer (Hele-Shaw cell). The evolution of thermal and concentration fields and fluid flows was studied applying the interferometric method. In contrast to a thermocapillary convection representing a stationary flow and stable temperature distribution, the periodic concentration disturbances around the bubble were observed in the solutocapillary case. The regularities of the discovered effect were revealed, and its interpretation was proposed.

Closure to “Discussion of ‘Axial Loading of Bonded Rubber Blocks’ ” (2005, ASME J. Appl. Mech., 72, p. 453)

Our immediate reaction to the comments of Pence was one of amazement that such a supposedly prestigious journal would consider it appropriate to devote valuable space to what, we feel, should be obvious to a reasonably well-informed reader who has delved into the related literature.In his first paragraph, Pence appears to review a few random elements of the very well-known basics of classical elasticity theory (even to the extent of giving the absolutely fundamental relationships between the displacement and strain components). Several of these were, in fact, willingly deleted from our original manuscript, upon receiving the observation of a reviewer that, “It is not necessary to remind readers of Journal of Applied Mechanics … for a linear elastic model.”He then, seemingly unnecessarily, simply reproduces a few of our expressions, before making the observation that the equilibrium equation in the z direction is not satisfied. Actually this would clearly not be expected with the basic objectives and assumptions of the analyses presented. However, he naively appears to regard this as a hugely serious flaw that casts doubt on the worth of the realistic approximate expressions derived for the apparent Young’s modulus, offering improvements on those previously available.The approximations developed by Gent and Lindley (1) and Gent (2) have been widely quoted and used in the engineering industry for assessing axial stiffness. As we hoped was clearly explained in our introduction in Sec. 1, they were derived on the basis of two fundamental assumptions: (i) that planes initially normal to the direction of loading remain normal after loading, and (ii) that the deformed shapes of the free lateral surfaces are parabolic. Subsequently, as we pointed out in Secs. 1 and 5.2, the validity of the assumption (ii) has been questioned by several authors in interpreting their experimental results—with comments including “the assumption of a parabolic profile is erroneous” and that the next step “would be an improved method of estimating the ‘bulgeability.’ ” It was our aim therefore to provide such estimates with this assumption of parabolic profiles removed, while maintaining the more reasonable first assumption.However, it is a natural consequence of this simplifying assumption (i) that, for an incompressible material, it becomes unrealistic to satisfy exactly the equilibrium equation in the z direction (except on the central plane, z=h∕2) on an infinitesimal volume. Further, this same assumption leads to the prediction of the existence of a shear stress on the unloaded boundary which, as observed in the paper, cannot actually physically exist.If Pence were to refer to the already cited references of Gent and Lindley (1) and Gent (2), he would deduce that the theories therein lead to solutions for the stress components that also do not satisfy the equilibrium equation in the direction of loading, nor do the expressions derived in the later considerations of, for example, Constantinuo, Kartoum, and Kelly (3), Chalhoub and Kelly (4), and Tsai and Lee (5).Additionally, it should perhaps be pointed out that all the above papers, and others, have assumed the rubber block to have a small thickness and have either predicted or assumed parabolic deformed profiles. In contrast, our analysis applies to a block of any thickness, and predicts that, especially for blocks of small shape factor, the profile is noticeably not parabolic. This is reassuringly in agreement with the experimental findings of Mott and Roland (6) and others.In conclusion, we would suggest that, contrary to Pence’s concerns in his final sentence, methodologies similar to that adopted in our paper have proved invaluable and extremely useful in related analyses. Particularly worthy of note are the expressions that Horton, Gover, and Tupholme (78) presented for the radial stiffness and tilting stiffness of a rubber bush mounting of finite length. Not only were there no useful estimates available previously, but moreover they yield numerical values that agree well with the available experimental data.We are grateful to the Editor of the Journal of Applied Mechanics for giving us this opportunity to respond. We hope that our comments will enhance the appreciation of the potential importance and value of our results, for those readers who have not worked directly in this area of rubber technology and are therefore less familiar with the relevant literature.

Morphological instability and contraction of a rectangular plate under stress

The contraction of a stressed rectangular plate-like sample has been investigated considering the mechanical stability of its two lateral free surfaces with respect to localized perturbation. The energy variation of the plate has been calculated to determine the condition of development of symmetric and non-symmetric wavelet fluctuations of the two lateral free surfaces when a constant and homogeneous stress is applied to the plate. The contraction has been then studied when a source of non-homogeneous strain is embedded into the plate.

