Search results

The purpose of this study is to measure the mass diffusion coefficient of nitrogen in jet fuel using digital holography interferometry for cost-effective designing and modeling of the aircraft tank inerting system.

The mass diffusion coefficients of N₂ in RP-3 and RP-5 jet fuels were measured by digital holography interferometry at temperatures ranging from 278.15 to 343.15 K. The Arrhenius equation is used to adequately describe the relationship between mass diffusion coefficients and temperature. The viscosities of RP-3 and RP-5 jet fuels were also measured to examine the accuracy of the Stokes–Einstein model in calculating mass diffusion coefficients.

As temperature increases from 278.15 to 343.15 K, the mass diffusion coefficients increase 4.23-fold for N₂ in RP-3 jet fuel and 5.13-fold for N₂ in RP-5 jet fuel. The value of Dµ/T is not constant as the Stokes–Einstein equation expressed, but is a weak linear function of temperature.

A more accurate diffusion model is proposed by fitting the measured Dµ/T with the temperature and calculating the mass diffusion coefficients of N₂ in RP-3 and RP-5 jet fuels within 10 per cent relative deviation.

A measurement system for mass diffusion coefficients of N₂ in RP-3 and RP-5 jet fuels was constructed based on the digital holography interferometry. The mass diffusion coefficient can be expressed by a uniform polynomial function of temperature and viscosity.

The purpose of this paper is to develop a new transversal method of lines for one-dimensional reaction–diffusion equations that is conservative and provides piecewise–analytical solutions in space, analyze its truncation errors and linear stability, compare it with other finite-difference discretizations and assess the effects of the nonlinear diffusion coefficients, reaction rate terms and initial conditions on wave propagation and merging.

A conservative, transversal method of lines based on the discretization of time and piecewise analytical integration of the resulting two-point boundary-value problems subject to the continuity of the dependent variables and their fluxes at the control-volume boundaries, is presented. The method provides three-point finite difference expressions for the nodal values and continuous solutions in space, and its accuracy has been determined first analytically and then assessed in numerical experiments of reaction-diffusion problems, which exhibit interior and/or boundary layers.

The transversal method of lines presented here results in three-point finite difference equations for the nodal values, treats the diffusion terms implicitly and is unconditionally stable if the reaction terms are treated implicitly. The method is very accurate for problems with the interior and/or boundary layers. For a system of two nonlinearly-coupled, one-dimensional reaction–diffusion equations, the formation, propagation and merging of reactive fronts have been found to be strong function of the diffusion coefficients and reaction rates. For asymmetric ignition, it has been found that, after front merging, the temperature and concentration profiles are almost independent of the ignition conditions.

A new, conservative, transversal method of lines that treats the diffusion terms implicitly and provides piecewise exponential solutions in space without the need for interpolation is presented and applied to someone.

The purpose of this paper is to develop a model that allows determining the boron concentration profile in silicon based on duration and temperature of the diffusion process.

The model was developed on the basis of the Fick’s second law, which is fundamental for describing the diffusion process. The explicit scheme of the finite difference method was used in the conducted simulations. Results of measurements made using the secondary ion mass spectrometry (SIMS) were used as template dopant concentration profiles. Solution of boric acid in ethanol is the dopant source for which this model was developed.

Based on the conducted simulations, it was proposed that besides the influence of electric field of ionized dopants, which is already described in literature, an appropriate factor reflecting the influence of the threshold concentration on the coefficient of diffusion of boron in silicone should also be introduced.

The developed model enables determination of the boron concentration profile in silicon consistent with the results of SIMS measurements. A factor taking into account the influence of threshold concentration on the coefficient of diffusion was introduced. The influence of concentration of boric acid in the dopant solution on the concentration profile was also considered.

This paper aims to study the mechanism of hydrogen embrittlement in 12Cr2Mo1R(H) steel, which will help to provide valuable information for the subsequent hydrogen embrittlement research of this kind of steel, so as to optimize the processing technology and take more appropriate measures to prevent hydrogen damage.

The hydrogen diffusion coefficient of 12Cr2Mo1R(H) steel was measured by the hydrogen permeation technique of double electrolytic cells. Moreover, the influence of hydrogen traps in the material and experimental temperature on hydrogen diffusion behavior was discussed. The first-principles calculations based on density functional theory were used to study the occupancy of H atoms in the bcc-Fe cell, the diffusion path and the interaction with vacancy defects.

