Reaction-diffusion Processes Research Articles

Multiscale computational fluid dynamics modelling of spatial ALD on porous li-ion battery electrodes

The self-limiting surface reaction characteristic of atomic layer deposition (ALD) makes it ideal for the surface modification of electrode materials for lithium-ion batteries (LIBs). Spatial ALD shows promise as a scalable method for the coating on pre-fabricated electrode sheets. As a strong-coupled multiscale process, various process conditions and microstructure parameters have great influences on the macroscale fluid dynamics and the pore-scale diffusion–reaction process, thus affecting the coating efficiency. This study presents a multiscale numerical model that combines computational fluid dynamics (CFD) with multilevel pore-scale diffusion–reaction kinetics to explore the spatial ALD process on porous LIB electrodes. The dynamic mesh method is utilized to simulate electrode movement. The considerable active surface-to-volume ratio of the porous structure limits the precursor infiltration depth due to the low diffusion rate and inadequate precursor supply. As the electrode velocity increases, an asymmetric distribution of precursor concentration under the injector is observed with a rapid decrease. Elevating both the precursor concentration and inlet gas velocity augments the coating depth by enhancing the supply of the precursor. The experimental data aligns well with our numerical results, verifying the accuracy of the multiscale CFD model. Our observations reveal that a relatively lower operating pressure, around 0.1 atm, compared to 0.01 atm and 1 atm, optimizes the deposition rate along the electrode depth during the half-ALD cycle, especially when the pore size is larger. Electrode porosity of about 0.4 notably improves coating uniformity by elevating the precursor diffusion rate. Predictions show that with a substrate velocity of 0.2 m/s, the coating depth on an electrode having higher porosity at the top compared to the bottom via atmospheric spatial ALD could reach a depth of 38 μm with a precursor utilization of 78 %.

Analytical expression for the model that describes the heterogeneous reaction-diffusion process with immobilized enzyme (penicillin G acylase)

This research article examines the reaction-diffusion process in an immobilized enzyme batch reactor. The model incorporates strongly non-linear factors that are associated with standard Michaelis-Menten kinetics. The non-linear reaction-diffusion equations for substrate and product concentrations have been approximated analytically. Employing two different semi-analytical methods, Akbari-Ganji's method (AGM) and the modified Adomian decomposition method (MADM), to compute the dimensionless steady-state solutions to the system of non-linear differential equations for all values of reaction parameters. In addition, the dynamics of the mean integrated effectiveness factor of penicillin acylase in porous spherical particles have been presented for the determination of the local effectiveness factor. In order to gauge the potency of our proposed solution, we compare two semi-analytical results with a numerical result that are in good agreement across the whole concentration range. The proposed formulation aims to simulate the dynamic performance of the system utilizing the parameters and would enhance the determination of the optimum particle size for enzyme catalysts.

Semi- Analytical Study on Non-Isothermal Steady R-D Equation in a Spherical Catalyst and Biocatalyst

The Lane-Emden Boundary Value Problem as it appears in chemical applications, science, and biochemical applications are employed. Two specific models are solved by applying the Ananthaswamy-Sivasankari method (ASM). The model in first problem is a reaction–diffusion equation of a spherical catalyst and the model in second problem is the reaction–diffusion process of a spherical biocatalyst. Obtain a reliable semi-analytical expression of the effectiveness factors and the concentrations. A graph is constructed for the obtained semi-analytical solutions.The effects of several parameters like dimensionless activation energy, Thiele modulus and dimensionless heat of reaction are shown in graphical representation. Our semi-analytical solution is compared with numerical simulation by using MATLAB and finds good fit in all parameters. The new analytical method ASM is helpful to solve many non-linear problems mainly Reaction-Diffusion equation.

Self-Assembly of Structured Colloidal Gels for High-Resolution 3D Micropatterning of Proteins at Scale.

