Search results for: diffusion equation

Authors: H. Namazi, H. T. N. Kuan

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Fick's first law relates the diffusive flux to the concentration field, by postulating that the flux goes from regions of high concentration to regions of low concentration, with a magnitude that is proportional to the concentration gradient (spatial derivative). It is clear that the diffusion of flux cannot be instantaneous and should be some time delay in this propagation. But Fick’s first law doesn’t consider this delay which results in some errors especially when there is a considerable time delay in the process. In this paper, we introduce a time delay to Fick’s first law. By this modification, we consider that the diffusion of flux cannot be instantaneous. In order to verify this claim an application sample in fluid diffusion is discussed and the results of modified Fick’s first law, Fick’s first law and the experimental results are compared. The results of this comparison stand for the accuracy of the modified model. The modified model can be used in any application where the time delay has considerable value and neglecting its effect reflects in undesirable results.

Keywords: Fick's first law, flux, diffusion, time delay, modified Fick’s first law

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Authors: Yasaman Tohidi, Rouzbeh Riazi, Shidvash Vakilipour, Masoud Mohammadi

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The objective of the present study is to numerically investigate the effect of CO₂ replacement of N₂ in air stream on the flame characteristics of the CH₄ turbulent diffusion flame. The Open source Field Operation and Manipulation (OpenFOAM) has been used as the computational tool. In this regard, laminar flamelet and modified k-ε models have been utilized as combustion and turbulence models, respectively. Results reveal that the presence of CO₂ in air stream changes the flame shape and maximum flame temperature. Also, CO₂ dilution causes an increment in CO mass fraction.

Keywords: CH4 diffusion flame, CO2 dilution, OpenFOAM, turbulent flame

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Authors: Anna Keuchenius

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Broadly speaking, scientific development is studied in either a qualitative manner with a focus on the behavior and interpretations of academics, such as the sociology of science and science studies or in a quantitative manner with a focus on the analysis of publications, such as scientometrics and bibliometrics. Both come with a different set of methodologies and few cross-references. This paper contributes to the bridging of this divide, by on the on hand approaching the process of scientific progress from a qualitative sociological angle and using on the other hand quantitative and computational techniques. As a case study, we analyze the diffusion of Granovetter's hypothesis from his 1973 paper 'On The Strength of Weak Ties.' A network is constructed of all scientists that have referenced this particular paper, with directed edges to all other researchers that are concurrently referenced with Granovetter's 1973 paper. Studying the structure and growth of this network over time, it is found that Granovetter's hypothesis is used by distinct communities of scientists, each with their own key-narrative into which the hypothesis is fit. The diffusion within the communities shares similarities with the diffusion of an innovation in which innovators, early adopters, and an early-late majority can clearly be distinguished. Furthermore, the network structure shows that each community is clustered around one or few hub scientists that are disproportionately often referenced and seem largely responsible for carrying the hypothesis into their scientific subfield. The larger implication of this case study is that the diffusion of scientific hypotheses and ideas are not the spreading of well-defined objects over a network. Rather, the diffusion is a process in which the object itself dynamically changes in concurrence with its spread. Therefore it is argued that the methodology presented in this paper has potential beyond the scientific domain, in the study of diffusion of other not well-defined objects, such as opinions, behavior, and ideas.

Keywords: diffusion of innovations, network analysis, scientific development, sociology of science

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Authors: Betim Bahtiri, B. Arash, R. Rolfes

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Epoxy-based materials are frequently exposed to high-humidity environments in many engineering applications. As a result, their material properties would be degraded by water absorption. A full characterization of the material properties under hygrothermal conditions requires time- and cost-consuming experimental tests. To gain insights into the physics of diffusion mechanisms, atomistic simulations have been shown to be effective tools. Concerning the diffusion of water in polymers, spatial trajectories of water molecules are obtained from molecular dynamics (MD) simulations allowing the interpretation of diffusion pathways at the nanoscale in a polymer network. Conventional MD simulations of water diffusion in amorphous polymers lead to discrepancies at low temperatures due to the short timescales of the simulations. In the proposed model, this issue is solved by using a combined scheme of autonomous basin climbing (ABC) with kinetic Monte Carlo and reactive MD simulations to investigate the diffusivity of water molecules in epoxy resins across a wide range of temperatures. It is shown that the proposed simulation framework estimates kinetic properties of water diffusion in epoxy resins that are consistent with experimental observations and provide a predictive tool for investigating the diffusion of small molecules in other amorphous polymers.

