Reaction-diffusion Coupling Research Articles

Reaction–Diffusion Coupling Facilitates the Sequential Precipitation of Metal Ions from Battery Feedstock Solutions

Reaction–Diffusion Coupling Facilitates the Sequential Precipitation of Metal Ions from Battery Feedstock Solutions

The computation of Lie point symmetry generators, modulational instability, classification of conserved quantities, and explicit power series solutions of the coupled system

The well-known Chaffee–Infante reaction hierarchy is examined in this article along with its reaction–diffusion coupling. It has numerous variety of applications in modern sciences, such as electromagnetic wave fields, fluid dynamics, high-energy physics, ion-acoustic waves in plasma physics, coastal engineering, and optical fibres. The physical processes of mass transfer and particle diffusion might be expressed in this way. The Lie invariance criteria is taken into consideration while we determine the symmetry generators. The suggested approach produces the six dimensional Lie algebra, where translation symmetries in space and time are associated to mass conservation and conservation of energy respectively, the other symmetries are scaling or dilation. Additionally, similarity reductions are performed, and the optimal system of the sub-algebra should be quantified. There are an enormous number of exact solutions can construct for the traveling waves when the governing system is transformed into ordinary differential equations using the similarity transformation technique. The power series approach is also utilized for ordinary differential equations to obtain closed-form analytical solutions for the proposed diffusive coupled system. The stability of the model under the limitations is ensured by the modulation instability analysis. The reaction diffusion hierarchy’s conserved vectors are calculated using multiplier methods using Lie Backlund symmetries. The acquired results are presented graphically in 2-D and 3-D to demonstrate the wave propagation behavior.

Molecular interaction-based reaction-diffusion coupling within catalytic nanochannels

The nanoconfinement effect on the inner reaction–diffusion coupling is significant, while the underlying common principle remains ambiguous, which is mainly attributed to the lack of a feasible model. Herein, the dynamic reaction density functional theory (DRxDFT) is extended, by involving the position-dependent local diffusion coefficient, to investigate the reaction–diffusion coupling of an irreversible unimolecular isothermal reaction within catalytic nanochannels. The local diffusion coefficient is jointly determined by the pore size and local density. For demonstration, the reaction–diffusion in a rectangle nanochannel is studied by means of DRxDFT, and the predicted steady-state productivities are in excellent agreement with reactive molecular dynamics simulations. The DRxDFT is further applied to analyze the RD coupling within generic catalytic nanochannels. Towards this end, a microscopic effectiveness factor is introduced to identify the dominant role in the competition between reaction and diffusion, with which it is found that the effect of nanochannel size on productivity exhibits a generic opposite trend under reaction-dominated and diffusion-dominated conditions. This work provides a microscopic insight into the coupling of reaction and diffusion in nanoconfinement.

Concentration fluctuation caused by reaction–diffusion coupling near catalytic active sites

The coupling of reaction and diffusion between neighboring active sites in the catalyst pore leads to the spatiotemporal fluctuation in component concentration, which is very important to catalyst performance and hence its optimal design. Molecular dynamics simulation with hard-sphere and pseudo-particle modeling has previously revealed the non-stochastic concentration fluctuation of the reactant/product near isolated active site due to such coupling, using a simple model reaction of A→B in 2D pores. The topic is further developed in this work by studying the concentration fluctuation due to such coupling between neighboring active sites in 3D pores. Two 3D pore models containing an isolated active site and two adjacent active sites were constructed, respectively. For the isolated site, the concentration fluctuation intensifies for larger pores, but the product yield decreases, and for a given pore size, the product yield reaches a peak at a certain reactant concentration. For two neighboring sites, their distance ( d ) is found to have little effect on the reaction, but significant to the diffusion. For the same reaction competing at both sites, larger d leads to more efficient diffusion and better overall performance. However, for sequential reactions at the two sites, higher overall performance presents at a smaller d . The results should be helpful to the catalyst design and reaction control in the relevant processes.

Mode selection mechanism in traveling and standing waves revealed by Min wave reconstituted in artificial cells.

