Arbitrary Pressures Research Articles

Inducing arbitrary vapor pressures, and quantifying leakages

We generalize the Maxwell drop evaporation equation to cover the range from closed system to open system through semiclosed system where the evaporation is restricted to an arbitrary degree which we show how to characterize. We first consider a suspended drop, and then a drop contacting a surface where the surface's vicinity restricts the evaporation paths. We show how to use these results to obtain arbitrary values of vapor pressure by simple manipulations of the numbers and sizes of droplets added to the system for a constant leak size, or, alternatively, control the leak size with a valve for given sizes of drops. We further show how to use this result to quantify a leakage in a system. Such a leakage is characterized using a single parameter (leakage length) which the described method calibrates. The calibrated leakage length can be used for systematic control of vapor concentrations within the chamber. © 2016 American Institute of Chemical Engineers AIChE J, 62: 4548–4553, 2016

Um estudo sobre grandezas constitutivas e diferença de pressões arbitrárias em uma suspensão particulada com restrição de incompressibilidade

Este trabalho, no contexto de meio poroso com restrição de incompressibilidade, trata de um estudo sobre grandezas constitutivas e diferença de pressões arbitrárias em uma suspensão particulada. São usadas duas soluções exatas de um sistema de equações do movimento da suspensão particulada, com tais soluções inseridas em modelagem matemática do movimento gravitacional de suspensões particuladas em proveta. A modelagem envolve sub-regiões que variam com o tempo e são delimitadas por interfaces em movimento, inclusive pela onda de aceleração. As soluções exatas e os movimentos da onda e das interfaces, juntamente com dados experimentais da literatura de altura versus tempo da interface superior descendente do próprio teste de proveta, são usados para o cálculo de parâmetros envolvidos em equações propostas para as partes constitutivas da força de interação e de cada tensor tensão. Com isso, é determinada a diferença de pressões arbitrárias. São mostrados resultados numéricos do cálculo dos parâmetros envolvidos nas equações do modelo, usando-se como ponto de partida a determinação dos parâmetros básicos velocidade da onda de aceleração, ponto de encontro da onda com a interface superior descendente e ponto de encontro das interfaces.

Three-dimensional analytical solutions for the axisymmetric bending of functionally graded annular plates

Based on the three-dimensional theory, the axisymmetric bending behavior of functionally graded annular plates made of magneto-electro-elastic, piezoelectric and elastic materials respectively, was investigated. The transverse loads were expanded in terms of a Fourier–Bessel series and the solutions corresponding to each item of the series were found by the direct displacement method. Then the superposition principle was utilized to determine the mechanical, electric and magnetic quantities of the annular plates subjected to the arbitrary transverse pressures. It was found that four unusual boundary conditions can be rigorously satisfied at the inner and outer circumferential edges by this method. Meanwhile, the common boundary conditions such as simply supported, clamped and free boundary conditions were approximately satisfied using the Saint-Venant's principle. An innovative isoparametric element was also developed to calculate the axisymmetric behavior of the functionally graded magneto-electro-elasticity for comparison. Numerical examples were finally given to validate the present method.

Sputter rate distribution and compositional variations in films sputtered from elemental and multi-element targets at different pressures

We report on the quantitative dependence of the deposition rate during magnetron sputtering as a function of the atomic mass, processing pressure and substrate location relative to the target. Targets made of four different materials (C, Al, Ti and Ta), ranging from very light to rather heavy atomic masses, were investigated theoretically initially to determine the deposition rate distribution of the sputtered atoms. In the second part, targets made of different combinations of these materials (Ta/C, Ta/Al, Ta/Ti and Ti/Al) were sputtered to investigate the compositional variations of deposited films. The different targets were sputtered at both low (0.27 Pa) and high (2.7 Pa) pressures, and both the deposition rates and compositions were determined at four different locations in the chamber. Further, Monte Carlo simulations were performed for the sputtered atoms in a simplified model of the vacuum chamber. Simulation and experiments are in adequate agreement and show a significant influence of the processing pressure on the deposition rate in various locations of the chamber. This effect is different for different target compositions and may sometimes result in very large compositional variations in films sputtered from segmented multi-element or alloy targets. Transport phenomena of the sputtered particles are also discussed based on a ballistic or diffusion-like process, depending on the sputtering pressure, mass and size of the sputtered atom as well as location in the deposition chamber. Since the materials studied range from light to heavy and the processing pressures cover the values where sputtering normally takes place, the results in this work can be extrapolated to predict the deposition profiles and compositional gradients for arbitrary material combinations and processing pressures.