Self-assembly, the spontaneous ordering of components into patterns, is widespread in nature and fundamental to generating function across length scales. Morphogen gradients in biological development are paradigmatic as both products and effectors of self-assembly and various attempts have been made to reproduce such gradients in biomaterial design. To date, approaches have typically utilized top-down fabrication techniques that, while allowing high-resolution control, are limited by scale and require chemical cross-linking steps to stabilize morphogen patterns in time. Here, a bottom-up approach to protein patterning is developed based on a novel binary reaction-diffusion process where proteins function as diffusive reactants to assemble a nanoclay-protein composite hydrogel. Using this approach, it is possible to generate scalable and highly stable 3D patterns of target proteins down to sub-cellular resolution through only physical interactions between clay nanoparticles and the proteins and ions present in blood. Patterned nanoclay gels are able to guide cell behavior to precisely template bone tissue formation in vivo. These results demonstrate the feasibility of stabilizing 3D gradients of biological signals through self-assembly processes and open up new possibilities for morphogen-based therapeutic strategies and models of biological development and repair.

Characterisation of gaseous iodine species detection using the multi-scheme chemical ionisation inlet 2 with bromide and nitrate chemical ionisation methods

Abstract. The multi-scheme chemical ionisation inlet 1 (MION1) enables rapid switching between the measurement of atmospheric ions without chemical ionisation and neutral molecules using various atmospheric pressure chemical ionisation methods. In this study, we introduce the upgraded version, the multi-scheme chemical ionisation inlet 2 (MION2). The new design incorporates enhanced ion optics, resulting in increased reagent ion concentration, ensuring a robust operation, and enabling the use of multiple chemical ionisation methods with the same ionisation time. In order to simplify the regular calibration of MION2, we developed an open-source flow reactor chemistry model called MARFORCE. This model enables quantification of the chemical production of sulfuric acid (H2SO4), hypoiodous acid (HOI), and hydroperoxyl radical (HO2). MARFORCE simulates the convection–diffusion–reaction processes occurring within typical cylindrical flow reactors with uniform inner diameters. The model also includes options to simulate chemical processes in the following two scenarios: (1) when two flow reactors with different inner diameters are connected and (2) when two flows are merged into one using a Y-shaped tee, although with reduced accuracy. Furthermore, the chemical mechanism files in the model are compatible with the widely used Master Chemical Mechanism (MCM), allowing for future adaptation to simulate other chemical processes in flow reactors. Furthermore, we conducted a comprehensive characterisation of the bromide (Br−) and nitrate (NO3-) chemical ionisation methods with different ionisation times. We performed calibration experiments for H2SO4, HOI, and HO2 by combining gas kinetic experiments with the MARFORCE model. The evaluation of sulfur dioxide (SO2), water (H2O), and molecular iodine (I2) involved dilution experiments from a gas cylinder (SO2), dew point mirror measurements (H2O), and a derivatisation approach combined with a high-performance liquid chromatography quantification (I2), respectively. Our findings indicate that the detection limit is inversely correlated with the fragmentation enthalpy of the analyte–reagent ion (Br−) cluster. In other words, stronger binding (resulting in a larger fragmentation enthalpy) leads to a lower detection limit. Additionally, a moderately longer ionisation time enhances the detection sensitivity, thereby reducing the detection limit. For instance, when using the Br− chemical ionisation method with a 300 ms ionisation time, the estimated detection limit for H2SO4 is 2.9×104 molec. cm−3. Notably, this detection limit is even superior to that achieved by the widely used Eisele-type chemical ionisation inlet (7.6×104 molec. cm−3), as revealed by direct comparisons. While the NO3- chemical ionisation method remains stable in the presence of high humidity, we have observed that the Br− chemical ionisation method (Br−–MION2) is significantly affected by the air water content. Higher levels of air water lead to reduced sensitivity for HO2 and SO2 under the examined conditions. However, we have found that a sharp decline in sensitivity for H2SO4, HOI, and I2 occurs only when the dew point exceeds 0.5–10.5 ∘C (equivalent to 20 %–40 % RH; calculated at 25 ∘C throughout this paper). For future studies utilising the atmospheric pressure Br− chemical ionisation method, including Br−–MION2, it is crucial to carefully consider the molecular-level effects of humidity. By combining approaches such as the water-insensitive NO3-–MION2 with Br−–MION2, MION2 can offer more comprehensive insights into atmospheric composition than what can be achieved by either method alone. By employing instrument voltage scanning, chemical kinetic experiments, and quantum chemical calculations, we have conclusively established that the presence of iodine oxides does not interfere with the detection of HIO3. Our comprehensive analysis reveals that the ions IO3-, HIO3⚫NO3-, and HIO3⚫Br−, which are detected using the Br− and NO3- chemical ionisation methods, are primarily, if not exclusively, generated from gaseous HIO3 molecules within atmospherically relevant conditions.