Reaction-diffusion coupling (RDc) generates spatiotemporal patterns, including two dynamic wave modes: traveling and standing waves. Although mode selection plays a substantial role in the spatiotemporal organization of living cell molecules, the mechanism for selecting each wave mode remains elusive. Here, we investigated a wave mode selection mechanism using Min waves reconstituted in artificial cells, emerged by the RDc of MinD and MinE. Our experiments and theoretical analysis revealed that the balance of membrane binding and dissociation from the membrane of MinD determines the mode selection of the Min wave. We successfully demonstrated that the transition of the wave modes can be regulated by controlling this balance and found hysteresis characteristics in the wave mode transition. These findings highlight a previously unidentified role of the balance between activators and inhibitors as a determinant of the mode selection of waves by RDc and depict an unexplored mechanism in intracellular spatiotemporal pattern formations.

An equivalent diffusion coefficient model of the oxidation of ceramic matrix composites

A multiscale analysis method was developed to simulate the reaction-diffusion process of SiC/SiC composite structures in a coupled thermo-chemo-mechanical environment. For the diffusion process, the airflow channel was characterized by an equivalent diffusion coefficient model, which was established in this study. The corresponding calculation was developed using a numerical analysis method to obtain the gas concentration distribution in the structure. For the reaction process, an oxidation kinetics model was adopted to calculate morphological evolution of the airflow channel. The equivalent diffusion coefficient was then updated, and the reaction–diffusion coupling calculation was performed through an iterative scheme. To validate the model, an oxidation tensile test was conducted at 1200 °C. Finally, an adjustment sheet model was calculated as an example to analyze its reaction-diffusion process, proving that this method can be applied to SiC/SiC components under complex aerodynamic and temperature loads.

A dynamic reaction density functional theory for interfacial reaction-diffusion coupling at nanoscale

Reaction-diffusion (RD) coupling lies in the heart of chemical engineering. Due to the inherent density inhomogeneity of interfacial systems, the existing continuum approaches for quantifying the coupling between reaction and diffusion do not translate into interfacial systems, which highlights the urgent need for developing new methods to describe the RD coupling at nanoscale. In this work, a dynamic reaction density functional theory (DRxDFT) is proposed by combining the classical dynamic DFT for describing reactant/product diffusion with the reaction collision theory for addressing chemical reaction. For demonstrating its applicability to interfacial systems, the DRxDFT is hereafter applied to investigate an irreversible model reaction A + 2B → 2C on a catalytic substrate, and the effects of temperature, substrate adsorption strength, reactant concentration, diffusion coefficient, and reaction activation energy on reaction efficiency are examined. The calculated results show that the enhancement of reaction efficiency weakly depends on the unilateral increase of reaction or diffusion rate, but is strongly determined by the incensement of the coupled degree of reaction and diffusion. The proposed theory provides a promising tool for guiding the optimization and intensification of interfacial RD processes.

Modeling the dissolution of thermosetting polymers and composites via solvent assisted exchange reactions

Thermosetting polymers and composites featuring chemical cross-linking are usually regarded as unrecyclable. Recently, novel thermosets containing dynamic chemical bonds or labile bonds have been developed to achieve chemical recycling under mild conditions via solvent assisted exchange or cleavage reactions. This concept has been extended to recycle conventional thermosets and composites using a proper catalyst/solvent system by selective bond cleavage. In this paper, we develop a modeling framework to probe into the complicated reaction-diffusion coupling and reveal the effect of reinforcement, such as carbon fiber, on the dissolution process of carbon fiber reinforced epoxy (CFRE). A model involving chemical species concentration dependent diffusion and reaction rates is developed to inquire into the evolution of different functional group concentrations and network structure via solvent assisted exchange reactions. We further apply the reaction-diffusion based model to a multiphase structure to simulate the CFRE dissolution process. The model is experimentally validated by the mass evolution of a virgin cured epoxy-anhydride resin matrix in an alcohol/catalyst solution proceeding with transesterification. The established model can predict the influence of dissolution processing parameters including catalyst concentration and solvent diffusivity. Parametric studies are used to further assess the structural parameters of fiber loading on the dissolution rate. This work provides a deep understanding on the dissolution of thermosets and their fiber-reinforced composites and can guide the future engineering application of sustainable recycling approaches of thermosets and composites.