Keywords: epoxy resins, water diffusion, autonomous basin climbing, kinetic Monte Carlo, reactive molecular dynamics

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Authors: Eugene Benilov, Mikhail Benilov

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The Enskog-Vlasov (EV) equation is a widely used semi-phenomenological model of gas/liquid phase transitions. We show that it does not generally conserve energy, although there exists a restriction on its coefficients for which it does. Furthermore, if an energy-preserving version of the EV equation satisfies an H-theorem as well, it can be used to rigorously derive the so-called Maxwell construction which determines the parameters of liquid-vapor equilibria. Finally, we show that the EV model provides an accurate description of the thermodynamics of noble fluids, and there exists a version simple enough for use in applications.

Keywords: Enskog collision integral, hard spheres, kinetic equation, phase transition

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Authors: Abdulrahman Abdulrahman

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When the Manning equation is used, a unique value of normal depth in the uniform flow exists for a given channel geometry, discharge, roughness, and slope. Depending on the value of normal depth relative to the critical depth, the flow type (supercritical or subcritical) for a given characteristic of channel conditions is determined whether or not flow is uniform. There is no general solution of Manning's equation for determining the flow depth for a given flow rate, because the area of cross section and the hydraulic radius produce a complicated function of depth. The familiar solution of normal depth for a rectangular channel involves 1) a trial-and-error solution; 2) constructing a non-dimensional graph; 3) preparing tables involving non-dimensional parameters. Author in this paper has derived semi-analytical solution to Manning's equation for determining the flow depth given the flow rate in rectangular open channel. The solution was derived by expressing Manning's equation in non-dimensional form, then expanding this form using Maclaurin's series. In order to simplify the solution, terms containing power up to 4 have been considered. The resulted equation is a quartic equation with a standard form, where its solution was obtained by resolving this into two quadratic factors. The proposed solution for Manning's equation is valid over a large range of parameters, and its maximum error is within -1.586%.

Keywords: channel design, civil engineering, hydraulic engineering, open channel flow, Manning's equation, normal depth, uniform flow

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Authors: Jiahui You, Kyung Jae Lee

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Hydraulic fracturing fluid (HFF) is widely used in shale reservoir productions. HFF contains diverse chemical additives, which result in the dissolution and precipitation of minerals through multiple chemical reactions. In this study, a new pore-scale Darcy–Brinkman–Stokes (DBS) model coupled with Level Set Method (LSM) is developed to address the microscopic phenomena occurring during the iron–HFF interaction, by numerically describing mass transport, chemical reactions, and pore structure evolution. The new model is developed based on OpenFOAM, which is an open-source platform for computational fluid dynamics. Here, the DBS momentum equation is used to solve for velocity by accounting for the fluid-solid mass transfer; an advection-diffusion equation is used to compute the distribution of injected HFF and iron. The reaction–induced pore evolution is captured by applying the LSM, where the solid-liquid interface is updated by solving the level set distance function and reinitialized to a signed distance function. Then, a smoothened Heaviside function gives a smoothed solid-liquid interface over a narrow band with a fixed thickness. The stated equations are discretized by the finite volume method, while the re-initialized equation is discretized by the central difference method. Gauss linear upwind scheme is used to solve the level set distance function, and the Pressure–Implicit with Splitting of Operators (PISO) method is used to solve the momentum equation. The numerical result is compared with 1–D analytical solution of fluid-solid interface for reaction-diffusion problems. Sensitivity analysis is conducted with various Damkohler number (DaII) and Peclet number (Pe). We categorize the Fe (III) precipitation into three patterns as a function of DaII and Pe: symmetrical smoothed growth, unsymmetrical growth, and dendritic growth. Pe and DaII significantly affect the location of precipitation, which is critical in determining the injection parameters of hydraulic fracturing. When DaII<1, the precipitation uniformly occurs on the solid surface both in upstream and downstream directions. When DaII>1, the precipitation mainly occurs on the solid surface in an upstream direction. When Pe>1, Fe (II) transported deeply into and precipitated inside the pores. When Pe<1, the precipitation of Fe (III) occurs mainly on the solid surface in an upstream direction, and they are easily precipitated inside the small pore structures. The porosity–permeability relationship is subsequently presented. This pore-scale model allows high confidence in the description of Fe (II) dissolution, transport, and Fe (III) precipitation. The model shows fast convergence and requires a low computational load. The results can provide reliable guidance for injecting HFF in shale reservoirs to avoid clogging and wellbore pollution. Understanding Fe (III) precipitation, and Fe (II) release and transport behaviors give rise to a highly efficient hydraulic fracture project.