Steady flows of compressible fluids in a rigid container with upper free boundary

We consider fluid in a smooth rigid container whose lateral boundary is a piece of vertical cylinder, bounded above by a free upper surface. As basic flow we consider the non homogeneous rest state in the presence of gravity, and of a surface tension. Under these assumptions, we study the existence of a steady free boundary Γ and a steady motion in Ω of an isothermal viscous gas, resulting as perturbation to the rest state in correspondence of small non potential perturbations to the (large potential) gravitational force. We linearize the problem by prescribing the unknown domain Ω, then we make use of the iterative scheme introduced by Heywood and Padula. Our method is based on an iteration between the Neumann problem for a non homogeneous Stokes system for the velocity, the Neumann problem for an elliptic problem on Γ for height, and a steady transport equation for the perturbation to the density. The difference of boundary condition between lateral boundary and free upper surfaces causes a singularity at the intersection (contact line). To avoid singularities on the contact line, we adopt weighted Sobolev spaces.

Pak1 and PIX regulate contact inhibition during epithelial wound healing.

Wound healing in epithelia requires coordinated cell migration and proliferation regulated by signaling mechanisms that are poorly understood. Here we show that epithelial cells expressing constitutively active or kinase-dead mutants of the Rac/Cdc42 effector Pak1 fail to undergo growth arrest upon wound closure. Strikingly, this phenotype is only observed when the Pak1 kinase mutants are expressed in cells possessing a free lateral surface, i.e. one that is not engaged in contact with neighboring cells. The Pak1 kinase mutants perturb contact inhibition by a mechanism that depends on the Pak-interacting Rac-GEF PIX. In control cells, endogenous activated Pak and PIX translocate from focal complexes to cell-cell contacts during wound closure. This process is abrogated in cells expressing Pak1 kinase mutants. In contrast, Pak1 mutants rendered defective in PIX binding do not impede translocation of activated Pak and PIX, and exhibit normal wound healing. Thus, recruitment of activated Pak and PIX to cell-cell contacts is pivotal to transduction of growth-inhibitory signals from neighboring cells in epithelial wound healing.

Influences of the geometrical conditions of die and workpiece on the barreling formation during forging–extrusion process

The main concern of this study is to investigate the material flow characteristics of solid cylinder upsetting with a hollow die subjected to different geometrical conditions such as taper angle and dimension of the aperture surface within the top die, and height-to-diameter ratio of the billet. During the forging–extrusion process, obviously two barrels, namely top barrel and bottom barrel, are successively formed along the lateral free surface of the workpiece, and an extrusion of the top free surface of the billet into the aperture surface within the top die is accompanied. A finite element-based methodology is utilized to examine the radii of the curvature of the barrels and the height of an extrusion of the top free surface into the aperture surface within the top die accordingly.

A sextic formalism for three–dimensional elastodynamics of cylindrically anisotropic radially inhomogeneous materials

Elasticity of arbitrary cylindrically anisotropic radially inhomogeneous media is considered. The system of six first–order ordinary differential equations describing time–harmonic cylindrical waves propagating along the cylinder axis is obtained. The matrix of the system coefficients has a specific algebraic symmetry underlying the structure of the formalism. The matricant solution in the form of the Peano expansion is discussed. The Wentzel–Kramers–Brillouin approximation is derived. Algebraic features of the solution are analysed and their physical content is elucidated. The dispersion equation for waves in a hollow cylinder with free or clamped lateral surfaces is formulated in terms of the impedance/admittance matrices. Their analytical properties are established, which are useful for analysis of the resulting frequency spectrum. The theory is extended to anisotropic radially inhomogeneous piezoelectric cylinders, for which the octet generalization of the formalism is developed and studied.

Radius ratio estimation and fold situation prediction of the deformation profile in forging–extrusion process

Application of the finite element method in conjunction with abductive network is presented to investigate the geometrical shape of the deformation profile and its related fold defect during forging–extrusion process. The geometrical shape of the deformation profile may be characterized by a parameter of radius ratio that is defined as the ratio of the radius at the equatorial plane to that at the end surfaces of the deformed workpiece. Different geometrical conditions combined with various frictional constraints are taken into account as the process variables in this study. During the forging–extrusion process, several barrels with different radius of curvature may be successively formed along the lateral free surface of the workpiece and the extrusions of the free surfaces of the billet into the aperture surfaces within the dies are accompanied. A finite element based code is utilized to investigate the material flow characteristics resulting in different shapes of the deformation profile, and the abductive network is then applied to synthesize the data sets obtained from the numerical simulation. Finally, the prediction models are established for radius ratio estimation of the barrels and fold occurrence situation judgment under various combinations of process variables.

Prediction of fold defect in barreling formations of cylinder upsetting

In this paper, the use of finite element method in conjunction with abductive network is presented for investigating fold defect that may occur in barreling formation during cylinder upsetting with hollow die. Different geometrical conditions combined with various frictional constraints are taken into account as the process parameters in this study. During the upsetting process, several barrels may be successively formed along the lateral free surface of the workpiece and the extrusions of the free surfaces of the billet into the aperture surfaces within the dies are accompanied. In addition, there are two locations where fold defect may occur during upsetting process, one occurs around the equatorial plane of the workpiece and the other takes place around the intersection zone of the barrels. A finite element based code is utilized to investigate the material flow characteristics resulting in the occurrence of fold defect, and the abductive network is then applied to synthesize the data sets obtained from the numerical simulation. Finally, a prediction model is established for fold occurrence judgment around different locations under various combinations of process parameters.