Misconceptions about quantifying animal encounter and interaction processes

The ability to quantify when and where animals interact is key to the understanding of a plethora of ecological processes, from the structure of social communities and predator–prey relations to the spreading of pathogens and information. Despite the ubiquity of interaction processes among animals and the revolution in tracking technologies that now allows for the monitoring of multiple individuals simultaneously, a common theoretical framework with which to analyze movement data and extract interaction events is still lacking. Given the wide spectrum of mechanisms that governs how a biological organism detects the proximity of other organisms, most of the proposed theoretical approaches have been tailored to specific species or empirical situations and so far have been lacking a common currency with which to evaluate and compare findings across taxa. Here, we propose such general framework by borrowing techniques from statistical physics, specifically from the theory of reaction diffusion processes. Some of these techniques have already been employed to predict analytically pathogen transmission events between pairs of animals living within home ranges, but have not yet pervaded the movement ecology literature. Using both continuous and discrete variables, we present the mathematical framework and demonstrate its suitability to study interaction processes. By defining interactions whenever a token of information is transferred from one individual to another, we show that the probability of transferring information for the first time is equivalent to the first-passage probability of reacting in a multi-target environment. As interaction events reduce to encounter events when information transfer is perfectly efficient, we compare our formalism to a recently proposed approach to study encounters. Such approach takes the joint occupation probability of two animals over a region of interaction as a measure of the probability of encounter, rather than the first-encounter probability. We show the discrepancy of the two approaches by analytically comparing their predictions with continuous variables, while with discrete space–time variables, we quantify their difference over time. We conclude by pointing to some of the open problems that the reaction diffusion formalism, alternatively, the reaction motion formalism, as it should be more appropriately called, might be able to tackle.

Dynamic Growth of Macroscopically Structured Supramolecular Hydrogels through Orchestrated Reaction-Diffusion.

Living organisms are capable of dynamically changing their structures for adaptive functions through sophisticated reaction-diffusion processes. Here we show how active supramolecular hydrogels with programmable lifetimes and macroscopic structures can be created by relying on a simple reaction-diffusion strategy. Two hydrogel precursors (poly(acrylic acid) PAA/CaCl2 and Na2 CO3 ) diffuse from different locations and generate amorphous calcium carbonate (ACC) nanoparticles at the diffusional fronts, leading to the formation of hydrogel structures driven by electrostatic interactions between PAA and ACC nanoparticles. Interestingly, the formed hydrogels are capable of autonomously disintegrating over time because of a delayed influx of electrostatic-interaction inhibitors (NaCl). The hydrogel growth process is well explained by a reaction-diffusion model which offers a theoretical means to program the dynamic growth of structured hydrogels. Furthermore, we demonstrate a conceptual access to dynamic information storage in soft materials using the developed reaction-diffusion strategy. This work may serve as a starting point for the development of life-like materials with adaptive structures and functionalities.

(Invited) Regimes of Reaction-Diffusion Processes Nearby the Plasma-Liquid Interface

Plasma-liquid systems are usually comprised of an atmospheric-pressure plasma electrode and a liquid surface, which can have a bubbly and irregular, or a smooth surface. When coupled with a metal counter electrode immersed in the liquid, this configuration has been shown to form capable electrochemical systems that can degrade recalcitrant pollutants, conduct organic chemistry and when reactive gases are used, can create unique gas-liquid reaction pathways for important processes such as N2 fixation and CO2 utilization. Up to date, many different types of plasmas with different frequencies, plasma electrode shapes, gas flow rates and applied powers have been utilized in literature. One common aspect of most plasma sources in plasma-liquid systems is that the current density at the interface is much higher than in conventional electrochemical systems. Consequently, the observed rate constants of some of the plasma-assisted processes mentioned above have been found to fall in a rather narrow range of values, despite the vast differences in plasma sources. This is an indication of mass transport playing a crucial role in the observed kinetics. This argument is supported by experimental results obtained through changing current in continuous plasmas and changing frequency in pulsed plasmas.When mass transport rate is of the same order with reaction rate or slower, the observed picture for kinetics requires a mathematical description of the interplay of reaction and diffusion to elucidate intrinsic kinetic data. A phenomenological, yet practical and predictive modeling framework has not yet been established for plasma-liquid systems. Despite new kinetics that arise from the unique species produced at the plasma liquid interface, gas-liquid contacting is a well-established field in chemical engineering. In this talk, early chemical engineering studies on gas-liquid contacting will be summarized and the reaction-diffusion models developed through these studies will be applied to plasma-electrochemical systems. According to the theory, multiple regimes of reaction-diffusion processes must exist, and some of these regimes can be reduced to simpler analytical models that allow compact expressions for the observed rate constant and faradaic efficiency. Examples on applying the modeling framework to published experimental data will be given and the criteria that determine the validity of the model equations will be discussed.