Keywords: reactive-transport , Shale, Kerogen, precipitation

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Authors: Giulio Mangano, Alberto De Marco, Giovanni Zenezini

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The concept of City Logistics (CL) has emerged to improve the impacts of last mile freight distribution in urban areas. In this paper, a System Dynamics (SD) model exploring the dynamics of the diffusion of a ICT platform for CL management across different populations is proposed. For the development of the model two sources have been used. On the one hand, the major diffusion variables and feedback loops are derived from a literature review of existing diffusion models. On the other hand, the parameters are represented by the value propositions delivered by the platform as a response to some of the users’ needs. To extract the most important value propositions the Business Model Canvas approach has been used. Such approach in fact focuses on understanding how a company can create value for her target customers. These variables and parameters are thus translated into a SD diffusion model with three different populations namely municipalities, logistics service providers, and own account carriers. Results show that, the three populations under analysis fully adopt the platform within the simulation time frame, highlighting a strong demand by different stakeholders for CL projects aiming at carrying out more efficient urban logistics operations.

Keywords: city logistics, simulation, system dynamics, business model

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Authors: H. Namazi, H. T. N. Kuan

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It is known that in humans, the adaptation to a given odor occurs within a quite short span of time (typically one minute) after the odor is presented to the brain. Different models of human olfaction have been developed by scientists but none of these models consider the diffusion phenomenon in olfaction. A novel microscopic model of the human olfaction is presented in this paper. We develop this model by incorporating the transient diffusivity. In fact, the mathematical model is written based on diffusion of the odorant within the mucus layer. By the use of the model developed in this paper, it becomes possible to provide quantification of the objective strength of odor.

Keywords: diffusion, microscopic model, mucus layer, olfaction

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Authors: Brahim Dennai, Abdelhak Bentaleb, Rachid Khelfaoui, Asma Abdenbi

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The diffusion flux given by the Fick’s law characterizethe mixing rate. A passive mixing strategy is proposed to enhance mixing of two fluids through perturbed jet low. A numerical study of passive mixers has been presented. This paper is focused on the modeling of a micro-injection systems composed of passive amplifier without mechanical part. The micro-system modeling is based on geometrical oscillators form. An asymmetric micro-oscillator design based on a monostable fluidic amplifier is proposed. The characteristic size of the channels is generally about a few hundred of microns. The numerical results indicate that the mixing performance can be as high as 99 % within a typical mixing chamber of 0.20 mm diameter inlet and 2.0 mm distance of nozzle - spliter. In addition, the results confirm that self-rotation in the circular mixer significantly enhances the mixing performance. The novel micro mixing method presented in this study provides a simple solution to mixing problems in microsystem for application in chemistry.

Keywords: micro oscillator, modeling, micro mixture, diffusion, size effect, chemical equation

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Authors: A. Zerarka, W. Djoudi

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We use some fractional transformations to obtain many types of new exact solutions of nonlinear lattice equation. These solutions include rational solutions, periodic wave solutions, and doubly periodic wave solutions.

Keywords: fractional transformations, nonlinear equation, travelling wave solutions, lattice equation

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Authors: Shubham Jaiswal

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During modeling of transport phenomena in porous media, many nonlinear partial differential equations (NPDEs) encountered which greatly described the convection, diffusion and reaction process. To solve such types of nonlinear problems, a reliable and efficient technique is needed. In this article, the numerical solution of NPDEs encountered in porous media is derived. Here Jacobi collocation method is used to solve the considered problems which convert the NPDEs in systems of nonlinear algebraic equations that can be solved using Newton-Raphson method. The numerical results of some illustrative examples are reported to show the efficiency and high accuracy of the proposed approach. The comparison of the numerical results with the existing analytical results already reported in the literature and the error analysis for each example exhibited through graphs and tables confirms the exponential convergence rate of the proposed method.