Effect of frictional constraints on the barreling formations in cylinder upsetting with a hollow die

The objective of this study is to investigate the material flow characteristics associated with solid cylinder upsetting using a hollow die subjected to different combinations of frictional constraints. During the upsetting process, obviously two barrels are formed along the lateral-free surface of the workpiece and correspond to some specific combination of frictional constraints. A finite element based methodology is utilized to examine the radii of curvature of the barrels and the height of the top free surface that is extruded into the aperture of the die. In addition, the effect of various combinations of interface friction at the top- and bottom- die surfaces on both the effective stress and strain distributions are also investigated.

Free Vibrations of Transversely Isotropic Hollow Cylinders

An asymptotic process for evaluating the frequencies of free axisymmetric vibrations of transversely isotropic hollow cylinders is proposed. This process is developed in detail for a cylinder with hinge-supported ends and free lateral surfaces. The approaches which make it possible to construct algorithms for identifying their natural frequencies within the given interval are tested on model problems. The results from the Kirchhoff-Love and Ambartsumyan theories are compared with those from the 3D elasticity theory. In the first term of an asymptotic expansion, two frequencies coinciding with those obtained using the applied shell theory are found and a countable set of frequencies absent in this theory is determined.

Polarization imprint and size effects in mesoscopic ferroelectric structures

Piezoresponse scanning force microscopy measurements performed on lead zirconate titanate mesoscopic structures revealed a negative shift of the initial piezoelectric hysteresis loop. The shift is dependent on the size of the structure and is most probably due to the pinning of ferroelectric domains at the free lateral surface and ferroelectric–electrode interface. Considering a simple model, the thickness of the pinned domain layers is found to be about 15 and 70 nm at the ferroelectric–electrode interface and lateral free surface, respectively.

A SINGULAR PROBLEM IN INCOMPRESSIBLE NONLINEAR ELASTOSTATICS

This paper represents a contribution to the numerical treatment of problems in incompressible elasticity theory for large deformations. We are especially concerned about the solution of plane problems with corners. A review of the literature on these problems indicates that the behavior of the solution in the vicinity of a corner is given little attention. We investigate the solution of the compressed bonded block problem corresponding to the compression of an incompressible elastic block of rectangular cross-section and infinite transverse length between two opposing bonded rigid surfaces, with the two remaining lateral faces traction-free. We are especially interested in the behavior at a corner where a bonded end is adjacent to a free lateral side. We employ a finite element method based on a reduced and selective integration technique with penalization to construct a numerical solution for this problem. Our computational method converges everywhere except in a small neighborhood of the corner. We appeal to an elementary a priori inequality concerning the angle of shear to show that the numerical calculations in this neighborhood are inaccurate and need a more refined study. Based on the inequality, we offer a conjecture concerning the local shape of the deformed free lateral surface at the corner.

Wave propagation modeling in human long bones

The dynamic behavior of a dry long bone that has been modeled as a piezoelectric hollow cylinder of crystal class 6 is investigated. The solution for the wave propagation problem is expressed in terms of a potential function which satisfies an eighth-order partial differential equation, whose solutions lead to the derivation of the explicit solution of the wave equation. The mechanical boundary conditions correspond to those of stress free lateral surfaces, while the electrical boundary conditions correspond to those of short circuit. The satisfaction of the boundary conditions leads to the dispersion relation which is solved numerically. The frequencies obtained are presented as functions of various parameters and they compare well with other researchers' theoretical results.

Three-dimensional elasticity solutions for free vibrations of rectangular plates by the differential quadrature method

This paper presents accurate three-dimensional elasticity solutions for free vibrations of six types of plates having free lateral surfaces, two opposite sides simply supported, and two other sides having combinations of simply supported, clamped, and free boundary conditions. The solution methodology adopted in the present work first reduces the spatial variables in the governing elasticity equations to two by using displacement functions in the forms which satisfy the boundary conditions of the assumed simply supported sides. The eigenvalue equations are then formulated from the reduced governing equations and the boundary conditions via the differential quadrature method. The numerical results include the first nine natural frequencies of the six plate configurations for combinations of three aspect ratios and two thickness ratios. These results are supported by appropriate convergence studies and comparisons with the results of other authors.

