Pure Diffusion Process Research Articles

Ag/Ag2O electrode for electrocatalytic oxidation of ethanol

A film of silver oxide is grown on an Ag electrode in KOH solutions, by repetitive cyclic voltammograms at a high scan rate of 2500 mV/s. The formed film is used for the electro-oxidation of ethanol in a dilute potassium hydroxide using the cyclic voltammetry technique. Some effective experimental parameters such as the ethanol concentration, KOH concentration, scanning rate, and temperature on the electrocatalytic oxidation of ethanol have been investigated and discussed. The data confirmed that the formed silver oxide electrode behaves as a good catalyst for the electrooxidation of ethanol. The mechanism of oxidation is likely to be dissociative chemisorption involving one electron transfer. The apparent activation energy, E*, for the electrooxidation, was found to be 68.23 kJ/mole, which is considered too high for a pure diffusion process and moderate for a pure adsorption process. Then the charge transfer is probably controlled by a mixed adsorption-diffusion process

Plasma-stimulated great reduction of diffusion activation energies for B, Al, and Ag in Si

This work made an in-depth study on the transport of B, Al and Ag ions in an inductively coupled plasma-Si system. The plasma-stimulated impurity ion transport is demonstrated to be described by an implantation-diffusion two-step process rather than a pure diffusion process reported previously. The first step is impurity ion implantation under sheath voltage induced by plasma, which determines the impurity ion quantity into Si. The second step is plasma-stimulated impurity ion diffusion, which determines impurity ion transport depth in Si. An approximate solution to this implantation-diffusion process is deduced. Plasma-stimulated diffusion coefficients (D) for B, Al and Ag ions in Si are obtained by fitting the measured secondary ion mass spectroscopy concentration profiles with this equation. Furthermore, plasma-stimulated diffusion activation energies for B, Al and Ag ions in p-Si at 0 °C–120 °C are determined to be 0.22, 0.36 and 0.18 eV by Arrhenius plots, which are much lower than diffusion activation energies of 0.4–0.7, 1.2 and 1.15 eV for interstitial B, Al and Ag ions in Si without plasma reported in literatures. The great reduction of diffusion activation energy makes it possible for impurities to diffuse at room temperature or lower temperatures. The view of plasma-stimulated impurity ion transport is of significant importance on semiconductor technology and device degradation research.

Contact networks have small metric backbones that maintain community structure and are primary transmission subgraphs.

The structure of social networks strongly affects how different phenomena spread in human society, from the transmission of information to the propagation of contagious diseases. It is well-known that heterogeneous connectivity strongly favors spread, but a precise characterization of the redundancy present in social networks and its effect on the robustness of transmission is still lacking. This gap is addressed by the metric backbone, a weight- and connectivity-preserving subgraph that is sufficient to compute all shortest paths of weighted graphs. This subgraph is obtained via algebraically-principled axioms and does not require statistical sampling based on null-models. We show that the metric backbones of nine contact networks obtained from proximity sensors in a variety of social contexts are generally very small, 49% of the original graph for one and ranging from about 6% to 20% for the others. This reflects a surprising amount of redundancy and reveals that shortest paths on these networks are very robust to random attacks and failures. We also show that the metric backbone preserves the full distribution of shortest paths of the original contact networks-which must include the shortest inter- and intra-community distances that define any community structure-and is a primary subgraph for epidemic transmission based on pure diffusion processes. This suggests that the organization of social contact networks is based on large amounts of shortest-path redundancy which shapes epidemic spread in human populations. Thus, the metric backbone is an important subgraph with regard to epidemic spread, the robustness of social networks, and any communication dynamics that depend on complex network shortest paths.