Keywords: nonlinear porous media equation, shifted Jacobi polynomials, operational matrix, spectral collocation method

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Authors: Barbora Chmelova, Radek Sachl

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Gangliosides are amphipathic membrane lipids. Due to the composition of bulky oligosaccharide chains containing one or more sialic acids linked to the hydrophobic ceramide base, gangliosides are classified among glycosphingolipids. This unique structure induces a high self-aggregating tendency of gangliosides and, therefore, the formation of nanoscopic clusters called nanodomains. Gangliosides are preferentially present in an extracellular membrane leaflet of all human tissues and thus have an impact on a huge number of biological processes, such as intercellular communication, cell signalling, membrane trafficking, and regulation of receptor activity. Defects in their metabolism, impairment of proper ganglioside function, or changes in their organization lead to serious health conditions such as Alzheimer´s and Parkinson´s diseases, autoimmune diseases, tumour growth, etc. This work mainly focuses on ganglioside organization into nanodomains and their dynamics within the plasma membrane. Current research investigates static ganglioside nanodomains characterization; nevertheless, the information about their diffusion is missing. In our study, fluorescence correlation spectroscopy is implemented together with stimulated emission depletion (STED-FCS), which combines the diffraction-unlimited spatial resolution with high temporal resolution. By comparison of the experiments performed on model vesicles containing 4 % of either GM1, GM2, or GM3 and Monte Carlo simulations of diffusion on the plasma membrane, the description of ganglioside clustering, diffusion of nanodomains, and even diffusion of ganglioside molecules inside investigated nanodomains are described.

Keywords: gangliosides, nanodomains, STED-FCS, flourescence microscopy, membrane diffusion

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Authors: Hebert Montegranario, Mauricio Londoño

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Solutions of Helmholtz equation are essential in seismic imaging methods like full wave inversion, which needs to solve many times the wave equation. Traditional methods like Finite Element Method (FEM) or Finite Differences (FD) have sparse matrices but may suffer the so called pollution effect in the numerical solutions of Helmholtz equation for large values of the wave number. On the other side, global radial basis functions have a better accuracy but produce full matrices that become unstable. In this research we combine the virtues of both approaches to find numerical solutions of Helmholtz equation, by applying a meshless method that produce sparse matrices by local radial basis functions. We solve the equation with absorbing boundary conditions of the kind Clayton-Enquist and PML (Perfect Matched Layers) and compared with results in standard literature, showing a promising performance by tackling both the pollution effect and matrix instability.

Keywords: Helmholtz equation, meshless methods, seismic imaging, wavefield inversion

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Authors: Ihab Elaff

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Simulating the heart’s electrical stimulation is essential in modeling and evaluating the electrophysiology behavior of the heart. For achieving that, there are two structures in concern: the ventricles’ Myocardium, and the ventricles’ Conduction Network. Ventricles’ Myocardium has been modeled as anisotropic material from Diffusion Tensor Imaging (DTI) scan, and the Conduction Network has been extracted from DTI as a case-based structure based on the biological properties of the heart tissues and the working methodology of the Magnetic Resonance Imaging (MRI) scanner. Results of the produced activation were much similar to real measurements of the reference model that was presented in the literature.

Keywords: diffusion tensor, DTI, heart, conduction network, excitation propagation

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Authors: Shayma Munqith Al-Baker, Fadhl Ahmed Saeed Al-Gasha’a, Samira Hamid Hanash, Ahmed Ali Al-Hazmi

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A total of 200 samples (180 fecal materials and 20 organ samples) were collected from (5 different poultry farms, 10 local poultry shops, 5 houses poultry, 5 Eggs stores shops and 5 hand slaughters centers) in Ibb city, Yemen, 2014. According to morphological, cultural, as well as biochemical characterization and serological tests, 59 29.5% isolates were identified as Salmonella spp. and all Salmonella isolates were categorized by serotype, which comprised of, 37 62.71% Salmonella Typhimurium serovar, 21 35.59%. Salmonella Enteritidis serovar and 11.69% Salmonella Heidelberg serovar. Antibiotic sensitivity test was done for bacterial isolates and the results showed there were clear differences in antibiotic resistant. Antimicrobial susceptibility of the isolates varies as follows: Ofloxacin 79.66%, Ciprofloxacin 67.80%, Colistin 59.32% and Gentamycin 52.54%. All of isolates were resistant to Erythromycin, Penicillin and Lincomycin. Antibacterial activity was done for both aqueous and ethanol extracts of Dodonaea viscosa plant by using well and disc diffusion assay. The results indicated that well diffusion assay had best results than disc diffusion assay, the highest inhibition zone was 22 mm for well diffusion and 15 mm for disc diffusion assay, the results observed that ethanol extract had best antibacterial effect than aqueous extract which the percentage of bacterial isolates affected with ethanol extract was 71.19% comparing with aqueous extract 28.81% by using disc diffusion assay, while the percentage of bacterial isolates affected with ethanol extract was 88.13% comparing with aqueous extract 52.54% by using will diffusion assay.

