Azimuthally dependent radiative transfer in a non-homogeneous cylindrical medium

This work applies the discrete-ordinate method (DOM) to study azimuthally dependent radiative transfer in a two-dimensional cylindrical medium with spatially varying properties. Product angular quadratures are selected to generate discrete-ordinate approximations. The validity of the present DOM scheme is examined by comparing the present results with the results available in the literature. The effects of the optical thickness and the spatially varying extinction coefficient, scattering albedo and coefficients of the phase function are investigated.     

A simulation model of a high-capacity methane adsorptive storage system

A two-dimensional model is developed to describe the hydrodynamics, heat transfer and adsorption phenomena associated with the adsorptive storage of natural gas (NG) in cylindrical reservoirs. Intraparticle and film resistances to both heat and mass transfer are neglected. In the momentum equation, Ergun's law is considered locally valid and is extended to two dimensions. These assumptions are fully justified in the paper. Numerical results are presented concerning the pressurization and blowdown of an ultra-lightweight 50 litre cylinder, commercially available for the storage of compressed NG, if it were filled with an activated carbon having a good adsorptive storage capacity. A simple formula is also proposed to predict the filling times for fast charges. The predicted temperature changes in the packed-bed are in good agreement with those reported in the literature for an experimental charge/discharge.     

Contact angles of drops on curved superhydrophobic surfaces

Superhydrophobic surfaces have contact angles that exceed 150 degrees and are known to reduce surface fouling, protect surfaces, and improve liquid-liquid separations. Electrospun sub-micron fiber mats can perform as superhydrophobic surfaces. Superhydrophobic behavior is typically measured on planar surfaces, whereas applications may require curved surfaces. This paper discuses the measurement of water contact angles of fiber mats formed on cylindrical surfaces to create superhydrophobic behavior on curved surfaces. Equations are derived that relate the radius of curvature of spherical and cylindrical surfaces and drop size to the observed contact angle on the curved surfaces. Calculations from the equations agree well with experimental observations on spherical surfaces reported in literature and on cylindrical surfaces created in our lab.     

在确定的热力学状态下测量气体导热系数与黏度

气体的导热系数和黏度是重要的热物性参数,其数值大小取决于所处的热力学状态。在目前的导热系数和黏度主要测量方法中,待测工质在测量时需经历非定常的过程或处于具有物性梯度的非平衡态之下,使得待测工质的物性在时间或者空间上不处于一个确定的热力学状态。本文利用圆柱定程干涉法,通过分析气体导热系数和黏度导致的声波能量耗散,结合气体输运理论中对稀疏气体的描述,探索了在确定的热力学状态下同时测量气体导热系数和黏度的方法,并以氩(Ar)为例进行了实验验证。测量结果与已有文献一致性较好,初步证实了方法的可行性。     

The Donnan potential-surface potential relationship for a cylindrical soft particle in an electrolyte solution

Transcendental equations, which avoid integration of the nonlinear Poisson-Boltzmann equations, are presented for obtaining the relationship between the Donnan potential and surface potential of a cylindrical soft particle (i.e., a polyelectrolyte-coated cylindrical particle) in a symmetrical electrolyte solution. Numerical results obtained by the present method are in excellent agreement with exact results obtained by solving the nonlinear cylindrical Poisson-Boltzmann equations both inside and outside the polyelectrolyte layer.     

Ribbon phases in surfactant systems Comparisons between experimental results and predictions of a theoretical model

