On the levitation of a charged body in an electrostatic field

The possibility of levitation of a body bearing a point electric charge in the electric field of a fixed point charge of the same sign is demonstrated. Stabilization of the unstable equilibrium state of the body in which the body weight is balanced by the Coulomb force is provided by gyro forces due to body rotation. The conservative stability of the levitating body corresponds to a finite range of angular velocities. It is shown that dissipative and circulatory forces considered together can improve the stability of the system to asymptotic stability. The attraction domain of the stable equilibrium position is studied numerically as a function of system parameters.     

Validation of a numerical model for the simulation of an electrostatic powder coating process

Numerical modeling of a complete powder coating process is carried out to understand the gas-particle two-phase flow field inside a powder coating booth and results of the numerical simulations are compared with experimental data to validate the numerical results. The flow inside the coating booth is modeled as a three-dimensional turbulent continuous gas flow with solid powder particles as a discrete phase. The continuous gas flow is predicted by solving Navier–Stokes equations using a standard k–ε turbulence model with non-equilibrium wall functions. The discrete phase is modeled based on a Lagrangian approach. In the calculation of particle propagation, a particle size distribution obtained through experiments is applied. The electrostatic field, including the effect of space charge due to free ions, is calculated with the use of the user defined scalar transport equations and user defined scalar functions in the software package, FLUENT, for the electrostatic potential and charge density.     

Stability of the equilibrium of a flat layer in a microconvection model

The stability of the equilibrium state of a flat layer bounded by rigid walls is studied using a microconvection model. The behavior of the complex decrement for longwave perturbations has an asymptotic character. Calculations of the full spectral problem were performed for melted silicon. Unlike in the classical Oberbeck–Boussinesq model, the perturbations in the microconvection model are not monotonic. It is shown that for small Boussinesq parameters, the spectrum of this problem approximates the spectra of the corresponding problems for a heatconducting viscous fluid or thermal gravitational convection when the Rayleigh number is finite.     

Bifurcation points of the elastic-plastic equilibrium in a simple frame model

Summary This is a study of the characteristics of equilibrium bifurcation in a geometrically symmetric simple frame model in which the beam is loaded symmetrically and gradually. The deformability of the model is concentrated in two Shanley cells for whose elements a nonholonomic bilinear force-lengthening (or force-contraction) relation is adopted.The equilibrium bifurcation characteristics of this model are compared with those of Shanley's uniformly stressed column model. The characteristics of the two models coincide when instantaneous plasticisation of the deformable elements for the frame model are assumed, as occurs in the column model. But with a succession of different plastic states as the load increases, differences emerge. The most important being: in the frame model the borderline between the interval of unstable bifurcation points and the interval of stable bifurcation points is not necessarily, as it is in the column model, marked by a neutral (stationary load) bifurcation point.

---

Sommario S'indagano i caratteri della biforcazione dell'equilibrio di un modello di portale, simmetrico nella geometria e simmetricamente caricato sul traverso in modo graduale. La deformabilità del modello è concentrata in due celle alla Shanley, per i cui elementi si adotta una relazione bilineare anolonoma tra forze ed allungamenti (od accorciamenti).Si confrontano tali caratteri con quelli della biforcazione dell'equilibrio del ben noto modello di asta caricata di punta studiato da Shanley.Quando si ipotizzi, per il modello di portale, una plasticizzazione istantanea degli elementi deformabili (proprio come avviene nel modello di asta), si ha perfetta coincidenza dei caratteri in esame.All'opposto, quando si ipotizzi un succedersi di diversi stati plastici al crescere del carico, si constatano delle differenze; in particolare, per il modello di portale esiste la possibilità, a differenza di quanto avviene nel modello di asta, che non sia un punto di biforcazione neutra (a carico stazionario) a segnare il confine tra l'intervallo dei punti di biforcazione instabile e quello dei punti di biforcazione stabile.

---

---

Study supported by the Plasticity Group of the National Research Council.     