(Invited) Cascading Catalytic Microenvironments for (photo)Electroreduction of CO2

Although copper is a useful electrocatalyst for generation of a variety of chemical products from CO2 and H2O, it has become widely recognized that the catalyst by itself is not capable of high selectivity for formation of pure streams of specific products. By controlling the local environment around the catalytic reaction center, and providing multiple types of catalysts that can perform a sequence of specific reactions, improved control over selectivity can be envisioned. The mesoscale design rules for such cascades are unknown, however. In this talk I will describe computational studies that begin to examine the molecular-level factors that control coupled reaction-diffusion processes involved in CO2 reduction via cascaded catalytic reactions, including interfacial reactivity and catalyst placement. Key design considerations and gaps in understanding that emerge from these calculations will be discussed.

An open-source pipeline for solving continuous reaction–diffusion models in image-based geometries of porous media

We present a versatile open-source pipeline for simulating inhomogeneous reaction–diffusion processes in highly resolved, image-based geometries of porous media with reactive boundaries. Resolving realistic pore-scale geometries in numerical models is challenging and computationally demanding, as the scale differences between the sizes of the interstitia and the whole system can lead to prohibitive memory requirements. The present pipeline combines a level-set method with geometry-adapted sparse block grids on GPUs to efficiently simulate reaction–diffusion processes in image-based geometries. We showcase the method by applying it to fertilizer diffusion in soil, heat transfer in porous ceramics, and determining effective diffusion coefficients and tortuosity. The present approach enables solving reaction–diffusion partial differential equations in real-world geometries applicable to porous media across fields such as engineering, environmental science, and biology.

Uphill in Reaction-Diffusion Multi-species Interacting Particles Systems

We study reaction-diffusion processes with multi-species particles and hard-core interaction. We add boundary driving to the system by means of external reservoirs which inject and remove particles, thus creating stationary currents. We consider the condition that the time evolution of the average occupation evolves as the discretized version of a system of coupled diffusive equations with linear reactions. In particular, we identify a specific one-parameter family of such linear reaction-diffusion systems where the hydrodynamic limit behaviour can obtained by means of a dual process. We show that partial uphill diffusion is possible for the discrete particle systems on the lattice, whereas it is lost in the hydrodynamic limit.

Encoding physics to learn reaction–diffusion processes

Encoding physics to learn reaction–diffusion processes

Extended fractional-polynomial generalizations of diffusion and Fisher–KPP equations on directed networks

In a variety of practical applications, there is a need to investigate diffusion or reaction–diffusion processes on complex structures, including brain networks, that can be modeled as weighted undirected and directed graphs. As an instance, the celebrated Fisher–Kolmogorov–Petrovsky–Piskunov (Fisher–KPP) reaction–diffusion equation is becoming increasingly popular for use in graph frameworks by substituting the standard graph Laplacian operator for the continuous one to study the progression of neurodegenerative diseases such as Alzheimer’s disease (AD). In this work, we establish existence, uniqueness, and boundedness of solutions for generalized Fisher–KPP reaction–diffusion equations on undirected and directed networks with fractional polynomial (FP) terms. This type of model has possible applications for modeling spreading of diseases within neuronal fibers whose porous structure may cause particles to diffuse anomalously. In the case of pure diffusion, convergence of solutions and stability of equilibria are also analyzed. Moreover, different families of positively invariant sets for the proposed equations are derived. Finally, we conclude by investigating nonlinear diffusion on a directed one-dimensional lattice.