The role of thermal path on the accuracy of gas hydrate phase equilibrium data using isochoric method

The aim of this paper is to investigate the role of thermal path on the accuracy of gas hydrate phase equilibrium data using isochoric method. In this regard, methane hydrate equilibrium conditions have been typically determined using different heating paths – continuous and stepwise. The step-heating path, with proper size and duration of temperature increment, provided the most accurate data of methane hydrate phase equilibrium conditions compared with other experimental data available in literature. We have concluded that equilibrium step-heating path had the potential for determining reliable hydrate phase diagrams, irrespective of the present components in the system. Generally, the sufficient time given to each isothermal step is based on approaching a constant number of moles of gas phase through partial hydrate dissociation whereas the size of temperature increment is limited by the amount of gas encaged in hydrate cages.Moreover, the advantage of isochoric method for pure gas systems in utilizing a section of hydrate phase diagram instead of the distinctive condition, at which the last piece of hydrate disappears, is confirmed. Finally, the possibility of obtaining hydrate phase diagram of pure gas systems at arbitrary pressures was examined by purging the system before hydrate dissociation process.

Steady-state modelling of the universal exhaust gas oxygen (UEGO) sensor

The universal exhaust gas oxygen (UEGO) sensor is a well-established device which was developed for the measurement of relative air fuel ratio in internal combustion engines. There is, however, little information available which allows for the prediction of the UEGO's behaviour when exposed to arbitrary gas mixtures, pressures and temperatures. Here we present a steady-state model for the sensor, based on a solution of the Stefan–Maxwell equation, and which includes a momentum balance. The response of the sensor is dominated by a diffusion barrier, which controls the rate of diffusion of gas species between the exhaust and a cavity. Determination of the diffusion barrier characteristics, especially the mean pore size, porosity and tortuosity, is essential for the purposes of modelling, and a measurement technique based on identification of the sensor pressure giving zero temperature sensitivity is shown to be a convenient method of achieving this. The model, suitably calibrated, is shown to make good predictions of sensor behaviour for large variations of pressure, temperature and gas composition.

Path-independent integrals around two circular holes in an infinite plate under biaxial loading conditions

An analytic solution is presented for stresses induced in an infinite plate with two unequal circular holes by remote uniform loadings and arbitrary internal pressures in the holes. The solution is obtained by using the general expression for a biharmonic function in bipolar coordinates. The Airy stress function is decomposed in the sum of a fundamental stress function for an infinite plate remotely loaded, which gives non vanishing tractions on the circular boundaries, and an auxiliary stress function required to satisfy the boundary conditions on the pressures at the edges of the holes, which produces vanishing stresses at infinity. Correspondingly, the variations of the stress concentration factor are determined in terms of the holes geometry and loading conditions. The path independent J k - ( k = 1, 2), M- and L-integrals are analytically calculated on a closed contour encircling the two holes, under remote loading, in order to evaluate the energy release rates accompanying unit translation, self similar expansion and rotation of the holes, respectively. Results are then presented for varying loading orientation angle, biaxial loading ratio and holes geometry.

Exact and numerical elastodynamic solutions for thick-walled functionally graded cylinders subjected to pressure shocks

In the present paper, analytical and numerical elastodynamic solutions are developed for long thick-walled functionally graded cylinders subjected to arbitrary dynamic and shock pressures. Both transient dynamic response and elastic wave propagation characteristics are studied in these non-homogeneous structures. Variations of the material properties across the thickness are described according to both polynomial and power law functions. A numerically consistent transfinite element formulation is presented for both functions whereas the exact solution is presented for the power law function. The FGM cylinder is not divided into isotropic sub-cylinders. An approach associated with dividing the dynamic radial displacement expression into quasi-static and dynamic parts and expansion of the transient wave functions in terms of a series of the eigenfunctions is employed to propose the exact solution. Results are obtained for various exponents of the functions of the material properties distributions, various radius ratios, and various dynamic and shock loads.

Natural neighbor Galerkin method for deflection analysis of inflatable structures

PurposeThe purpose of this paper is to extend the application of natural neighbor Galerkin Method (NNGM) to deflection analysis of inflatable structures such as new and modern textile structures under arbitrary conditions.Design/methodology/approachInflatable structures have a proper mechanical strength when they are inflated at different pressures. NNGM or natural element method (NEM) is defined as a new meshfree method based on the natural neighbor interpolation to analyze the deflections of these structures under arbitrary pressures, load and support conditions. The whole interpolation is built with regard to the natural neighbor nodes and Voronoi tessellation of the given point.FindingsThe performance of NNGM is investigated in the deflection analysis of inflatable tubes and panels. The excellent agreement between the presented modeling and analytical results and also finite element solutions and experiment are observed.Originality/valueDespite the wide usage of NNGM in many engineering problems, this comparison shows the other aspect of application of NNGM in the deflection analysis of inflatable structures, not previously examined.