The equilibrium field near the tip of a crack for finite plane strain of incompressible elastic materials

This investigation is concerned with the deformations and stresses in a slab of all-around infinite extent containing a traction-free plane crack, under conditions of plane strain. The analysis is carried out within the framework of the fully nonlinear equilibrium theory of homogeneous and isotropic incompressible elastic solids. For a fairly wide class of such materials and general loading conditions at infinity, assymptotic estimates appropriate to the various field quantities near the crack-tips are deduced. For a subclass of the materials considered, these results — in contrast to the analogous predictions of the linearized theory — lead to the conclusion that the crack opens up in the neighborhood of its tips even if the applied loading is antisymmetric about the plane of the crack, (e.g., Mode II loading). It is shown further that the non-linear global crack problem corresponding to such a loading in general cannot admit an antisymmetric solution.The results communicated in this paper were obtained in the course of an investigation supported in part by Contract N00014-75-C-0196 with the Office of Naval Research in Washington, D.C.     

The influence of the space charge in an electron beam accelerated in a constant electrostatic field up to energies of several MeV

Summary To realize a pulsed electron beam of high energy (2.5 MeV) and great intensity (ca 1 A) the influence of space charge has to be taken into account. A calculation in this article shows that at an average field strength in the acceleration tube of 10⁶ V/m the influence of the space charge begins to play a dominating part at a current density of 2A/cm².     

Stability of the equilibrium state in a convection model with nonlinear temperature and pressure dependences of density

The convection of a heat-conducting viscous liquid is considered. It is assumed that the liquid density depends quadratically on the temperature and pressure. The instability of the equilibrium state of a free-boundary horizontal layer with respect to small perturbations is studied using a linearization method. It is found that the state of mechanical equilibrium is unstable. Neutral curves are constructed and the critical Rayleigh numbers are found. The results are compared with the well-known solution of the same problem for the limiting case where the density is a quadratic function of temperature and does not depend on pressure. __________ Translated from Prikladnaya Mekhanika i Tekhnicheskaya Fizika, Vol. 48, No. 2, pp. 66–74, March–April, 2007.     

An empirically validated model of the pressure within a droplet confined between plates at equilibrium for low Bond numbers

An analytical model is presented that describes the equilibrium pressure within a confined droplet for small Bond numbers without prior knowledge of the interface shape. An explicit equation for the pressure was developed as a function of the gap height, surface tension, and contact angle. This equation was verified empirically. The shape of the interface was found based on the pressure predicted by both the proposed model and a model commonly used in electrowetting on dielectric (EWOD) investigations. These shapes were compared against experimentally observed interfaces for aspect ratios between 3.5 and 18. The pressures and shapes predicted by the proposed model were at least an order of magnitude more accurate than those predicted with a more commonly used model. At an aspect ratio of 3.5, the average error in the predicted shape was almost 4%, but decreased below the experimental error at an aspect ratio of 6. An aspect ratio of 15 is required for an EWOD device to split water droplets in air. The error in the model pressure and its predicted interface in this case were approximately 0.3%. The analytical pressure model proposed here can be used to increase the accuracy of models of practical EWOD devices. Better accuracy can be attained for small aspect ratios by iteratively calculating pressure using the model proposed here.     

A Numerical Study of the Critical Gas Saturation in a Porous Medium

We use porenetwork simulations to study the dependence of the critical gas saturation in solutiongas drive processes on the geometric parameters of the porous medium. We show that for a variety of growth regimes (including global and local percolation, instantaneous and sequential nucleation, and masstransfer driven processes), the critical gas saturation, Sgc, follows a powerlaw scaling with the final nucleation fraction (fraction of sites activated), fq. For 3D processes, this relation reads Sgcfq0.16, indicating a sensitive dependence of Sgc to fq at very small values of fq.     

Differentiation of the energy functional in the equilibrium problem for a Timoshenko plate containing a crack

The variational formulation of the equilibrium problem for a Timoshenko plate containing a vertical plane crack is considered. Nonpenetration conditions in the form of inequalities (Signorini type conditions) are specified on the crack faces. The behavior of the solution and the corresponding energy functional of the plate with variation in the crack length is analyzed. A formula for the derivative of the energy functional along the crack length is obtained. The solutions are found to continuously depend on the parameter characterizing the crack length.     