Keywords: Salmonella spp, Dodonaea viscosa, antimicrobial and salmonellosis

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Authors: Tsun-Hui Huang, Shyue-Cheng Yang, Chiou-Fen Shieha

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In this paper, a nonlinear constitutive law and a curve fitting, two relationships between the stress-strain and the shear stress-strain for sandstone material were used to obtain a second-order polynomial constitutive equation. Based on the established polynomial constitutive equations and Newton’s second law, a mathematical model of the non-homogeneous nonlinear wave equation under an external pressure was derived. The external pressure can be assumed as an impulse function to simulate a real earthquake source. A displacement response under nonlinear two-dimensional wave equation was determined by a numerical method and computer-aided software. The results show that a suit pressure in the sandstone generates the phenomenon of stress solitary waves.

Keywords: polynomial constitutive equation, solitary, stress solitary waves, nonlinear constitutive law

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Authors: John Knight, Fuchun Li, Yan Xu

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Based on a new method of the nonparametric estimator of the drift function, we propose a consistent test for the parametric specification of the drift function in the short rate diffusion process using observations from a panel of yields. The test statistic is shown to follow an asymptotic normal distribution under the null hypothesis that the parametric drift function is correctly specified, and converges to infinity under the alternative. Taking the daily 7-day European rates as a proxy of the short rate, we use our test to examine whether the drift of the short rate diffusion process is linear or nonlinear, which is an unresolved important issue in the short rate modeling literature. The testing results indicate that none of the drift functions in this literature adequately captures the dynamics of the drift, but nonlinear specification performs better than the linear specification.

Keywords: diffusion process, nonparametric estimation, derivative security price, drift function and volatility function

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Authors: Fadi Awawdeh, O. Alsayyed, S. Al-Shará

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Considering the inhomogeneities of media, the variable-coefficient Sharma-Tasso-Olver (STO) equation is hereby investigated with the aid of symbolic computation. A newly developed simplified bilinear method is described for the solution of considered equation. Without any constraints on the coefficient functions, multiple kink solutions are obtained. Parametric analysis is carried out in order to analyze the effects of the coefficient functions on the stabilities and propagation characteristics of the solitonic waves.

Keywords: Hirota bilinear method, multiple kink solution, Sharma-Tasso-Olver equation, inhomogeneity of media

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Authors: Elragig Aiman, Dreiwi Hanan, Townley Stuart, Elmabrook Idriss

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In this paper, we reconsider the analysis of the Oregonator model. We highlight an error in this analysis which leads to an incorrect depiction of the parameter region in which diffusion driven instability is possible. We believe that the cause of the oversight is the complexity of stability analyses based on eigenvalues and the dependence on parameters of matrix minors appearing in stability calculations. We regenerate the parameter space where Turing patterns can be seen, and we use the common Lyapunov function (CLF) approach, which is numerically reliable, to further confirm the dependence of the results on diffusion coefficients intensities.

Keywords: diffusion driven instability, common Lyapunov function (CLF), turing pattern, positive-definite matrix

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Authors: Mohammad Shams Esfand Abadi, Mohammad Ranjbar, Reza Ebrahimpour

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This work presents the distributed processing solution problem in a diffusion network based on the adapt then combine (ATC) and combine then adapt (CTA)selective partial update normalized least mean squares (SPU-NLMS) algorithms. Also, we extend this approach to dynamic selection affine projection algorithm (DS-APA) and ATC-DS-APA and CTA-DS-APA are established. The purpose of ATC-SPU-NLMS and CTA-SPU-NLMS algorithm is to reduce the computational complexity by updating the selected blocks of weight coefficients at every iteration. In CTA-DS-APA and ATC-DS-APA, the number of the input vectors is selected dynamically. Diffusion cooperation strategies have been shown to provide good performance based on these algorithms. The good performance of introduced algorithm is illustrated with various experimental results.