Plasma induced by resonance enhanced multiphoton ionization in inert gas

We present a detailed model for the evolution of resonance enhanced multiphoton ionization (REMPI) produced plasma during and after the ionizing laser pulse in inert gas (argon, as an example) at arbitrary pressures. Our theory includes the complete process of the REMPI plasma generation and losses, together with the changing gas thermodynamic parameters. The model shows that the plasma expansion follows a classical ambipolar diffusion and that gas heating results in a weak shock or acoustic wave. The gas becomes involved in the motion not only from the pressure gradient due to the heating, but also from the momentum transfer from the charged particles to gas atoms. The time dependence of the total number of electrons computed in theory matches closely with the results of coherent microwave scattering experiments.

Examining the Accuracy of Ideal Adsorbed Solution Theory without Curve-Fitting Using Transition Matrix Monte Carlo Simulations

Ideal adsorbed solution theory (IAST) is a well-known approach to predicting multicomponent adsorption isotherms in microporous materials from experimental or simulation data for single-component adsorption. A limitation in practical applications of IAST is that useful calculations often require extrapolation of fitted single-component isotherms beyond the range for which data are available. We introduce a molecular simulation approach in which the intrinsic accuracy of IAST can be examined in a context that avoids any need to perform curve fitting with single-component data. Our approach is based on using transition matrix Monte Carlo to define single-component adsorption isotherms for arbitrary bulk-phase pressures from a single simulation. We apply our approach to several light gas mixtures in silica zeolites and a carbon nanotube to examine the intrinsic accuracy of IAST for these model systems.

The problem of a self-consistent description of the equilibrium distribution of particles in three states of aggregation

The possibility of unified self-consistent calculations of equilibrium distributions of molecules in three states of aggregation within the framework of the lattice gas model is considered. The corresponding approach was generalized to arbitrary pressures with including the compressibility of lattice structures. Closed equations were obtained for calculating thermodynamic functions (including an equation for the chemical potential of mixture components) in the continuum quasi-chemical approximation. Their use ensures equally accurate calculations of interphase equilibria in gas-liquid-solid systems and the determination of the triple and critical points. Possibilities for simplifying the equations by passing to the effective pair interaction potential, which takes into account averaged vibrations and volume accessible to the translational motion of molecules of commensurate sizes, are considered.

Effect of pressure on electrophoretic mobility of polystyrene latex particles.

A capillary electrophoresis system that can apply arbitrary helium gas pressures at both inlet and outlet reservoirs was constructed. The system was used to investigate the effect of pressure on electrophoretic behavior of polystyrene latex particles. The electrophoretic mobility of latex particles was increased with the application of pressure (< 3.0 kgf/cm2). The shrinkage of particle diameter under pressurization was observed using a microscope, however, the magnitude of shrinkage was not enough to explain the increase in electrophoretic mobility. Therefore, the application of pressure might increase the electric charge of the latex particle. Since methanol inhibited the enhancement in the electrophoretic mobility of the latex particles, water might play an important role in increasing mobility.

Correlation Equations for Predicting the Temperature Depression in Boiling of Aqueous Solutions of Nonvolatile Substances

Three-constant correlation equations describing the boiling point of aqueous solutions of non-volatile substances and temperature depression in boiling of the solutions under normal and arbitrary pressures are considered. The three constants appearing in the correlation equations are tabulated for aqueous solutions of 19 nonvolatile substances, and formulas for determining these constants for other aqueous solutions of nonvolatile substances from experimental data are presented.

A SYMMETRIC FORMULATION OF COUPLED BEM/FEM IN SOLVING RESPONSES OF SUBMERGED ELASTIC STRUCTURES FOR LARGE DEGREES OF FREEDOM

This work presents a symmetric formulation for the coupling of boundary element method (BEM) with finite element method (FEM) to compute responses of submerged elastic structures in a heavy acoustic medium. The acoustic loading derived from BEM is formulated in a symmetric complex matrix. The symmetry of the acoustic loading matrix is proven by an acoustic reciprocal principle, which relate two sets of arbitrary surface normal velocities and surface pressures in terms of surface integrals. The structural equation is represented by FEM. The fact that the acoustic loading and the structural equation are symmetric allows us to take the storage and computational advantages of the banded matrix which has been widely used in conventional finite element methods. Consequently, the computational efficiency of the proposed coupled FEM/BEM is significantly increased. The proposed method involving 20 000 degrees of freedom can be implemented on a personal computer. Numerical results are verified by analytical solutions of a constant thickness spherical shell subject to a point alternating force as well as the previously published variational solution of a constant thickness spheroidal shell excited by a concentrated force.