Self-organization Assay for Min Proteins of Escherichia coli in Micro-droplets Covered with Lipids

The Min system determines the cell division plane of bacteria. As a cue of spatiotemporal regulation, the Min system uses wave propagation of MinD protein (Min wave). Therefore, the reconstitution of the Min wave in cell-sized closed space will lead to the creation of artificial cells capable of cell division. The Min waves emerge via coupling between the reactions among MinD, MinE, and ATP and the differences in diffusion rate on the cell membrane and in the cytoplasm. Because Min waves appear only under the balanced condition of the reaction-diffusion coupling, special attentions are needed towards several technical points for the reconstitution of Min waves in artificial cells. This protocol describes a technical method for stably generating Min waves in artificial cells.

Cell-sized confinement controls generation and stability of a protein wave for spatiotemporal regulation in cells.

The Min system, a system that determines the bacterial cell division plane, uses changes in the localization of proteins (a Min wave) that emerges by reaction-diffusion coupling. Although previous studies have shown that space sizes and boundaries modulate the shape and speed of Min waves, their effects on wave emergence were still elusive. Here, by using a microsized fully confined space to mimic live cells, we revealed that confinement changes the conditions for the emergence of Min waves. In the microsized space, an increased surface-to-volume ratio changed the localization efficiency of proteins on membranes, and therefore, suppression of the localization change was necessary for the stable generation of Min waves. Furthermore, we showed that the cell-sized space strictly limits parameters for wave emergence because confinement inhibits both the instability and excitability of the system. These results show that confinement of reaction-diffusion systems has the potential to control spatiotemporal patterns in live cells.

Concentration fluctuation due to reaction-diffusion coupling near an isolated active site on catalyst surfaces

The coupling of reaction and diffusion processes on catalytic surfaces leads to spatio-temporal heterogeneity in concentration. Understanding of this phenomenon is very important for better catalyst design and higher reaction efficiency. In this work, molecular dynamics simulations combing hard-sphere and pseudo-particle modeling are carried out to investigate the coupling between the reaction and diffusion near an isolated active site in 2D pores with a simple reaction model. The local fluctuation in concentration caused mainly by the reaction-diffusion coupling is observed and proved to be non-stochastic using quantitative parameters proposed in this work. The reaction factor R and diffusion factor D are defined to quantitatively characterize the reaction and diffusion performance, respectively. The results show that the fluctuation is weak when the process is reaction-limited (e.g., R/D is very small) or diffusion-limited (e.g., R/D is very large). When R/D is within a certain range, the strongest fluctuation appears. Besides, the diffusion factor D has a relatively larger effect on the fluctuation than the reaction factor R. Similarly, it is found that the highest overall yield of the pore is obtained only when R/D is within a specific range due to the reaction and diffusion coupling. It is also found that the local fluctuation must be considered when studying complex reaction processes with different reaction orders. The results are expected to be helpful for understanding the reaction and diffusion coupling and the complex reaction kinetics at the atomic scale, as well as for the design of catalysts and the improvement of catalytic efficiency.

The Impact of Reaction on the Effective Properties of Multiscale Catalytic Porous Media: A Case of Polymer Electrolyte Fuel Cells

Reaction–diffusion processes in multiscale catalytic porous media are found in a wide range of scientific areas as, for example, electrochemical energy conversion and storage devices, geological systems and bioengineering. The dependency of effective transport properties on reaction rate has been long debated in the literature, and traditionally ignored in emerging fields, such as polymer electrolyte fuel cells (PEFCs). In this work, a 1D upscaling method is presented to evaluate the effective properties (effective diffusivity and catalyst utilization) of PEFC catalyst layers featuring first-order kinetics. Unlike Whitaker’s closure method, the present algorithm is easy to implement and well suited for porous media with arbitrarily complex 3D geometries. The numerical results show that the normalized effective diffusivity and catalyst utilization are not passive geometrical properties but are influenced by the reaction–diffusion coupling when the Thiele modulus is higher than 1. This effect can be important at high current densities in the cathode catalyst layer of state-of-the-art PEFCs.