Experimental evaluation of through-thickness stresses in a welded pipe using the consistent-splitting model

Experimental data for evaluating through-thickness residual stresses in a girth-welded pipe have been reanalyzed using an improvement in the analysis method. Data were obtained using a destructive experimental technique which involves three steps: parting-out, splitting, and layer removal. The improved analysis, called the consistent-splitting model, has been applied to the data in the splitting step. In addition to satisfying necessary equilibrium and compatibility conditions for the splitting step, the consistent-splitting model is easy to apply and requires no more data than are usually gathered for existing analysis models. Results from the consistent-splitting model show substantial corrections when compared to the originally computed residual-stress distributions. Comparisons of the results based on the consistent-splitting model with values from a finite-element computational model show generally good agreement. Questions about the assumptions embodied in analysis methods applied to the parting-out and layer-removal steps of the experimental procedure suggest future areas of potential improvement.     

A methodology for an accurate evaluation of the linearization procedures in nonlinear mean field homogenization

A systematic methodology for the evaluation of the linearization procedures sustaining mean field homogenization theories for nonlinear composite materials is proposed and applied as an illustration to various recently proposed ‘affine’ and ‘second-order’ formulations for nonlinear elasticity. It relies on the analysis of composites for which both the exact nonlinear homogenization problem and the homogenization problem associated with the ‘linear comparison material’ defined by the linearization procedure can be solved numerically with the same accuracy and for the same microstructure. The comparison of the results then provides a rigorous evaluation of the effects of the sole linearization method. To cite this article: A. Rekik et al., C. R. Mecanique 333 (2005).     

Flow field and diffusional precipitation of aerosols in the simplest model of a polydisperse fibrous filter

A theoretical and experimental investigation was made of the resistance, the flow field, and the diffusional precipitation of aerosols in the simplest model of a polydisperse fibrous filter, i.e., in a system of parallel cylinders of different diameter, arranged perpendicular to the direction of the flow, at small Reynolds numbers. It is shown that the resistance and the diffusional precipitation of particles in such systems can be calculated from the mean radius of the cylinders, even in the case when the radii of the cylinders differ by several times.Translated from Izvestiya Akademii Nauk SSSR. Mekhanika Zhidkosti i Gaza, No. 4, pp. 149–155, July–August, 1973.     

A mathematical model for an alloy solidification problem in the presence of an electric field

A one-dimensional mathematical model for a process of solidification of a binary alloy in the presence of an electric field is studied. A situation in which the thermal properties of each phase are different and the latent heat is non-zero is considered. A quasi-static approximation for the thermal and electric fields is used. Local existence and uniqueness of a classical solution to the resulting free boundary problem are proved for two kinds of boundary conditions. Moreover, under particular hypotheses, the monotonicity of the free boundary and the global existence of the solution is proved.

---

Sommario Si studia un modello matematico unidimensionale per un processo di solidificazione di una lega binaria in presenza di un campo elettrico. Si considera una situazione in cui le proprietà termiche di ogni fase sono differenti e il calore latente è non nullo. Si usa una approssimazione quasi-statica per i campi elettrico e termico. Si dimostra l'esistenza locale e l'unicità di una soluzione classica per il problema di frontiera libera risultante con due tipi di condizioni di bordo. Inoltre si dimostra, sotto particolari ipotesi, la monotonia della frontiera libera e l'esistenza di soluzione globale.

     

Critical Exponents for the Decay Rate of Solutions in a Semilinear Parabolic Equation

This paper is concerned with the Cauchy problem A solution u is said to decay fast if as uniformly in R, and is said to decay slowly otherwise. For each nonnegative integer k, let be the set of uniformly bounded functions on R which change sign k times, and let be defined by . It is shown that any nontrivial bounded solution with decays slowly if , whereas there exists a nontrivial fast decaying solution with if . (Accepted April 24, 1998)     

A prediction of the pressure field in a plane turbulent jet using an algebraic stress model

A numerical prediction is obtained for the mean pressure field in the similarity region of a plane turbulent jet. An algebraic stress model, which introduces non-isotropic relations for the Reynolds stress components, is used to close the mean momentum equation. The full two-dimensional form of the transport equations is retained and the resultant equation set solved elliptically. The numerical prediction simulates many of the characteristics of the pressure field measured by experimental studies. However, the overall level of the predicted field is lower than the experimental values. The level obtained for the mean pressure field depends strongly on the prediction for the transverse normal Reynolds stress component 〈u₂u₂〉. The pressure field is shown to represent a small negative contribution to the net strearnwise momentum balance.