Keywords: selective partial update, affine projection, dynamic selection, diffusion, adaptive distributed networks

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Authors: Seyed Sadegh Naseralavi

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This paper presents a Kernel parallelization equation for damage identification in structures under unknown periodic excitations. Herein, the dynamic differential equation of the motion of structure is viewed as a mapping from displacements to external forces. Utilizing this viewpoint, a new method for damage detection in structures under periodic loads is presented. The developed method requires only two periods of load. The method detects the damages without finding the input loads. The method is based on the fact that structural displacements under free and forced vibrations are associated with two parallel subspaces in the displacement space. Considering the concept, kernel parallelization equation (KPE) is derived for damage detection under unknown periodic loads. The method is verified for a case study under periodic loads.

Keywords: Kernel, unknown periodic load, damage detection, Kernel parallelization equation

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Authors: Ankur Dixit, Hiroaki Wagatsuma

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The crack detection on a concrete bridge is an important and constant task in civil engineering. Chronically, humans are checking the bridge for inspection of cracks to maintain the quality and reliability of bridge. But this process is very long and costly. To overcome such limitations, we have used a drone with a digital camera, which took some images of bridge deck and these images are processed by morphological component analysis (MCA). MCA technique is a very strong application of sparse coding and it explores the possibility of separation of images. In this paper, MCA has been used to decompose the image into coarse and fine components with the effectiveness of two dictionaries namely anisotropic diffusion and wavelet transform. An anisotropic diffusion is an adaptive smoothing process used to adjust diffusion coefficient by finding gray level and gradient as features. These cracks in image are enhanced by subtracting the diffused coarse image into the original image and the results are treated by Sobel edge detector and binary filtering to exhibit the cracks in a fine way. Our results demonstrated that proposed MCA framework using anisotropic diffusion followed by Sobel operator and binary filtering may contribute to an automation of crack detection even in open field sever conditions such as bridge decks.

Keywords: anisotropic diffusion, coarse component, fine component, MCA, Sobel edge detector and wavelet transform

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Authors: Johnson Oladele Fatokun, I. P. Akpan

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In this paper, the one-dimensional time dependent Schrödinger equation is discretized by the method of lines using a second order finite difference approximation to replace the second order spatial derivative. The evolving system of stiff ordinary differential equation (ODE) in time is solved numerically by an L-stable trapezoidal-like integrator. Results show accuracy of relative maximum error of order 10-4 in the interval of consideration. The performance of the method as compared to an existing scheme is considered favorable.

Keywords: Schrodinger’s equation, partial differential equations, method of lines (MOL), stiff ODE, trapezoidal-like integrator

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Authors: Takashi Shimizu, Tomoaki Hashimoto

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Controlling the flow of fluids is a challenging problem that arises in many fields. Burgers’ equation is a fundamental equation for several flow phenomena such as traffic, shock waves, and turbulence. The optimal feedback control method, so-called model predictive control, has been proposed for Burgers’ equation. However, the model predictive control method is inapplicable to systems whose all state variables are not exactly known. In practical point of view, it is unusual that all the state variables of systems are exactly known, because the state variables of systems are measured through output sensors and limited parts of them can be only available. In fact, it is usual that flow velocities of fluid systems cannot be measured for all spatial domains. Hence, any practical feedback controller for fluid systems must incorporate some type of state estimator. To apply the model predictive control to the fluid systems described by Burgers’ equation, it is needed to establish a state estimation method for Burgers’ equation with limited measurable state variables. To this purpose, we apply unscented Kalman filter for estimating the state variables of fluid systems described by Burgers’ equation. The objective of this study is to establish a state estimation method based on unscented Kalman filter for Burgers’ equation. The effectiveness of the proposed method is verified by numerical simulations.

Keywords: observer systems, unscented Kalman filter, nonlinear systems, Burgers' equation

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Authors: Varun A Baheti, Sanjay Kashyap, Kamanio Chattopadhyay, Praveen Kumar, Aloke Paul

