Transient Diffusion Process Research Articles

Modelling plasticiser loss inside closed environments

Plasticiser loss, a fundamental mechanism in the degradation of polymeric materials, leads to material instability and contamination of the environment. The process depends on environmental conditions, but the size of the container in which an object is housed and the thickness of the material also play key roles in the rate of plasticiser loss and the time at which equilibrium is reached. Understanding these dependencies provides valuable insight into the degradation of plastic museum artefacts inside enclosures as typified by museum storage and, more broadly, the deterioration of polymeric materials in closed environments. Migration of low molecular weight plasticisers, like diethyl phthalate or dimethyl phthalate, from plastics has been widely studied in accelerated ageing experiments at elevated temperatures and different airflows. Here, to investigate these effects, we modelled plasticiser loss in a stagnant environment inside an enclosure at room temperature. Our model is one-dimensional and describes loss through a two-phase transient diffusion process, between the solid plastic and the air. The comparison of numerical simulations to FTIR and 1H NMR spectroscopic data from cellulose acetate samples plasticised with diethyl phthalate aged at T = 70 °C and 50% relative humidity indicates that the model is appropriate for thin enclosed plastics. We applied the model over a range of diffusion coefficients [10−21–10−14 m2 s−1] and partition coefficients [103–107] to represent different polymeric materials. Under the investigated scenarios, thin plastics tolerate a maximum total plasticiser loss of 10% and the timescales vary between 1 and 109 years. The model provides insight into the relationship between plasticiser loss, enclosure dimensions and material thickness for different plastics and can suggest how to improve packaging dimensions of thin plastic products to minimise loss, as well as future conservation strategies and guidelines for plastic museum artefacts.

A thin-layer diffusion model-based intelligent cyclic voltammetry analysis method to capture electrochemical parameters in flow batteries

Contrary to the conventional approach that utilizes the planar electrode model to achieve the electrochemical parameters of the electrode in flow batteries, this work proposes an intelligent cyclic voltammetry (CV) analysis method to accurately capture the electrochemical parameters of the carbon-based porous electrode: (i) the transient diffusion process is elaborated by the Fick's second law; (ii) the thin-layer diffusion boundary condition is determined based on the structural characteristics of porous electrodes; (iii) CV response on the porous electrode is obtained by the Bulter-Volmer equation in assocition with the Fick's first law; and (iv) the electrochemical parameters of the porous electrode are automatically extracted from the experimental data via the genetic algorithm. The feasibility of the intelligent CV analysis method is proven by studying the electrochemical parameters including the diffusion coefficient D and the standard rate constant k0 of [Fe(CN)6]4−/[Fe(CN)6]3−. Additionally, this analysis method is applied to investigate the vanadium redox flow battery by providing accurate electrochemical parameters for the 3D multi-physics model to predict the charge/discharge performance at different current densities. The simulation results demonstrate a maximum relative error of 2% in comparison to the experimental data, suggesting the good reliability in developing the advanced model. The proposed intelligent CV analysis method provides a potential application in accurately capturing the electrochemical parameters in other electrochemical energy conversion and storage devices.

A simple method to predict transient diffusion processes in ellipsoids

This work is focused on transient diffusion processes inside semi-solid and solid agri-food products presenting ellipsoidal shape, i.e. prolate and oblate spheroids and general ellipsoid. Many typical industrial operations like drying, soaking, rehydration, heating, cooking, and cooling, can be effectively modelled by using Fick's law for mass diffusion and Fourier's law for heat conduction, with constant properties and neglecting volume/shape variations. To predict such processes, there are some methods available in the literature, although they are limited to certain shapes and/or operating conditions and their implementation can be quite complicated. Therefore, our objective was to develop a simple method to predict transient diffusion processes in ellipsoids and spheroids, considering both local and average values of industrial interest. The methodology to obtain such a simple method consisted in first generating numerical data by simulating a wide range of shapes and conditions, and then fitting a simple two-parameter expression, which is based on the analytical solution for regular geometries. The developed method can be easily implemented through the use of tabulated values provided in this article. Finally, the capability of the proposed method was verified by using previously reported data, showing very good results and demonstrating that it is easily implementable. It is expected that the developed simple method can be helpful for industrial applications and to improve calculations in related fields of research, which may not be familiar with transport phenomena modelling. • Many food processes involve transient mass and/or heat diffusion in ellipsoids. • A semi-analytical, user-friendly and accurate prediction method is developed. • Different prolate, oblate and general ellipsoids, and Biot values are covered. • Evolution of average, central and surface values of dependent variable is predicted. • The simple method can also estimate transport properties by inverse methodology.