Concurrent reaction and diffusion in photo-responsive hydrogels

A hydrogel is a polymer network dispersed in an aqueous solvent. A hydrogel with photo-reactive molecules bonded on the polymer network can change its volume in response to light. The light triggers a chemical reaction of the photo-reactive molecules, for example the photo-isomerization of spirobenzopyran, and alters the interaction parameter between the polymer network and the solvent molecules, which drives the diffusion of the solvent molecules, inducing a volumetric change of the hydrogel. The photo-response kinetics of the hydrogel is governed by concurrent reaction and diffusion. In this paper, we establish a theoretical framework to describe the constitutive behavior of photo-responsive hydrogels based on non-equilibrium thermodynamics. The framework, coupling deformation of hydrogels with diffusion of solvent molecules and reaction of photo-reactive molecules, allows us to predict the spatiotemporal response of photo-responsive hydrogels under light and in the dark. We show the significantly different photo-response kinetics, including reaction-limited, diffusion-limited, and reaction-diffusion coupling processes, with constrained and free swelling of a hydrogel thin film as examples. Particularly, we demonstrate how slow diffusion postpones the onset of post-illumination kinetic response of a photo-responsive hydrogel in the dark. This framework provides us understanding and design guidelines for photo-responsive hydrogels.

Cell-Space Confinement Effects on Min Protein Waves Inside Microdroplets

Min system is the determinant mechanism of the position of division plane in bacterial cells. Reaction-diffusion coupling of Min system components (MinD, MinE, and ATP) emerges pole-to-pole oscillation of Min proteins (Min wave), and it inhibits assemblies of cell division initiator (Z ring) except at the center of cell. Although Min wave has been successfully reconstituted on 2D planar membrane and in fully confined systems, we found that physiological concentration of Min system components does not emerge Min wave in microdroplets covered with E. coli polar lipids. This finding is contrary to the results from previous studies, and thus, we investigated the mechanism underlying this difference.Consequently, we found “cell-space confinement effects” are the cause of the difference. Recent studies have shown that “cell-space confinement effects” changes behaviors and dynamics of biological systems. In the case of Min system, our biochemical investigations showed that the cell-space confinement changes physicochemical parameters of Min proteins, and hence, behaviors of Min wave were altered by the confinement. Furthermore, we showed a macromolecular crowding reagent counteract the change of the physicochemical parameters of Min proteins, and ensure stable emergence of Min wave inside microdroplets covered with E.coli polar lipids. We also found that artificial lipid composition of the previous study using microdroplets works similarly to the macromolecular crowding reagent we used.Our results predict that undefined factors are critical for stable emergence of Min wave in living cells, and evoke that importance of cell-size confinement effect for understanding coupling of reaction with diffusion in living systems.

Simulation Study on the Reaction-Diffusion Coupling in Simple Pore Structures.

Most porous media (just like catalyst pellets) have complicated pore structures, and understanding the coupling of the diffusion and reaction processes in these pores is very important for improving their performance. In this work, a diffusion factor (D) and a reaction factor (R) are proposed to quantitatively describe the diffusion and reaction performance in these pores respectively at molecular level. The yield in unit time is used to quantify their productivity and is expressed as the product of D and R. Molecular dynamic simulations with the hard-sphere algorithm are carried out to study the reaction-diffusion coupling in several simple pore structures with the same volume, such as straight, T-shaped, and cross-shaped pores. The reaction formula based on activation energy is given for a simple irreversible reaction process from A to B. In terms of the proposed factors, D and R, analysis on the simulation results shows clearly that the overall productivity of these pore structures depends on the competition of D and R, which are both determined by the size and shape of the pore structures. The results demonstrate the effectiveness of the simulation approach used for evaluating the performance of the simple pore structures for simple reactions and the potential of its application in more complicated and practical cases. It also suggests the effectiveness of the proposed factors, D and R, for charactering the diffusion and reaction processes at molecular level.

Synchronization of coupled reaction–diffusion neural networks with hybrid coupling via aperiodically intermittent pinning control

This paper investigates the complete synchronization for linearly coupled neural networks with time-varying delays and reaction–diffusion terms by using the aperiodically intermittent pinning control. The coupling matrix for the network can be asymmetric. Compared with state coupling in the synchronization literature, we design a novel distributed coupling protocol by using the reaction–diffusion coupling: spatial coupling, which can accelerate the synchronization process. This can be regarded as the main difference between this paper and previous works. Using the Lyapunov function and theories in the aperiodically intermittent control, we present some criteria for the complete synchronization with a static coupling strength. In this case, there is no constraint on the bound of time-varying delays, so it can be larger than the length of control span. On the other hand, we also consider the network with an adaptive coupling strength. In this case, the infimum of the control time span should be larger than the upper bound of time delay. Numerical simulations are given to show correctness of obtained results.