Magnetic Dipole Equilibrium Solution at Finite Plasma Pressure

A realistic equilibrium with finite plasma pressure is derived for a plasma confined by the magnetic field of a point dipole. The low and high pressure forms of the solution are explicitly displayed. The energy principle is used to demonstrate the interchange stability of the equilibrium solution for arbitrary pressures and shows that it remains stable as the plasma pressure increases.

Considerations of defect equilibria in high temperature proton-conducting cerates

Acceptor doped perovskites such as strontium cerate form a variety of point defects through reaction with surrounding gases at high temperature, namely protons by dissolution of water vapour, electron holes by dissolution of oxygen and electrons by loss of oxygen. The defect equilibria can be described by three equilibrium constants coupled with electroneutrality and site conservation constraints. This work describes a numerical solution of these equations for arbitrary oxygen and water vapour partial pressures, without the need to neglect minority defects. It further examines the charge compensation mechanisms that dominate under the different regimes and their implications for transport properties.

Microphase segregation in bridging polymeric brushes: Regular and singular phase diagrams

A mean-field theory of deformation-induced microphase segregation in bridging polymeric brushes anchored to two parallel surfaces is presented. Models with isotropic and orientation-dependent liquid-crystalline interactions between segments are considered. For the first model, the problem is similar to that of classical liquid-vapor phase separation, and the phase diagram in the P-T plane has a line of first-order transitions terminating at the critical point. We show that the critical pressure is negative implying that a free brush tethered only to one surface always exists at supercritical conditions and hence cannot undergo the collapse phase transition. In the second model, the free energy density depends on two coupled order parameters, one related to segment density and the other to the orientational order, which strongly modifies the phase behavior. Depending on the grafting density the system is described by a phase diagram of a regular or a singular type. In the regular phase diagram the first-order transition line terminates at the critical point. In a singular diagram, the first-order transition line extends to infinity; the critical point corresponds to infinite pressure so that the system undergoes the phase transition at arbitrary external pressures. Regular phase diagrams correspond to dense grafting, and singular ones to sparse grafting. The change from a regular phase behavior to another occurs at a certain marginal value of the grafting density. On approaching this value the critical point on the regular diagram moves to infinity, logarithmically with the deviation from the critical grafting density. We relate the analytical properties of the free energy density as a function of the segment concentration to the type of the phase diagram and the shape of the coexistence curve in the temperature- concentration plane.

Microphase segregation in bridging polymeric brushes: Regular and singular phase diagrams

A mean-field theory of deformation-induced microphase segregation in bridging polymeric brushes anchored to two parallel surfaces is presented. Models with isotropic and orientation-dependent liquid-crystalline interactions between segments are considered. For the first model, the problem is similar to that of classical liquid-vapor phase separation, and the phase diagram in the P-T plane has a line of first-order transitions terminating at the critical point. We show that the critical pressure is negative implying that a free brush tethered only to one surface always exists at supercritical conditions and hence cannot undergo the collapse phase transition. In the second model, the free energy density depends on two coupled order parameters, one related to segment density and the other to the orientational order, which strongly modifies the phase behavior. Depending on the grafting density the system is described by a phase diagram of a regular or a singular type. In the regular phase diagram the first-order transition line terminates at the critical point. In a singular diagram, the first-order transition line extends to infinity; the critical point corresponds to infinite pressure so that the system undergoes the phase transition at arbitrary external pressures. Regular phase diagrams correspond to dense grafting, and singular ones to sparse grafting. The change from a regular phase behavior to another occurs at a certain marginal value of the grafting density. On approaching this value the critical point on the regular diagram moves to infinity, logarithmically with the deviation from the critical grafting density. We relate the analytical properties of the free energy density as a function of the segment concentration to the type of the phase diagram and the shape of the coexistence curve in the temperature- concentration plane.

Ellipsomicroscopy for surface imaging: A novel tool to investigate surface dynamics

This article focuses on the technical issues of imaging of dynamic adsorbate pattern formation on platinum surfaces using laser light to illuminate the area of interest. In particular, ellipsomicroscopy for surface imaging (EMSI) is a powerful tool to follow spatio-temporal patterns of adsorbate layers on catalyst surfaces at arbitrary pressures. This novel method is uniquely sensitive to submonolayer coverages of adsorbates. It expands the range of observable pressure conditions by many orders of magnitude, thus bridging the pressure gap in imaging surface reactions. EMSI is a versatile technique that opens new avenues of potential applications to resolve dynamic surface processes, such as adsorbate diffusion or coating formation.