A model for transient diffusion in bidisperse pore structures

A bidisperse model for transient diffusion and adsorption processes in porous materials is presented in this paper. The mathematical model is solved by numerical methods based on finite elements combined with the linear driving force approximation. A criterion based on the model to identify the diffusion controlling mechanism (macropore diffusion, micropore diffusion, or both) is proposed. The effects of different adsorption isotherms (linear, Freundlich, or Langmuir) on the concentration profiles and on curves of fractional uptake versus time are investigated. In addition, the influences of model parameters concerning the pore networks on the fractional uptake are studied as well.

Revealing the role of lattice distortions in the hydrogen-induced metal-insulator transition of SmNiO3

The discovery of hydrogen-induced electronic phase transitions in strongly correlated materials such as rare-earth nickelates has opened up a new paradigm in regulating materials’ properties for both fundamental study and technological applications. However, the microscopic understanding of how protons and electrons behave in the phase transition is lacking, mainly due to the difficulty in the characterization of the hydrogen doping level. Here, we demonstrate the quantification and trajectory of hydrogen in strain-regulated SmNiO3 by using nuclear reaction analysis. Introducing 2.4% of elastic strain in SmNiO3 reduces the incorporated hydrogen concentration from ~1021 cm−3 to ~1020 cm−3. Unexpectedly, despite a lower hydrogen concentration, a more significant modification in resistivity is observed for tensile-strained SmNiO3, substantially different from the previous understanding. We argue that this transition is explained by an intermediate metastable state occurring in the transient diffusion process of hydrogen, despite the absence of hydrogen at the post-transition stage.

OPTIMAL STOPPING FOR THE LAST EXIT TIME

Given a one-dimensional downwards transient diffusion process $X$, we consider a random time $\unicode[STIX]{x1D70C}$, the last exit time when $X$ exits a certain level $\ell$, and detect the optimal stopping time for it. In particular, for this random time $\unicode[STIX]{x1D70C}$, we solve the optimisation problem $\inf _{\unicode[STIX]{x1D70F}}\mathbb{E}[\unicode[STIX]{x1D706}(\unicode[STIX]{x1D70F}-\unicode[STIX]{x1D70C})_{+}+(1-\unicode[STIX]{x1D706})(\unicode[STIX]{x1D70C}-\unicode[STIX]{x1D70F})_{+}]$ over all stopping times $\unicode[STIX]{x1D70F}$. We show that the process should stop optimally when it runs below some fixed level $\unicode[STIX]{x1D705}_{\ell }$ for the first time, where $\unicode[STIX]{x1D705}_{\ell }$ is the unique solution in the interval $(0,\unicode[STIX]{x1D706}\ell )$ of an explicitly defined equation.

Transient anomalous diffusion with Prabhakar-type memory.

In this paper, we derive the general properties of anomalous diffusion and non-exponential relaxation from the Fokker-Planck equation with the memory function related to the Prabhakar integral operator. The operator is a generalization of the Riemann-Liouville fractional integral and permits one to study transient anomalous diffusion processes with two-scale features. The aim of this work is to find a probabilistic description of the anomalous diffusion from the Fokker-Planck equation, more precisely from the memory function. The temporal behavior of such phenomena exhibits changes in time scaling exponents of the mean-squared displacement through time domain-a more general picture of the anomalous diffusion observed in nature.

Markov processes conditioned on their location at large exponential times

Suppose that (Xt)t≥0 is a one-dimensional Brownian motion with negative drift −μ. It is possible to make sense of conditioning this process to be in the state 0 at an independent exponential random time and if we kill the conditioned process at the exponential time the resulting process is Markov. If we let the rate parameter of the random time go to 0, then the limit of the killed Markov process evolves like X conditioned to hit 0, after which time it behaves as X killed at the last time X visits 0. Equivalently, the limit process has the dynamics of the killed “bang–bang” Brownian motion that evolves like Brownian motion with positive drift +μ when it is negative, like Brownian motion with negative drift −μ when it is positive, and is killed according to the local time spent at 0.An extension of this result holds in great generality for a Borel right process conditioned to be in some state a at an exponential random time, at which time it is killed. Our proofs involve understanding the Campbell measures associated with local times, the use of excursion theory, and the development of a suitable analogue of the “bang–bang” construction for a general Markov process.As examples, we consider the special case when the transient Borel right process is a one-dimensional diffusion. Characterizing the limiting conditioned and killed process via its infinitesimal generator leads to an investigation of the h-transforms of transient one-dimensional diffusion processes that goes beyond what is known and is of independent interest.

Diffusion coupling in multiply associating electrolyte solutions

Diffusion coupling in multiply associating aqueous electrolyte solution is studied. The process is illustrated in the case of zinc(II) ion which forms a set of complexes, ZnCln2−n (with n=1,..,4), in the presence of chloride ions. The transport of zinc ion, taken in radioactive form 65Zn2+, in the electric field created by a gradient of LiCl, is investigated experimentally by employing an adaptation of the closed capillary technique. The transient diffusion process is modeled by using two different treatments: finite difference (FD) simulation and normal-mode (NM) analytic solution. Deviations from ideality are taken into account with the use of the mean spherical approximation (MSA), and the internal electric field is calculated using the dynamical electroneutrality condition. The theoretical FD and NM results are compared with the experimental data about the diffusion of zinc.