MeV-proton capillary microbeam PIXE mapping study of solution diffusion in paper

A tapered glass capillary MeV-ion microbeam setup, previously home-developed, was recently upgraded. To check the upgraded microbeam system quality and accuracy, microbeam particle induced X-ray emission (PIXE) mapping of potassium permanganate (KMnO4) solution diffusion in filter paper was carried out to study how the measured solvent diffusion followed the diffusion laws. Two initial boundary conditions and diffusion situations were applied: (1) the paper vertically placed in air with one end soaked in the solution for ten minutes, and (2) the paper horizontally placed on water with the solution dropped at a side of the paper for three minutes. 2-MeV-proton microbeam PIXE analyzed the paper pixel by pixel and the GUPIXWIN software was used to calculate the elemental concentrations in the pixels to map the concentration changes in the pixels as a function of the distance between the pixel position and the origin of the solution. The resulting maps demonstrated the solution diffusions in two cases indeed well following the diffusion laws, a steady-state diffusion dominated process where the elemental concentration was a linear function with the distance but joined by other non-diffusion factors for case 1, and a pure diffusion process where the elemental concentration was an error function with the distance for case 2.

Transient liquid phase (TLP) bonding as reaction–controlled diffusion

The transient liquid phase bonding process has long been dealt with as a pure diffusion process at the joint interface, that is, as a mass phenomenon. In spite of the advances in the application of this technique to bond complex engineering alloys, the available models have failed to incorporate the effect of surface phenomena on the joining process. In this work, a new reaction–controlled diffusion formulation model is proposed, and the observation of experimental results of joining Al6061 alloy using thin single (50, 100 micron) and double Cu foils is recorded. This work directly unveils the unique role played by surface reaction–controlled diffusion rather than purely mass diffusion bonding process. Our experimental and modeling results reveal a conceptually new understanding that may well explain the joint formation in TLP bonding process.

Selective transport-recovery of bismuth(III) by a polymer inclusion membrane containing polyvinyl chloride base polymer and bis(2-ethylhexyl)phosphoric acid

Recently, it has been shown that a polymer inclusion membrane (PIM) containing 50 wt% of polyvinyl chloride (PVC) and 50 wt% bis(2-ethylhexyl)phosphoric acid (D2EHPA) is able to extract efficiently Bi(III) from sulfate solutions. The advantages of the transport processes motivated us to evaluate the potential of the proposed PIM for the recovery of Bi(III). Efficient transport of Bi(III) was achieved by using the PIMs (14 μm thickness, and 33.2 cm2 surface area) from the source phase, initially contained 20 mg L-1 of Bi(III) adjusted to pH 1.3 and 0.2 mol L-1 Na2SO4, to the receiving phase (H2SO4, 2 mol L-1). It is demonstrated that the transfer is carried out by a pure diffusion process. Under selected conditions, the highest permeability coefficient and initial flux are found to be 1.08 × 10-5 m s−1 and 1.03 × 10-6 mol m−2 s−1, respectively. The investigated PIM is more stable and can be used at least for 10 successive transport experiments. A pronounced selectivity is observed for Bi(III) in the competitive transport experiments of Bi(III) from its solutions containing some other associated metals. The preliminary experiments show that a dual-PIM system significantly increases transport efficiency.

Detailed numerical analysis of the effect of radial column heterogeneities on peak parking experiments with slowly diffusing analytes

The origin of the peak skewness that can be observed when applying the deconvolution method to isolate the diffusion process from the flow processes for peak parking experiments conducted under conditions of slow radial equilibration and strong trans-column velocity gradients was investigated. Numerical simulations were carried out for a variety of trans-column velocity profiles and a broad range of experimental conditions and system parameters were investigated. Results show that, under the aforementioned conditions, the traditionally employed variance subtraction method displays a consistent error which follows the dynamics of the diffusive relaxation during both the peak parking and the flow steps. It is also found that, under the same conditions, the peak deconvolution method is bound to produce deconvoluted “parking-only” peaks that are strongly asymmetric, despite the perfectly symmetric nature of the pure diffusion process marking this parking step. It is shown that this asymmetry is acquired during the flow step following the parking stop. During this step, parked and non-parked peaks are deformed in different ways, despite being subjected to the same trans-column velocity profile. This different deformation cannot be filtered away with the deconvolution or the variance subtraction method, hence introducing an error. Solutions to alleviate the peak skewness and the variance error consist of parking the peak close to the inlet or the outlet or exiting the parked peak through the column inlet (flow reversal method). Under the considered conditions, these approaches could reduce the error on the measured effective diffusion coefficient up to 87%. Carrying out the variance subtraction or the deconvolution process with a peak that has also been parked for a substantially long parking time instead of using a “no-parking” peak as is customary done, is another option to counter the effect.