The results revealed that the logarithm of the hydrogen diffusion coefficient of the material has a linear relationship with the reciprocal of temperature and the activation energy of hydrogen atom diffusion in 12Cr2Mo1R(H) steel is 23.47 kJ/mol. H atoms stably exist in the nearly octahedral interstices in the crystal cell with vacancies. In addition, the solution of Cr/Mo alloy atom does not change the lowest energy path of H atom, but increases the diffusion activation energy of hydrogen atom, thus hindering the diffusion of hydrogen atom. Cr/Mo and vacancy have a synergistic effect on inhibiting the diffusion of H atoms in α-Fe.

This article combines experiments with first-principles calculations to explore the diffusion behavior of hydrogen in 12Cr2Mo1R(H) steel from the macroscopic and microscopic perspectives, which will help to establish a calculation model with complex defects in the future.

This paper aims to present development and application of the Bayesian inverse approach for retrieving parameters of non-linear diffusion coefficient based on the integral information.

The Bayes formula was used to construct posterior distribution of the unknown parameters of non-linear diffusion coefficient. The resulting aposteriori distribution of sought parameters was integrated using Markov Chain Monte Carlo method to obtain expected values of estimated diffusivity parameters as well as their confidence intervals. Unsteady non-linear diffusion equation was discretised with the Global Radial Basis Function Collocation method and solved in time using Crank–Nicholson technique.

A number of manufactured analytical solutions of the non-linear diffusion problem was used to verify accuracy of the developed inverse approach. Reasonably good agreement, even for highly correlated parameters, was obtained. Therefore, the technique was used to compute concentration dependent diffusion coefficient of water in paper.

An original inverse technique, which couples efficiently meshless solution of the diffusion problem with the Bayesian inverse methodology, is presented in the paper. This methodology was extensively verified and applied to the real-life problem.

The purpose of this paper is to develop a new finite-volume method of lines for one-dimensional reaction-diffusion equations that provides piece-wise analytical solutions in space and is conservative, compare it with other finite-difference discretizations and assess the effects of the nonlinear diffusion coefficient on wave propagation.

A conservative, finite-volume method of lines based on piecewise integration of the diffusion operator that provides a globally continuous approximate solution and is second-order accurate is presented. Numerical experiments that assess the accuracy of the method and the time required to achieve steady state, and the effects of the nonlinear diffusion coefficients on wave propagation and boundary values are reported.

The finite-volume method of lines presented here involves the nodal values and their first-order time derivatives at three adjacent grid points, is linearly stable for a first-order accurate Euler’s backward discretization of the time derivative and has a smaller amplification factor than a second-order accurate three-point centered discretization of the second-order spatial derivative. For a system of two nonlinearly-coupled, one-dimensional reaction-diffusion equations, the amplitude, speed and separation of wave fronts are found to be strong functions of the dependence of the nonlinear diffusion coefficients on the concentration and temperature.

A new finite-volume method of lines for one-dimensional reaction-diffusion equations based on piecewise analytical integration of the diffusion operator and the continuity of the dependent variables and their fluxes at the cell boundaries is presented. The method may be used to study heat and mass transfer in layered media.

In the textile industry, liquid ammonia treatment is an important way to modify the structure of natural fibers. The purpose of this paper is to reveal the diffusion behaviors of liquid ammonia in cellulose.

To analysis the diffusion behaviors of liquid ammonia in cellulose, the cellulose model and the system of ammonia and cellulose are built. Infrared spectrum is carried out to test the model of cellulose, which is found to agree with experiment. Diffusion coefficients, free volume and hydrogen bonds are discussed to explain diffusion behaviors.

The results demonstrate that diffusion coefficients and free volume of systems rise with increasing temperature. The diffusion coefficients of ammonia are larger than those of water, a result in agreement with free volume. To understand the mechanism of diffusion, the numbers of hydrogen bonds are tracked. It is found that without ammonia, intrachain hydrogen bonds decrease with the increase of temperature, which indicate that the structural stability of cellulose is deteriorated. And the increased interchain hydrogen bonds show that swelling properties of cellulose become better with the increase of temperature. After ammonia treatment, the numbers of intrachain hydrogen bonds remain stable, indicating that the structure stability of cellulose chain is maintained. But, there is a substantial rupture of interchain hydrogen bonds, ammonia molecule destroys the hydrogen bond network between the original cellulose molecular chains, which intensifies the activity of cellulose molecular chains and enlarges the distance between cellulose molecular chains, showing good swelling properties.

The research findings give a detailed information about the diffusion behaviors of liquid ammonia in cellulose, which provide the theoretical evidence for liquid ammonia treatment.