On the distribution of integral functionals of a homogeneous diffusion process

In this article, we study homogeneous transient diffusion processes. We provide the basic distributions of their local times. It helps to get exact formulas and upper bounds for the moments, exponential moments, and potentials of integral functionals of transient diffusion processes. Some of the results generalize the corresponding results of Salminen and Yor for the Brownian motion with drift.

GAMBLING IN CONTESTS WITH REGRET

AbstractThis paper discusses the gambling contest introduced in Seel and Strack (2013, Gambling in Contests, Journal of Economic Theory, 148(5), 2033–2048) and considers the impact of adding a penalty associated with failure to follow a winning strategy. The Seel and Strack model consists of n‐agents each of whom privately observes a transient diffusion process and chooses when to stop it. The player with the highest stopped value wins the contest, and each player's objective is to maximize her probability of winning the contest. We give a new derivation of the results of Seel and Strack based on a Lagrangian approach. Moreover, we consider an extension of the problem to a behavioral finance context in the sense of regret theory. In particular, an agent is penalized when her chosen strategy does not win the contest, but there existed an alternative strategy that would have resulted in victory.

Three-dimensional Brownian motion and the golden ratio rule

Let $X=(X_t)_{t\ge0}$ be a transient diffusion process in $(0,\infty)$ with the diffusion coefficient $\sigma>0$ and the scale function $L$ such that $X_t\rightarrow\infty$ as $t\rightarrow \infty$, let $I_t$ denote its running minimum for $t\ge0$, and let $\theta$ denote the time of its ultimate minimum $I_{\infty}$. Setting $c(i,x)=1-2L(x)/L(i)$ we show that the stopping time \[\tau_*=\inf\{t\ge0\vert X_t\ge f_*(I_t)\}\] minimizes $\mathsf{E}(\vert\theta-\tau\vert-\theta)$ over all stopping times $\tau$ of $X$ (with finite mean) where the optimal boundary $f_*$ can be characterized as the minimal solution to \[f'(i)=-\frac{\sigma^2(f(i))L'(f(i))}{c(i,f(i))[L(f(i))-L(i)]}\int_i^{f(i)}\frac{c_i'(i,y)[L(y) -L(i)]}{\sigma^2(y)L'(y)}\,dy\] staying strictly above the curve $h(i)=L^{-1}(L(i)/2)$ for $i>0$. In particular, when $X$ is the radial part of three-dimensional Brownian motion, we find that \[\tau_ *=\inf\biggl\{t\ge0\Big\vert\frac{X_t-I_t}{I_t}\ge\varphi\biggr\},\] where $\varphi=(1+\sqrt{5})/2=1.61\ldots$ is the golden ratio. The derived results are applied to problems of optimal trading in the presence of bubbles where we show that the golden ratio rule offers a rigorous optimality argument for the choice of the well-known golden retracement in technical analysis of asset prices.

Influence of radiation damage on strontium and iodine diffusion in silicon carbide

The transport behaviour of strontium and iodine through single and polycrystalline SiC wafers was investigated using ion beam analysis and electron microscopy. Fluences of 2×1016 Sr+ cm−2 and 1×1016 I+ cm−2 were implanted at temperatures between 23°C and 600°C with an energy of 360keV, producing an atomic density of approximately 1.5% at the projected ranges of about 120nm and 90nm respectively. The broadening of the implantation profiles and its dependence on implantation parameters was determined by isochronal and isothermal annealing studies at temperatures up to 1400°C. The strong influence of radiation damage on diffusion after room temperature implantations was observed in all cases during the initial annealing stages at 1000°C. This is a result of the highly disordered crystal lattice, which re-crystallizes at this temperature. In hot implantations this effect is largely reduced but an additional transient diffusion process was observed at 1400°C for strontium, which is related to defect annealing. Impurity trapping by extended defects is obviously an important effect. Volume diffusion is below our detection limit of 10−21m2s−1 for both diffusors. Hence, grain boundary diffusion is responsible for the observed iodine transport in CVD-SiC at 1300°C, while no significant diffusion of strontium was detected at 1400°C.

Experimental verification of mathematical model for multiphase flow in air-agitated seed precipitation tank

In order to check the validity of the mathematical model for analyzing the flow field in the air-agitated seed precipitation tank, a scaled down experimental apparatus was designed and the colored tracer and KCl tracer were added in the apparatus to follow the real flow line. Virtue tracers were considered in the mathematical model and the algorithm of tracers was built. The comparison of the results between the experiment and numerical calculation shows that the time of the tracer flows out of stirring tube are 40 s in the experiment and 42 s in numerical calculated result. The transient diffusion process and the solution residence time of the numerical calculation are in good agreement with the experimental results, which indicates that the mathematical model is reliable and can be used to predict the flow field of the air-agitated seed precipitation tank.