Penetration and distribution efficacy of chemotherapeutic drugs in biological tissues: A computational investigation

Many chemotherapeutic drugs, developed so far, show significant anticancer activities during the clinical trials; however, their treatment efficacy is limited in practice. The limited efficacy is attributed to the inadequate knowledge of interplay between a drug and the physicochemical properties of tissues. This study employs the finite volume heterogeneous multiscale method to study the penetration and distribution efficacy of chemotherapeutic agents such as, fluorouracil, carmustine, cisplatin, methotrexate, doxorubicin, and paclitaxel. The physical properties of these drugs are incorporated in the model to provide physiological scenario. The effects of fluid flow, drug elimination, and microscopic cellular structures are analysed on penetration and distribution of these chemotherapeutic drugs. It is observed that carmustine penetrates deeper into the tissue, followed by paclitaxel, methotrexate, fluorouracil, doxorubicin, whereas cisplatin penetrates least. In order to explain advection–diffusion–reaction processes, a novel dimensionless number KT=Ka/Th2 is introduced, where Ka and Th are Karlovitz and Thiele modulus numbers, respectively. This number may be defined as the ratio of time-scale of reaction rate with the cumulative time-scale of advection and diffusion processes. As the model involves several parameters, the global sensitivity analysis is also performed to determine the sensitivity of uncertainties in the input parameters to the model output.

Reaction–Diffusion Process for Hydrogels with a Tailored Layer Structure

The architecture of hydrogel composites results in not only synergistic property enhancement but also superior functionality. The reaction–diffusion (RD) process is acommon phenomenon throughout nature which induced ordered structure on a length scale from microscopic to macroscopic. Different from commonly used inorganic salts or oppositely charged nanoparticles for the RD process, a modified RD process was used for layered chitosan hydrogel (L-CH) and layered magnetic chitosan hydrogel (L-MCH). During the modified RD process reported in this paper, the protonated chitosan (CS-NH3+) with iron ions (Fe3+ and Fe2+) was used as an inner-reactant and hydroxide ion (-OH−) was used as an out-reactant. The protonated chitosan (CS-NH3+) not only played the role of an inner-reactant but also the reaction medium which controlled the diffusion behavior of the out-reactant (-OH−). A series of ordered layers were constructed and the ordered layers were parallel with the longitudinal axis. The layer width of L-CH and L-MCH can be tailored by varying interval time T. The mean layer width of L-MCH increased from 50 ± 5.8 μm to 90 ± 6.4 μm when the interval time T increased from 2 min to 5 min. The tailored layer structure of L-CH and L-MCH obeyed the time law and spacing law, which declared that the L-CH and L-MCH were constructed via the reaction–diffusion process. We also show that the tailored layer structure endows hydrogel with enhanced mechanical properties, especially toughness. The yield strength of magnetic chitosan hydrogel was improved significantly (from 95.1 ± 7.6 kPa to 401.7 ± 12.1 kPa, improved by about 4 times) when 10 wt. % magnetite nanoparticles were involved. The enhancement of the mechanical propertieswas due to a physical crosslinking effect of magnetite nanoparticles on chitosan. For L-MCH, the probe displacement reached 28.93 ± 2.6 mm when the rupture occurred, which was as high as 284.7% compared with that of the non-layered hydrogel. The tailor-made hydrogels might be possible for application as a tough implantable scaffold.

Learning system parameters from turing patterns.

The Turing mechanism describes the emergence of spatial patterns due to spontaneous symmetry breaking in reaction-diffusion processes and underlies many developmental processes. Identifying Turing mechanisms in biological systems defines a challenging problem. This paper introduces an approach to the prediction of Turing parameter values from observed Turing patterns. The parameter values correspond to a parametrized system of reaction-diffusion equations that generate Turing patterns as steady state. The Gierer-Meinhardt model with four parameters is chosen as a case study. A novel invariant pattern representation based on resistance distance histograms is employed, along with Wasserstein kernels, in order to cope with the highly variable arrangement of local pattern structure that depends on the initial conditions which are assumed to be unknown. This enables us to compute physically plausible distances between patterns, to compute clusters of patterns and, above all, model parameter prediction based on training data that can be generated by numerical model evaluation with random initial data: for small training sets, classical state-of-the-art methods including operator-valued kernels outperform neural networks that are applied to raw pattern data, whereas for large training sets the latter are more accurate. A prominent property of our approach is that only a single pattern is required as input data for model parameter predicion. Excellent predictions are obtained for single parameter values and reasonably accurate results for jointly predicting all four parameter values.