Ribbon phases consist of long cylindrical aggregates that have non-circular normal sections. We have recently pointed out that scattering data for a large number of different intermediate ribbon phases of lower than hexagonal symmetry found in ionic surfactant systems indicate that these phases have a structure possessing a centred rectangular symmetry. In this communication, we have investigated the aggregate dimensions for the phases with cylindrical aggregates, i.e., the hexagonal phases and the centred rectangular ribbon phases. Previously published phase diagrams, small angle X-ray and neutron scattering data and ²HNMR data for these phases in different systems have been used for this purpose. The results are that the axial ratios of the aggregates increase when the temperature decreases, when the surfactant concentration increases, and when the average surfactant charge decreases. Models that semi-quantitatively describe the thermodynamics of the micellar, hexagonal and lamellar phases, which are based on the Poisson-Boltzmann cell model approach, have previously been presented in the literature. We have extended these models to treat also the ribbon phases. The results from the calculations show the same trends with respect to changes in the dimensions of the non-circular aggregates upon changes in temperature, surfactant concentration and average surfactant charge, as those obtained experimentally. Theoretically calculated phase diagrams with ribbon phases are also presented. Based on the predictions of the model and some previously published experimental data for hexagonal phases, it is proposed that the formation of non-circular, cylindrical aggregates is a general property of single-chain, ionic surfactant/water systems, and that these aggregates in general pack on hexagonal lattices. The normal sections of these aggregates are circular on average, on account of the fact that the degree of deformation and the orientation of deformation changes along the axis of the aggregates and with time. Only for some systems, temperatures and surfactant concentrations do the asymmetric aggregates line up and ribbon phases with centred rectangular symmetry are obtained. The driving mechanisms for the transition from the hexagonal phase with asymmetric (fluctuating) cylinders and further to the centred rectangular phase with asymmetric (stiff) cylinders is also discussed. It is argued that this phase transition is of the first order.     

The simple procedure of the calculation of diffusion coefficient for adsorption on spherical and cylindrical adsorbent particles--experimental verification

A recently proposed simplified procedure for calculating the effective diffusion coefficient (D(e)) for adsorption on spherical and cylindrical adsorbent particles is now experimentally verified for adsorption systems: paracetamol-activated carbon. Adsorption kinetics was measured on nine carbons; for seven of them, measurements were taken at three temperatures. Since for adsorption on spherical adsorbent particles the approximate methods of D(e) calculation are already available in literature, only two systems have been studied, and the results of the new procedure are compared with those calculated from previously published methods. However, for cylinders the proposed method is the first simplification of this kind available in literature, thus, we focus our attention on the comparison of the results of the analytical approach with the simplified approaches for the systems where an adsorbent possesses cylindrically shaped granules. It is shown that for adsorption on spherical as well as on cylindrical adsorbent granules the proposed simplification leads to satisfactory results that, taking into account an experimental error, are practically the same as those obtained from exact time-consuming and mathematically advanced numerical fitting procedure. It is also shown that, for the studied carbons, the surface diffusion process dominates, and this explains the recently obtained correlation between the effective diffusion coefficient and the enthalpy of carbon immersion in water.     

Design of a high-sensitivity negative ion source time-of-flight mass analyzer assembly created by cylindrical electrodes with a common axis

The new design incorporates the negative ion source and the mass analyzer, both constructed from cylindrical electrodes. The ion source is formed by three gridded cylindrical electrodes: a pulsed grid, the intermediate grid and the final accelerating grid. During a first time lapse, the electrons penetrate through the pulsed grid into the retarding field between this grid and the intermediate grid. The electrons are turning at some depth inside this intergrid space, where the attachment to neutral molecules most probably occurs. Next, the pulsed grid becoming strongly negative and ions are extracted towards the final acceleration grid. The ions from the cylindrical surface where they were created concentrate on the common axis of the electrodes (lateral focusing). The source lateral and time focus are coincident. A cylindrical electrostatic mirror is fitted to the source. The design, with a single stage, ensures also lateral focusing of the ions diverging from the common axis of the electrodes. The mirror electric and geometric parameters were selected to ensure both lateral and time focusing on the final detector with subsequent high luminosity. The basic parameters of the specific negative ion source time-of-flight mass analyzer design proposed here, are ion source final acceleration, intermediate, pulsed cylindrical grid radii 10, 20 and 30 mm, respectively, electrostatic mirror earthed grid and ion turning points surface radii 0.6 and 0.8 m, respectively. Ion packet smearing by the ion energy spread (resulting from the initial electron energy spread as electrons are turning at different depths inside the ionization region, from the moment when ions were created, being accelerated towards the pulsed grid during ionization) and by the turnaround time inside the cylindrical field was accounted for. Maintaining very high sensitivity, a resolution of the order of 100 is expected.     