Modelling of moisture diffusion in multilayer woven fabric composites

Advanced woven fibre reinforced composites have wide applications in industries. However, the mechanical performance of this kind of composites is significantly affected by the moisture absorption of the polymer matrix. This paper presents a numerical investigation on the moisture diffusion taking place in multilayer woven fabric composites. The transient diffusion process of moisture is examined based on the repeating Representative Unit Cell (RUC) of woven fabrics. Using finite element analysis methods, the microscopic heterogeneity of RUC is described in terms of the tow size, tow cross-section shape and tow weaving configuration of fabrics. The model is then applied to simulate the moisture diffusion within the composites of varied number of plies. Finally, by using a data fitting function for the modelling results, a simple predicting model for moisture saturation time with the increase of the number of plies is proposed for the purpose of practical applications.

Gas sorption and transport in coals: A poroelastic medium approach

Abstract In this paper, single-component gas sorption and transient diffusion processes are described within coal matrix exhibiting bimodal pore structure. The coal matrix is treated as a poroelastic medium manifesting swelling and shrinkage effects due to the sorption of gas under effective overburden stress. Gas transport is considered Fickian with molecular (bulk) and surface diffusion processes simultaneously taking place in the macro- and micropores of coal, respectively. The numerical formulation is intended to be explicit in nature to investigate the influences of sorption phenomena on the macropore volumes and on the overall gas transport for the cases of gas uptake by and release from coal. Results of the study show the presence of hysteresis during a sorption–desorption cycle of the gas. It is also found that the overall gas transport takes place at a rate significantly less than that in the macropores only. Thus the existence of a retardation effect in the overall gas transport is concluded. This retardation effect is primarily due to the micropore resistances, in particular gas adsorption, and is independent of the changes in the macropore volumes. It is shown that macroporosity of the coal matrix may change during gas transport due to combined effects of pressure and sorption-induced swelling or shrinkage of the coal. It is estimated that the macroporosity variation is non-uniform in space and time, as it is expected in reality, and typically taking values less than ± 10 percent of the initial porosity.

Transient diffusion and cluster formation of water molecules on Rh(111) at 20K

The authors investigated the initial stage of water adsorption on Rh(111) at 20 K, using infrared reflection absorption spectroscopy. In this low coverage region, isolated water molecules and small water clusters are observed. Since thermal diffusion is suppressed at 20 K, the formation of water clusters at low coverage is controlled by both coverage and transient diffusion on the surface. Within a simple random walk model of the transient diffusion and clustering process, the authors estimate the mean lateral displacement from the first impact point to the final adsorption site to be 7.6 A; an incoming water molecule on Rh(111) is trapped with eight postcollision hops on the average.

Numerical Evaluation of Separation Characteristics of Open Gradient Magnetic Separation Using Quadrupole Magnetic Field

Numerical study on the open gradient magnetic separation using the quadrupole magnetic field is presented in this paper. The characteristics of separating multiple kinds of magnetic particles with different magnetic susceptibility are numerically evaluated by the model to analyze the transient diffusion process developed in our previous study. We consider two methods for the separation of multiple kind particles. In the first method, the numerical results show that the two kinds of particles with different magnetic susceptibility can be selectively separated. The second method is one of the field flow fractionation which is called the magnetic chromatography. The calculated time evolutions of the particle concentration in the thin cylindrical channel show the flow velocity difference of the particle transport corresponding to the difference of the magnetic susceptibility. It is considered that the open gradient quadrupole magnetic field can be applied for the magnetic chromatography.

Influence of Insulation Properties on Steady Normal-Zone Velocity Inside Superconducting Magnet

Features of steady normal-zone evolution in the transverse and longitudinal directions of multi-strand region composed of superconducting composite and insulation are discussed. It is shown that allowance for a transient diffusion process in insulation does not practically change the results of quantitative description of the normal-zone kinetics in superconducting coil. The propagation of the normal zone in a layer structure of conductor and nonconductor parts is mainly affected by the thermal resistance of insulation.

고온 초전도체 관에서의 과도 자기확산 해석

Transient magnetic diffusion process in a melt-cast BSCCO-2212 tube is analyzed by an analytical method. The transient diffusion partial differential equation is transformed into an ordinary differential equation by integral method. The penetration depth of magnetic field into a superconducting tube is obtained by solving the differential equation numerically. The results show that the penetration depth as a function of time which is somewhat different from the results by Bean's critical state model. The reason of the difference between the present results and that of Bean's model is discussed and compared in this paper.