Modeling drug delivery from multiple emulsions

We present a mechanistic model of drug release from a multiple emulsion into an external surrounding fluid. We consider a single multilayer droplet where the drug kinetics are described by a pure diffusive process through different liquid shells. The multilayer problem is described by a system of diffusion equations coupled via interlayer conditions imposing continuity of drug concentration and flux. Mass resistance is imposed at the outer boundary through the application of a surfactant at the external surface of the droplet. The two-dimensional problem is solved numerically by finite volume discretization. Concentration profiles and drug release curves are presented for three typical round-shaped (circle, ellipse, and bullet) droplets and the dependency of the solution on the mass transfer coefficient at the surface analyzed. The main result shows a reduced release time for an increased elongation of the droplets.

A new model for predicting the thickness of intermetallic compounds in friction stir welding

Abstract The thickness of intermetallic compounds (IMCs) is one of the main factors affecting the weld quality. In addition, the IMC thickness will affect the product functionality, e.g., the thermal or electrical conductivity of the IMC layer can be the limiting factor in the related applications. Modeling and prediction of the IMC thickness in the friction stir welding (FSW) process is an important role that has not been elaborated in the literature. Additionally, many studies used a model for the IMC thickness that is related to the classical diffusion phenomenon. That model is suitable for the pure (intrinsic) diffusion process and does not consider the main unique characteristic of FSW, i.e., the stirring and subsequent linear velocity of particles (that has an impact on the diffusion process). To address this research gap, first, we develop a new model for the IMC thickness that takes the velocity of particles into account. Second, we provide an analysis on the velocity of particles in FSW based on vortex dynamics. Third, we analyze the proposed IMC thickness model with experimental data from the literature, discuss the added values of our model, and finally examine a case study. Understanding various manufacturing processes can further lead to the improvement of the existing processes and the development of novel processes.

Transient Natural Convection in a Thermally Insulated Annular Cylinder Exposed to a High Temperature from the Inner Radius

Extensive numerical analysis was performed for the unsteady state, natural convection in the annular cylinders. The cylinder’s boundaries were thermally insulated, except the inner surface. The fluid (water) in the cylinder initially was assumed at a cold temperature while the inner surface was subjected to a high temperature. The time history for the heat transfer by diffusion and advection was studied. The time needed for fully charging the storage tank and rate of heat transfer was calculated. The predicted results were compared with the pure heat diffusion process and with a steady-state convection system. Therefore, CFD simulations were performed for natural convection in the storage tank. The main objective of this study was to establish correlations for the rate of heat transfer as a function of time and other controlling parameters. The correlation is needed in designing a thermal energy storage system for domestic and industrial heating processes. One of the drawbacks of the conventional thermal storage systems is the slow charging and discharging, where the heat transfer is mainly diffusion dominated. To overcome such a problem, a system was designed based on the natural convective heat transfer mechanism. Therefore, the heat transfer and fluid flow in a cylindrical storage tank were simulated for a range of Rayleigh numbers (104 to 108) and radius ratio. It was found that a convection-operated storage tank reduces the thermal charging process time drastically compared with the thermally diffusion charging process. The rate of reduction in the charging time mainly depends on the rate of heating and geometric parameter of the tank. To the best of the authors’ knowledge, the work is novel.