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Ni–Sn system finds applications in the microelectronics industry, especially with respect to flip–chip or direct chip, attach technology. Here the region of interest is under bump metallization (UBM), and solder bump (Sn) interface due to the formation of brittle intermetallic phases there. Understanding the growth of these phases at UBM/Sn interface is important, as in many cases it controls the electro–mechanical properties of the product. Cu and Ni are the commonly used UBM materials. Cu is used for good bonding because of fast reaction with solder and Ni often acts as a diffusion barrier layer due to its inherently slower reaction kinetics with Sn–based solders. Investigation on the growth kinetics of phases in Ni–Sn system is reported in this study. Just for simplicity, Sn being major solder constituent is chosen. Ni–Sn electroplated diffusion couples are prepared by electroplating pure Sn on Ni substrate. Bulk diffusion couples prepared by the conventional method are also studied along with Ni–Sn electroplated diffusion couples. Diffusion couples are annealed for 25–1000 h at 50–215°C to study the phase evolutions and growth kinetics of various phases. The interdiffusion zone was analysed using field emission gun equipped scanning electron microscope (FE–SEM) for imaging. Indexing of selected area diffraction (SAD) patterns obtained from transmission electron microscope (TEM) and composition measurements done in electron probe micro−analyser (FE–EPMA) confirms the presence of various product phases grown across the interdiffusion zone. Time-dependent experiments indicate diffusion controlled growth of the product phase. The estimated activation energy in the temperature range 125–215°C for parabolic growth constants (and hence integrated interdiffusion coefficients) of the Ni₃Sn₄ phase shed light on the growth mechanism of the phase; whether its grain boundary controlled or lattice controlled diffusion. The location of the Kirkendall marker plane indicates that the Ni₃Sn₄ phase grows mainly by diffusion of Sn in the binary Ni–Sn system.

Keywords: diffusion, equilibrium phase, metastable phase, the Ni-Sn system

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Authors: Michael Tupý, Vít Petránek

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The paper is focused on testing of the poly(vinyl butyral) (PVB) layer which had the function of a CO2 insulating protection against concrete and mortar carbonation. The barrier efficiency of PVB was verified by the measurement of diffusion characteristics. Two different types of PVB were tested; original extruded PVB sheet and PVB sheet made from PVB dispersion which was obtained from recycled windshields. The work deals with the testing CO2 diffusion when polymer sheets were exposed to a CO2 atmosphere (10% v/v CO2) with 0% RH. The excellent barrier capability against CO2 permeability of original and also recycled types of PVB layers was observed. This application of PVB waste can bring advantageous use in civil engineering and significant environmental contribution.

Keywords: windshield, poly(vinyl butyral), mortar, diffusion, carbonatation, polymer waste

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Authors: Narumol Chintaganun

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In this paper we present the second-order central differencing scheme with the staggered version (STG) for solving the advection equation and Burger's equation. This scheme based on staggered evolution of the re-constructed cell averages. This scheme results in the second-order central differencing scheme, an extension along the lines of the first-order central scheme of Lax-Friedrichs (LxF) scheme. All numerical simulations presented in this paper are obtained by finite difference method (FDM) and STG. Numerical results are shown that the STG gives very good results and higher accuracy.

Keywords: central differencing scheme, STG, advection equation, burgers equation

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Authors: Thanisa Sirithaporn

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The study aims to examine the diffusion of social innovation among Thai Community Enterprises in conjunction with a singular case study of a medium-sized corporation that has successfully transitioned from a charitable foundation to a sustainable, profitable entity creating value for both shareholders and the communities in which it operates. It seeks to bridge the gap between different streams of aligned research in the fields of diffusion, social innovation, and community enterprises into a more cohesive conceptual framework and thus to better understand the historical and current impediments that have resulted in so many enterprises failing to be sustainable. The methodology is mixed and dual phased. The initial quantitative phase uses a questionnaire as the main research instrument distributed among community enterprises throughout Thailand which will provide the themes for the qualitative phase through semi-structured interviews with key stakeholders at a commercial enterprise actively engaged in social innovation. The findings seek to present a more comprehensive conceptual framework and actionable guidelines to aid community enterprises to develop social innovation in a sustainable manner that creates value to its beneficiaries.

Keywords: diffusion, community enterprises, social innovation, Thailand

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Authors: M. Mortada, A. Seleem, M. El-Morsi, M. Younan

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The present study introduces the folding technology to be utilized for the first time in vertical diffusion stills. This work represents a model of the distillation process by utilizing chevron pattern of folded structure. An experimental setup has been constructed, to investigate the performance of the folded sheets in the vertical effect diffusion still for a specific range of operating conditions. An experimental comparison between the folded type and the flat type sheets has been carried out. The folded pattern showed a higher performance and there is an increase in the condensate to feed ratio that ranges from 20-30 % through the operating hot plate temperature that ranges through 60-90°C. In addition, a parametric analysis of the system using Design of Experiments statistical technique, has been developed using the experimental results to determine the effect of operating conditions on the system's performance and the best operating conditions of the system has been evaluated.

Keywords: chevron pattern, fold structure, solar distillation, vertical diffusion still

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