Front Transport Reduction for Complex Moving Fronts

This work addresses model order reduction for complex moving fronts, which are transported by advection or through a reaction–diffusion process. Such systems are especially challenging for model order reduction since the transport cannot be captured by linear reduction methods. Moreover, topological changes, such as splitting or merging of fronts pose difficulties for many nonlinear reduction methods and the small non-vanishing support of the underlying partial differential equations dynamics makes most nonlinear hyper-reduction methods infeasible. We propose a new decomposition method together with a hyper-reduction scheme that addresses these shortcomings. The decomposition uses a level-set function to parameterize the transport and a nonlinear activation function that captures the structure of the front. This approach is similar to autoencoder artificial neural networks, but additionally provides insights into the system, which can be used for efficient reduced order models. In addition to the presented decomposition method, we outline a tailored hyper-reduction method that is based on the reduced integration domain method. The capability of the approach is illustrated by various numerical examples in one and two spatial dimensions, including an advection–reaction–diffusion system with a Kolmogorov–Petrovsky–Piskunov reaction term and real life application to a two-dimensional Bunsen flame.

Sn Diffusion Behavior and Microstructure in Nb<sub>3</sub>Sn Wires with Third Elemental Addition

Element addition plays an important role in the improvement of the physical properties of the Nb3Sn phase itself and of growth kinetics in the Nb3Sn diffusion reaction process. This paper first reviews the fundamental reaction behavior between Nb and Sn in the presence of Cu, which is the integral element for the thick Nb3Sn layer formation at a low temperature reaction, and interprets it in view of Sn chemical potential. Then the paper reviews several advanced element additions to realize breakthrough grain refinement, touching on their grain refinement mechanism. Subsequently, the recent topic of Ti and Ta addition is examined, followed by the addition of unique elements that bring functional enhancement such as mechanical strengthening of the wire.

The Steady State Bifurcation for General Network-Organized Reaction-Diffusion Systems and Its Application in a Metapopulation Epidemic Model

Because of the high dimensionality of reaction-diffusion systems on networks, exploration for the bifurcation properties of such systems has been far less thorough than their corresponding parabolic PDE systems. With the overcoming of this long-standing difficulty, we consider the steady state bifurcation for the general network-organized reaction-diffusion system and derive the algorithm of calculating the perturbation incorporated restricted system associated with the simple zero singularity, through seeking out the parameter dependent center manifolds belonging to the unique zero eigenvalue. Rigorous theoretical analysis for the third-order truncated restricted system shows that the complex underlying networks can trigger some bifurcation types differing from the usual supercritical and subcritical pitchfork bifurcations and so enrich the dynamical behaviors of reaction-diffusion process in networks. To illustrate the application for our obtained theoretical results, we conduct a strict steady state bifurcation analysis for a metapopulation epidemic system defined on four typical connected undirected underlying networks, and find that there exist some new multistability phenomena and hysteresis effects in the irregular small-word and scale-free lattice network.

Growth of self-integrated atomic quantum wires and junctions of a Mott semiconductor.

Continued advances in quantum technologies rely on producing nanometer-scale wires. Although several state-of-the-art nanolithographic technologies and bottom-up synthesis processes have been used to engineer these wires, critical challenges remain in growing uniform atomic-scale crystalline wires and constructing their network structures. Here, we discover a simple method to fabricate atomic-scale wires with various arrangements, including stripes, X-junctions, Y-junctions, and nanorings. Single-crystalline atomic-scale wires of a Mott insulator, whose bandgap is comparable to those of wide-gap semiconductors, are spontaneously grown on graphite substrates by pulsed-laser deposition. These wires are one unit cell thick and have an exact width of two and four unit cells (1.4 and 2.8 nm) and lengths up to a few micrometers. We show that the nonequilibrium reaction-diffusion processes may play an essential role in atomic pattern formation. Our findings offer a previously unknown perspective on the nonequilibrium self-organization phenomena on an atomic scale, paving a unique way for the quantum architecture of nano-network.