This paper aims to study the diffusion of Zn, Ni and Sn in the liquid state during the reflow ageing of the Sn-Zn solder above its melting point on an Ni/Cu substrate in relation to the formation of intermetallic compounds (IMCs).

The Sn-Zn solder is reflowed on Ni/Cu substrates and is aged at 503 K. The formation of IMCs and their composition is characterized using scanning electron microscopy (SEM) and energy-dispersive X-ray spectroscopy (EDX). Diffusion coefficients and diffusion distances of Zn, Ni and Sn in the liquid state during reflow and ageing are theoretically calculated. Both experimental and theoretical behaviours for Ni and Zn diffusions are compared.

Calculations show a linear increment in the liquid-state diffusion coefficients of Ni, Zn and Sn in the solder matrix with a rise in temperature, but they remained constant during ageing. However, diffusion distances increased slowly with temperature but manifold with ageing time. The experimental results revealed segregation of Zn and Ni at the interface in the as-reflow aged specimens. The Zn was concentrated at the solder–substrate interface and it reacted with Ni diffusing from the substrate to form Ni-Sn-Zn IMCs. The rapid diffusion of Zn and Ni with the increase in ageing time increased their atomic concentrations in the IMCs against the reduction in Sn concentration owing to a comparatively slower diffusion.

The novelty of the paper is the detailed study of theoretical diffusion of Zn, Sn and Ni in the liquid state during reflow ageing of Sn-Zn above its melting points on a Ni/Cu substrate. This is compared with values obtained experimentally and related to the mechanisms of IMC formation.

The purpose of this paper is to evaluate the efficacy and kinetics along with diffusion properties of a new source of natural dye obtained from leaves and fine stems of the Sesbania aculeata plant, using metallic mordants for cotton dyeing.

The approach followed in this work is to conduct experiments with the application of the natural dye obtained from Sesbania aculeata plant and to study the kinetics, dye uptake and the diffusion properties of this dye.

Sesbania aculeata with simultaneous mordanting with different metal mordants imparted shades which varied from cream to light brown to dark brown in case of aqueous extract. The different mordants used not only changed the hue colour and K/S values but also L* and brightness index values. The results of fastness properties of the dyes were found to vary from fair to good. The percentage dye exhaustion values varied with different mordants. The dye uptake value increased with time and reached its saturation limit after 4 hours of dyeing. In the absence of mordants, the diffusion coefficient values increased with increase in the temperature. In the presence of mordants, the diffusion process appears to slow down, which could be attributed to the binding effects of mordants.

The extraction and dyeing process of Sesbania aculeata plant is less tedious and time consuming compared to the other sources of natural dyes.

Sesbania aculeata is relatively easier to grow and does not require much tending operations. Thus, it promises to be an affordable source of natural dye. If this dye is commercialised, it will help to generate sustainable employment and income for the farmers in rural and sub-urban areas. This could be both for dyeing and for non-food crop farming.

An advantageous feature of this plant, in contrast to the other natural dyes based on vegetable and fruit sources, is that its usage in making the natural dye does not result in any wastage of an otherwise highly commercial product. The current experimental study on a new source of natural dye would be a significant contribution to the existing database of knowledge regarding the kinetics and diffusion properties of natural dyes. There are several reported studies in the literature pertaining to the application of natural colourants and evaluation of their dyeing properties on various fibers. However, relatively fewer studies exist on the kinetic and exhaustion aspects. Thus, the current study would help to develop a set of predictable settings for application of natural dyes on various textiles.

The purpose of this paper is to present a diffusion-controlled healing model for predicting fused deposition modeling (FDM) bond strength between layers (z-axis strength).

Diffusion across layers of an FDM part was predicted based on a one-dimensional transient heat analysis of the interlayer interface using a temperature-dependent diffusion model determined from rheological data. Integrating the diffusion coefficient across the temperature history with respect to time provided the total diffusion used to predict the bond strength, which was compared to the measured bond strength of hollow acrylonitrile butadiene styr (ABS) boxes printed at various processing conditions.

The simulated bond strengths predicted the measured bond strengths with a coefficient of determination of 0.795. The total diffusion between FDM layers was shown to be a strong determinant of bond strength and can be similarly applied for other materials.

Results and analysis from this paper should be used to accurately model and predict bond strength. Such models are useful for FDM part design and process control.

This paper is the first work that has predicted the amount of polymer diffusion that occurs across FDM layers during the printing process, using only rheological material properties and processing parameters.