Electrophoretic mobility of a charged cylindrical colloidal particle covered with an ion-penetrable uncharged polymer layer

Expressions are derived for the electrophoretic mobility of a cylindrical charged colloidal particle carrying a low zeta potential covered with an ion-penetrable uncharged polymer layer in an electrolyte solution. These expressions involve numerical integration of modified Bessel functions but are easily calculable with Mathematica. The obtained mobility expressions are a modification of Henry's mobility formula for a cylindrical particle taking into account the presence of the uncharged polymer layer.     

Experimental validation of some thermal neutron self-shielding calculation methods for cylindrical samples in INAA

Neutron self-shielding has been a factor of concern in the history of Instrumental Neutron Activation Analysis. When the sample to be analyzed cannot be made small enough in size and/or sufficiently diluted, this undesired phenomenon must be accounted for. Several analytical, semi-empirical and computational methods for estimating the thermal neutron self-shielding effects have been extensively discussed in the literature and this work aims at the experimental validation of some of these methods by neutron irradiation of cylindrical samples containing strong thermal neutron absorbers. The accuracy and the relative differences in the results between these methods are discussed for cylindrical samples with up to 40% thermal self-shielding, showing that a semi-empirical sigmoidal function can be more accurate in modeling this effect than other exact algorithms, where a maximum 2% relative difference to the experimental values was obtained.     

Unidimensional Approximation of the Diffuse Electrical Layer in the Inner Volume of Solid Electrolyte Grains in the Absence of Background Ions

In this paper we continue working on our theory of electrical double layers resulting exclusively from dissociation of a solid electrolyte, which we previously proposed as a medium for catalytic interaction between solid cellulose and solid acid catalysts of hydrolysis. Two theoretical unidimensional models of the inner grain volume are considered: an infinitely long cylindrical pore, and a gel electrolyte near a grain outer surface. Despite the model simplicity, the predictions for the cylindrical pore case are in semi-quantitative agreement with literature data on electroosmotic experiments, adequately explaining high proton selectivity of sulfonic membranes, and decline of such selectivity at high background acid concentration. The gel model predicts less concentrated diffuse layer in comparison to electrolytes with impenetrable skeleton (e. g., sulfonated carbons). This suggests limited suitability of gel electrolytes as catalysts if a substrate cannot diffuse into the gel bulk and the reaction is thereby spatially limited to the near-surface region, for example if a substrate is solid like aforementioned cellulose.     

Model for thermal conductivity of composites with carbon nanotubes

This paper presents a model for evaluation of effective thermal conductivity for the composites with carbon nanotubes (CNT) having log-normal function of distribution of CNT, with direct effect over depolarization factor. The CNT are considered having cylindrical shape with L/d ratio very high. The model parameters are calculated in function of the data from literature. The influence of volume fraction of reinforced materials, of the aspect ratio of the particles included and of the ratio of the two thermal conductivities is presented.     

Electrical potential in a cylindrical double layer: a functional theory approach

Employing an iterative method in functional theory, the electrical potential distribution for the case of a cylindrical surface is solved. Although the analytical result derived is of an iterative nature, the second-order solution is found to be sufficiently accurate under conditions of practical significance. For the case of constant surface potential, the radius and the surface potential of a cylindrical surface can be estimated based on the extreme of the electrical potential distribution. The effects of the key parameters, including the number and the valence of the ions on a surface, the length of a particle, the relative permittivity of the liquid phase, the temperature, and the concentration of electrolyte on the surface potential, are examined. The general behavior of these effects is similar to that for a spherical surface, except that the surface potential of a cylindrical surface is independent of the electrolyte concentration. The present approach is also applicable to the case where a cylindrical surface remains at a constant charge density.     

Motion of a spherical particle in a cylindrical channel using arbitrary Lagrangian-Eulerian method

A finite element particle transport model, consisting of Navier-Stokes and continuity equations defined in arbitrary Lagrangian-Eulerian (ALE) kinematics, is employed to describe the motion of a rigid uncharged spherical particle in a cylindrical channel of uniform cross-section. The wall correction factors for the spherical particle moving with a fluid confined in an infinitely long cylindrical channel, as well as in finite length channels are presented. Two finite channel effects are considered, namely, motion of the particle at the entrance and exit of an open channel, and the motion of a particle toward the capped end of the channel. The numerical model demonstrates good agreement with many existing analytical results for infinite channels in the Stokes flow regime. Simple correlations for the hindrance factors are presented.     