Simulation of the effect of coke deposition on the diffusion of methane in zeolite ZSM-5

Coke deposition is one of the main reasons for catalyst deactivation, which is often associated with coverage of the active sites and diffusion restrictions. In this article, the self-diffusion coefficient of methane in ZSM-5 (MFI) with different amounts of coke is studied through molecular dynamics simulation combining hard-sphere and pseudo-particle modeling at a gas loading of 4 molecules per unit cell at 723K. The T12 tetrahedral sites are considered as the possible coke deposition sites at which the pore is blocked. It is shown that the self-diffusion coefficient of methane in ZSM-5 without coke (D0) is approximately 7.0×10−9m2/s. Two coke distribution models are proposed to simulate the actual process of coke formation. At the initial stage of coke deposition, the coke with uniform distribution has little influence on the diffusion process. Once the coke deposits are randomly concentrated on some sites and a few pores are therefore completely blocked, the coke has a significant influence on the self-diffusion coefficient, which decreases to 37.0% of D0 almost linearly with increasing coke amount to 20%. The distribution of coke deposition is the result of the coupling of reaction and diffusion processes. These results may be useful for understanding the reaction–diffusion coupling mechanism of the catalyst deactivation.

Origination, Variation, and Conservation of Animal Body Plan Development

Multicellular organisms develop from fertilized eggs or asexual propagules. In the case of animals the developmental processes by which their bodies take form originated in several phases beginning between 600 and 700 million years ago, in the Ediacaran period. Genes and signaling pathways, many of which were present in unicellular ancestors, came to mediate morphogenesis and cell pattern formation by virtue of bringing into play physical effects that were newly relevant on the scale of cell aggregates. Focusing on “liquid-like” properties of cell clusters and their capacity to act as “excitable media,” this review explores how the products of ancient and some novel genes of what became the “developmental toolkit” were variously employed to mobilize well-characterized physical effects and processes (cohesivity, phase separation and disaggregation, surface and shape polarization of cells, chemical oscillation, reaction–diffusion coupling) in the cell aggregates that eventually evolved into animal bodies and organs. This interplay of physics and genetics led to the generation of morphological motifs such as the tissue layering of gastrulation, lumen formation, body elongation, triploblasty, segmentation, and patterning of endoskeletal elements. Since not all founding lineages had identical sets of toolkit genes, not all morphogenetic and patterning processes were equally present in their descendents. These “physico-genetic” factors collectively account for the conservation and diversity of body plans seen in the present-day animal phyla. Keywords: “basal” metazoans; basal lamina; convergent extension; diploblasts; liquid tissue; lumen formation; multilayering; saltational evolution; segmentation; triploblasts; tetrapod limbs

Emergence of microstructural patterns in skin cancer: a phase separation analysis in a binary mixture

Clinical diagnosis of skin cancers is based on several morphological criteria, among which is the presence of microstructures (e.g. dots and nests) sparsely distributed within the tumour lesion. In this study, we demonstrate that these patterns might originate from a phase separation process. In the absence of cellular proliferation, in fact, a binary mixture model, which is used to represent the mechanical behaviour of skin cancers, contains a cell–cell adhesion parameter that leads to a governing equation of the Cahn–Hilliard type. Taking into account a reaction–diffusion coupling between nutrient consumption and cellular proliferation, we show, with both analytical and numerical investigations, that two-phase models may undergo a spinodal decomposition even when considering mass exchanges between the phases. The cell–nutrient interaction defines a typical diffusive length in the problem, which is found to control the saturation of a growing separated domain, thus stabilizing the microstructural pattern. The distribution and evolution of such emerging cluster morphologies, as predicted by our model, are successfully compared to the clinical observation of microstructural patterns in tumour lesions.

CELLULAR NEURAL NETWORK MODELS OF GROWTH AND IMMUNE OF EFFECTOR CELLS RESPONSE TO CANCER

Four reaction-diffusion cellular neural network (R-D CNN) models are set up based on the differential equation models for the growths of effector cells and cancer cells, and the model of the immune response to cancer proposed by Allison et al. The CNN models have different reaction-diffusion coefficients and coupling parameters. The R-D CNN models may provide possible quantitative interpretations, and are good in agreement with the in vitro experiment data reported by Allison et al.