A redox reaction model for self-heating and aging prediction of Al/CuO multilayers

Sputter-deposited Al/CuO multilayers capable of highly energetic reactions have been the subject of intense studies for tunable initiation and actuation. Designing high performance Al/CuO-based initiator devices definitively requires reliable prediction of their ignition and reaction kinetics including self-heating or ageing as a function of heating rate and environmental conditions. The paper proposes a heterogeneous reaction model integrating an ensemble of basic mechanisms (oxygen diffusion, structural transformations, polymorphic phase changes) that have been collected from recent experimental investigations. The reaction model assumes that the rate of reaction is limited by the transport of oxygen across the growing layer of Al2O3 separating Al and CuO. Importantly, we show that the model predicts reasonably all exotherms through a wide range of temperature (ambient – 1000°C), all resulting from a pure diffusion process as experimentally observed for such Al/CuO multilayers. The model shows how the temperature ramp affects the structure of the multilayer and especially the growth of alumina-based interfacial regions. It highlights the importance of the interfacial chemistry evolution such as the native mixture of AlxCuyOz transformation into a thin amorphous alumina, and the polymorphic phase transformation of this latter. The first one occurring at ∼350°C results in a loss of continuity of the interface leading to the accelerated redox reaction whereas the second one occurring between 500 and 600°C produces a denser barrier to oxygen diffusion leading to the stop of redox reaction. We finally use the model to simulate thermal annealing as usually performed in accelerated ageing experiments. We theoretically observe and experimentally validate that a two weeks exposure of the multilayers at 200°C starts degrading the multilayers thermal properties whereas when the temperature remains below 200°C, the material keeps its entire integrity.

Numerical investigation of SVOC mass transport in a tube by an axisymmetric lattice Boltzmann method

This paper presents an adsorption boundary condition based on linear adsorption isotherm for Lattice Boltzmann (LB) model. An axisymmetric 2-D LB model is built for an axisymmetric device. The model is used to study the effects of surface adsorption and airflow on SVOC mass transport in the device. In terms of surface adsorption, the research is divided in two parts: pure diffusion and convection-diffusion. The results show that the simulated data based on the presented adsorption boundary agree well with experimental data. In both the pure diffusion and advection-diffusion process, surface adsorption has no impact on the steady-state concentration, but it affects the time to reach steady state. Airflow greatly reduces both the time to reach steady state and the steady-state concentration. An exponential relationship involving hm, ACH and velocity is proposed and verified experimentally. Discussion on the parameter n in the exponential relation is conducted.

Spatially Different Tissue-Scale Diffusivity Shapes ANGUSTIFOLIA3 Gradient in Growing Leaves

The spatial gradient of signaling molecules is pivotal for establishing developmental patterns of multicellular organisms. It has long been proposed that these gradients could arise from the pure diffusion process of signaling molecules between cells, but whether this simplest mechanism establishes the formation of the tissue-scale gradient remains unclear. Plasmodesmata are unique channel structures in plants that connect neighboring cells for molecular transport. In this study, we measured cellular- and tissue-scale kinetics of molecular transport through plasmodesmata in Arabidopsis thaliana developing leaf primordia by fluorescence recovery assays. These trans-scale measurements revealed biophysical properties of diffusive molecular transport through plasmodesmata and revealed that the tissue-scale diffusivity, but not the cellular-scale diffusivity, is spatially different along the leaf proximal-to-distal axis. We found that the gradient in cell size along the developmental axis underlies this spatially different tissue-scale diffusivity. We then asked how this diffusion-based framework functions in establishing a signaling gradient of endogenous molecules. ANGUSTIFOLIA3 (AN3) is a transcriptional co-activator, and as we have shown here, it forms a long-range signaling gradient along the leaf proximal-to-distal axis to determine a cell-proliferation domain. By genetically engineering AN3 mobility, we assessed each contribution of cell-to-cell movement and tissue growth to the distribution of the AN3 gradient. We constructed a diffusion-based theoretical model using these quantitative data to analyze the AN3 gradient formation and demonstrated that it could be achieved solely by the diffusive molecular transport in a growing tissue. Our results indicate that the spatially different tissue-scale diffusivity is a core mechanism for AN3 gradient formation. This provides evidence that the pure diffusion process establishes the formation of the long-range signaling gradient in leaf development.