A note on the geometric scaling of long-rod penetration

The paper describes a set of experiments with copper and tungsten alloy long-rods, which were aimed at finding the sources of non-scaling effects recently discovered in terminal ballistics. Our basic assumption was that geometrical scaling should hold for ductile penetrators (like copper) and that any deviation from this scaling should be attributed to brittle failure mechanisms at the penetrator's head. Our experimental results support this assumption as far as the depth of penetration into steel of two penetrators, differing by a factor of 2, is considered. Thus, copper penetrators scaled well, within experimental error, while a difference of about 10% was found between the depth of penetration of 1:2 and 1:4 tungsten alloy penetrators. We also present two-dimensional simulations, which were performed with the PISCES 2DELK code, in order to determine lateral edge effects. These simulations enabled us to choose the right size for our “infinite” targets, avoiding any influence from their lateral-free surface.

THREE-DIMENSIONAL VIBRATION ANALYSIS OF SOLID CYLINDERS OF POLYGONAL CROSS-SECTION USING THEp-RITZ METHOD

Theoretical and numerical analyses and some observations on the physical phenomena of free vibration of solid cylinders having square and hexagonal cross-sections with combinations of fixed and free ends are reported. The formulation is established based on the linear, small-strain, three-dimensional elasticity principle, and thep-Ritz method is employed for computing the solution of the problem. By expanding the displacements in spatial co-ordinates, integral expressions for strain and kinetic energies in a three-dimensional setting are derived in Cartesian form. Sets of one-and two-dimensional orthogonal polynomials are constructed to represent the three dimensional variations in the longitudinal and lateral surface directions. A basic function is introduced in these polynomials to cater for the stress free lateral surfaces and the kinematic constraints at both ends. Several examples are solved to demonstrate the applicability of the method. First known results in terms of vibration frequency parameters and mode shapes of cylinders having square and hexagonal cross-sections for various symmetry classes and ends constraints are presented and the physics behind the results is highlighted. These new results may serve as benchmark data for future research development in simplified beam theories.

Study of the stability of the film casting process

AbstractA theoretical study of the film casting process has been carried out. In this industrial process, a molten polymer is extruded through a flat die, then stretched in air and cooled on a chill roll. This involves mainly an extensional flow. Between the die and the chill roll, thick edges are formed and a neck‐in phenomenon is observed. Above a critical take‐up speed, a drawing instability, known as draw resonance, may occur. In this paper, a one‐dimensional model adapted from the classical model of the fiber spinning is developed (for a Newtonian or a Maxwell fluid). The influence of the processing parameters (draw ratio, Deborah number, and aspect ratio) on geometry of the lateral free surface (the so‐called neck‐in phenomenon) is studied. An unattainable zone very similar to the one encountered in fiber spinning is predicted, which only slightly depends on the stretching geometry (initial film width and stretching distance). The onset of draw resonance is studied through the linear stability method. A stability zone, depending on the geometry of the process, the elasticity of the polymer, and the draw ratio, has been obtained. This instability is observed with simultaneous width and thickness film variations. It is proved that the aspect ratio (stretching distance divided by die width) has a strong influence on the onset of the draw resonance instability.

Local Non-similarity Solutions for Mixed Convection Flow with Lateral Mass Flux over an Inclined Flat Plate Embedded in a Saturated Porous Medium

The problem of mixed convection along an inclined wall, acting as a source or sink with lateral mass flux, embedded in a porous medium is solved by the local non similarity method. The wall surface temperature, the flow free stream velocity and lateral surface velocity vary in a power law along the wall. The two components of buoyancy force are retained. The inclination of the plate ranges from horizontal to vertical. Numerical solutions are carried out up to the third level of truncation and results are presented for a wide range of mass flux parameter at different wall temperature distributions and inclination angles.

Epiphysial ossification centres in iliosacral joints: anatomy and computed tomography.

Bilateral apparently bony structures of different forms and sizes located in the inferior and superior ventral parts of the sacroiliac joints were observed on axial CT images of the pelvic region of juvenile patients. No other pathological changes were noted in the sacroiliac joints of these individuals. In one patient the bony structures could also be seen on a conventional plain radiograph. We also examined 3 juvenile autopsy specimens of this joint using radiology, CT, macroscopical evaluation and histology. In two of them, structures could be detected on the CT scans which were similar to those observed in the young patients. Macroscopic investigations revealed the structures to be secondary ossification centres located in the articular cartilage of the lateral part of the os sacrum at the levels of the first and third sacral segments. According to older anatomical literature, these epiphysial ossification centres contribute to the auricular surface of the lateral part of the os sacrum and the free lateral surface of the inferior sacral parts. They can be observed between the ages of 12 and 25 years and begin to synostose with the lateral part around the age of 18 years. In macerated juvenile specimens of the bony pelvis, free ossicles were not detectable in the region of the sacroiliac joints. Histological peculiarities of the ossification process observed are discussed. These physiologically occurring ossification centres are to be differentiated from pathological alterations appearing as bony or bone-like structures on CT scans.