On the measurement of the fracture resistance of polyacrylamide hydrogels by wire cutting tests

The applicability of wire cutting in determining the fracture resistance, G_c, of polyacrylamide (PAAm) hydrogels, with different polymer contents and mechanical stiffness, was investigated. The various gels were synthesized both in the form of cylindrical and bar-shaped samples. Following the experimental scheme proposed in literature for wire cutting, each hydrogel, in the form of cylindrical specimen, was subjected to wire cutting with wires of different diameters. For each hydrogel, G_c was also separately measured by more conventional fracture tests on notched specimens prepared from the bar-shaped samples.The results demonstrated that, although G_c of the PAAm hydrogels here examined could not be evaluated by the direct application of the simple scheme proposed in literature, wire cutting is a promising approach for the measurement of the fracture resistance of chemical gels with relatively high stiffness, also in consideration of its proven experimental simplicity.     

Integral equation theory for hard spheres confined on a cylindrical surface: anisotropic packing entropically driven

The structure of two-dimensional (2D) hard-sphere fluids on a cylindrical surface is investigated by means of the Ornstein-Zernike integral equation with the Percus-Yevick and the hypernetted-chain approximation. The 2D cylindrical coordinate breaks the spherical symmetry. Hence, the pair-correlation function is reformulated as a two-variable function to account for the packing along and around the cylinder. Detailed pair-correlation function calculations based on the two integral equation theories are compared with Monte Carlo simulations. In general, the Percus-Yevick theory is more accurate than the hypernetted-chain theory, but exceptions are observed for smaller cylinders. Moreover, analysis of the angular-dependent contact values shows that particles are preferentially packed anisotropically. The origin of such an anisotropic packing is driven by the entropic effect because the energy of all the possible system configurations of a dense hard-sphere fluid is the same. In addition, the anisotropic packing observed in our model studies serves as a basis for linking the close packing with the morphology of an ordered structure for particles adsorbed onto a cylindrical nanotube.     

Symmetric diblock copolymers in nanopores: Monte Carlo simulations and strong-stretching theory

We have performed lattice Monte Carlo simulations to study the self-assembled morphology of symmetric diblock copolymers in nanopores. The pore diameter and surface preference are systematically varied to examine their effects on the chain conformations, structures of various morphologies, and their phase transition. Various ensemble-averaged profiles and quantities are used to provide detailed information about the system. The simulation results are also compared with the predictions of a strong-stretching theory commonly used in the literature. Such comparisons reveal the deficiencies of this theory in describing the morphologies under cylindrical confinement, and call for further theoretical studies using more accurate formalisms.     

An assessment of a microwave-induced plasma generated in argon with a cylindrical TM010 cavity as an excitation source for emission spectrometric analysis of solutions

A cross-flow pneumatic nebulizer with spray chamber was directly coupled to a microwave-induced plasma (MIP) generated with a cylindrical TMO₀₁₀ cavity in argon flowing through an alumina capillary. The detection limits of 15 elements were determined with 23 spectral lines and the interference effect of KCl on these spectral lines was measured. The results were compared with those reported in the literature for MIP systems based on conventional or newly designed cavities, and incorporating desolvation facilities. A comparison was also made with an inductively coupled plasma (ICP) and a capacitively coupled microwave plasma (CMP) for which the reported results were obtained under spectrometric conditions that closely matched those used in the present work and for which the rate of sample injection into the plasma was approximately the same as that used here.     

Self-Consistent Analysis of a Helium Plasma in a Cylindrical Hollow Cathode

The helium plasma in a cylindrical, axially symmetric direct current hollow cathode discharge is theoretically investigated. A self-consistent hybrid method is used to describe the radial behaviour of the plasma components and the electric field around the axial centre of the discharge. The hybrid method includes the solution of an equation system consisting of Poissons equation and fluid equations for electrons, ions and excited helium atoms. Using the electric field and excited atom densities obtained in this system, the space-dependent transport and collision rate coefficients of the electrons are obtained by a kinetic treatment of the electrons. This treatment is based on a powerful multi-term method for solving the inhomogeneous Boltzmann equation in cylindrical coordinates. The theoretical results obtained for a discharge current of some mA and a pressure of few Torr are compared with available experimental ones.