Nonlinear simulation of miscible displacements with concentration-dependent diffusion coefficient in homogeneous porous media

The nonlinear dynamics of miscible flow displacements in homogeneous porous media are examined for the special case of concentration-dependent diffusion coefficient (CDDC) models. Highly accurate numerical methods are used to simulate the time evolution of fingering with both mobility and diffusion coefficient contrasts of two components in a fully miscible solution system. The simulations revealed that, when compared with a constant diffusion coefficient (CDC), the CDDC models show drastically different viscous fingering structures and mixing of the two components. In particular, for a pure diffusion process with a stable front, using a CDDC results in less mixing, with a non-symmetric concentration gradient. While for the unstable displacements with relatively large mobility contrasts, it is found that using a CDDC tends to trigger fingers at the very beginning of the displacements. The diffusion-dominated period is therefore very short and can nearly be neglected. Moreover, the fingers reach the downstream boundary much earlier with fingering structures about 2–4 times more complex than the CDC case. Quantitative analysis indicates that the exponential CDDC models can enhance the mixing by shortening the diffusive regime but not change the growth rate of mixing in the convective regime. In addition, in contrast with the CDC case, the time required for the appearance of fingers for the CDDC seems to be independent of Peclet number Pe at a relatively large log mobility ratios R. As Pe increases for the CDDC cases, more complex dynamics of the fingers are observed, which can only be found at very high Pe and R values for the CDC case. In addition, a small increase in R is able to significantly enhance the instabilities since it can result in not only larger mobility contrast but also a steeper diffusion gradient.

English

Option pricing models are an important part of financial markets worldwide. The PDE formulation of these models leads to analytical solutions only under very strong simplifications. For more general models the option price needs to be evaluated by numerical techniques. First, based on an ideal pure diffusion process for two risky asset prices with an additional path-dependent variable for continuous arithmetic average, we present a general form of PDE for pricing of Asian option contracts on two assets. Further, we focus only on one subclass—Asian options with floating strike—and introduce the concept of the dimensionality reduction with respect to the payoff leading to PDE with two spatial variables. Then the numerical option pricing scheme arising from the discontinuous Galerkin method is developed and some theoretical results are also mentioned. Finally, the aforementioned model is supplemented with numerical results on real market data.

A TWO-FACTOR JUMP-DIFFUSION MODEL FOR PRICING CONVERTIBLE BONDS WITH DEFAULT RISK

The current literature on convertible bonds (CBs) comprises only models where the stock price and the interest rate are governed by pure-diffusion processes. This paper fills a gap by developing and implementing a two-factor model where both underlying factors follow jump-diffusion processes, and which also incorporates default risk. We derive the partial integro-differential equation satisfied by the CB price in our model, and solve it by a spectral method based on Chebyshev discretizations and Clenshaw–Curtis quadratures. The conversion, call, and put constraints give rise to a linear complementarity problem, which is solved by an operator-splitting (OS) method. Through numerical experiments, we investigate the effects that the various parameters have on the CB price. In particular, our numerical experiments show that jumps in the stock price have a significant impact on the CB price, while jumps in the interest rate tend to have a minor effect on the price. In general, the dynamics of the stock price have more impact in pricing the CB than the dynamics of the interest rate.

The 4% strategy revisited: a pre-commitment mean-variance optimal approach to wealth management

In contrast to single-period mean-variance (MV) portfolio allocation, multi-period MV optimal portfolio allocation can be modified slightly to be effectively a down-side risk measure. With this in mind, we consider multi-period MV optimal portfolio allocation in the presence of periodic withdrawals. The investment portfolio can be allocated between a risk-free investment and a risky asset, the price of which is assumed to follow a jump diffusion process. We consider two wealth management applications: optimal de-accumulation rates for a defined contribution pension plan and sustainable withdrawal rates for an endowment. Several numerical illustrations are provided, with some interesting implications. In the pension de-accumulation context, Bengen (1994)’s [J. Financial Planning, 1994, 7, 171–180], historical analysis indicated that a retiree could safely withdraw 4% of her initial retirement savings annually (in real terms), provided that her portfolio maintained an even balance between diversified equities and U.S. Treasury bonds. Our analysis does support 4% as a sustainable withdrawal rate in the pension de-accumulation context (and a somewhat lower rate for an endowment), but only if the investor follows an MV optimal portfolio allocation, not a fixed proportion strategy. Compared with a constant proportion strategy, the MV optimal policy achieves the same expected wealth at the end of the investment horizon, while significantly reducing the standard deviation of wealth and the probability of shortfall. We also explore the effects of suppressing jumps so as to have a pure diffusion process, but assuming a correspondingly larger volatility for the latter process. Surprisingly, it turns out that the MV optimal strategy is more effective when there are large downward jumps compared to having a high volatility diffusion process. Finally, tests based on historical data demonstrate that the MV optimal policy is quite robust to uncertainty about parameter estimates.

The influence of some model parameters on the impurity distribution implanted into substrate surface

The model for description of the initial stage of ion implantation into the surface layer of the metal is presented. The interdependence of embedded impurity concentration and deformations arising from the impact of particles on the surface is investigated. The model takes into account the particle diffusion, the finite time of mass flux relaxation; the stress appearance due to a composition change of the surface layer and a mass transfer phenomenon under a stress gradient action. It is established that the interaction of mechanical waves and concentration leads to a distribution of concentration not corresponding to a pure diffusion process. The examples of coupled problems solution for different sets of model parameters are presented.

An evolutionary model of bi-flux diffusion processes

In previous papers, we presented a new theory of bi-flux diffusion processes. The bi-flux consists of the simultaneous flux of two sets of particles scattering with two distinct velocities. The first set obeys the classical Fick’s law, it is the primary flux. The complementary set follows a new law, it is the secondary flux. The primary and secondary fluxes are excited into two distinct energy states. The fundamental energy source for the primary flux is the translational energy or active energy. For the secondary flux, linear and angular momentum, both, contribute to the excitation state. Two cases are analyzed. The first one refers to an isolated system in a particular phase state S1 where active energy decreases continuously. The system tends to an energy state where active energy is absent. In the second case, the system is in a different phase state S2 where active energy increases continuously. The system recovers active energy and tends to a pure Fickian diffusion process. In both processes, the fractions representing the density distribution functions for the primary and secondary fluxes vary with time. It is remarkable that the fourth order equation provides a consistent approach to take into account the rotational energy which otherwise would not be possible with the classical theory. A particular law for the variation of the fraction of particles following Fick’s law is derived. A notion of entropy related to the particular energy states is introduced. Selected examples are presented showing the concentration profile evolution for different rates of energy transfer.

Stable, Extrinsic, Field Effect Passivation for Back Contact Silicon Solar Cells

A new technique is described by which ionic species can be rapidly transported into oxide films, and once there provide effective and stable field effect passivation to silicon surfaces. Field effect passivation in thermally grown oxide films has been achieved by embedding potassium ions using a combined drift and diffusion mechanism at high temperature. This process has been shown to be over 10 times faster than a pure diffusion process. The resulting passivation stable for periods exceeding 600 days, with lifetimes reaching 1.4 ms, equivalent to a surface recombination velocity (SRV) ≤ 5.7 cm/s, on 1 Ωcm, n-type, FZ-Si.