Chemical Potential Gradient Research Articles

Mass transport modelling of two partially miscible, multicomponent fluids in nanoporous media

High-pressure fluid transport in nanoporous media such as shale formations requires further understanding because conventional continuum approaches become inadequate due to their ultralow permeability and complexity of transport mechanisms. We propose a species-based approach for modelling two partially miscible, multicomponent fluids in nanoporous media – one that does not rely on conventional bulk fluid transport frameworks but on species movement. We develop a numerical model for species transport of partially miscible, non-ideal fluid mixtures using the chemical potential gradient as the driving force. The model considers the binary friction concept to include the friction between fluid molecules as well as between fluid molecules and pore walls, and incorporates the key multicomponent transport mechanisms – Knudsen, viscous and molecular diffusion. Under single-phase conditions, the system under consideration is quantified by introducing multicomponent Sherwood number (Sh), Péclet number (Pe) and fluid–solid friction modulus (φ). Despite the complexity of fluid transport in nanopores, the steady-state single-phase transport results reveal the contribution of diffusion in nanopores, where all parameters collapse on a set of master curves for the multicomponent Sh with a dependence on multicomponent Pe and φ. Unsteady state, two-phase transport modelling of the codiffusion process shows that light and intermediate alkanes are produced much higher than heavy alkanes when the vapour phase appears. We demonstrate that the pressure gradient is also crucial in promoting CO2 and alkane mixing during counterdiffusion processes. These results stress the need for a paradigm shift from classical bulk flow modelling to species-based transport modelling in nanoporous media.

Semiclassical transport in two-dimensional Dirac materials with spatially variable tilt

We use Boltzmann theory to study the semi-classical dynamics of electrons in a two-dimensional (2D) tilted Dirac material in which the tilt varies in space. The spatial variation of the tilt parameter induces a non-trivial spacetime geometry on the background of which the electrons roam about. As the first manifestation of graivto-electric phenomena, we find a geometric planar Hall effect according to which a current flows in a direction transverse to the chemical potential gradient and is proportional to gxy component of the emergent spacetime structure. The longitudinal conductivity contains information about the gravitational red-shift factors. Furthermore, in the absence of externally applied electric field there can be “free-fall” or zero-bias currents that can be used as detectors of terahertz radiation.

Computational Fluid Dynamics Modelling of Hydrogen Production via Water Splitting in Oxygen Membrane Reactors.

The utilization of oxygen transport membranes enables the production of high-purity hydrogen by the thermal decomposition of water below 1000 °C. This process is based on a chemical potential gradient across the membrane, which is usually achieved by introducing a reducing gas. Computational fluid dynamics (CFD) can be used to model reactors based on this concept. In this study, a modelling approach for water splitting is presented in which oxygen transport through the membrane acts as the rate-determining process for the overall reaction. This transport step is implemented in the CFD simulation. Both gas compartments are modelled in the simulations. Hydrogen and methane are used as reducing gases. The model is validated using experimental data from the literature and compared with a simplified perfect mixing modelling approach. Although the main focus of this work is to propose an approach to implement the water splitting in CFD simulations, a simulation study was conducted to exemplify how CFD modelling can be utilized in design optimization. Simplified 2-dimensional and rotational symmetric reactor geometries were compared. This study shows that a parallel overflow of the membrane in an elongated reactor is advantageous, as this reduces the back diffusion of the reaction products, which increases the mean driving force for oxygen transport through the membrane.

Water vapor corrosion behavior of SiC-Al40Y ceramics fabricated by reactive melt infiltration and thermal diffusion

The corrosion resistance of Y-Al diffused SiC ceramics (SiC-Al40Y) at 1100-1300 °C was investigated. The results show that the weight gain curves comply with the parabolic fitting formula, then the oxidation rate constant and the activation energy were calculated to be 1.653×10-5 (1100 °C), 3.704×10-5 (1200 °C), 9.306×10-5 (1300 °C) mg2/cm4s and 154.7 kJ/mol. Compared with reported SiC (41-147 kJ/mol), the higher activation energy indicates the better corrosion-resistant performance. And it is found that the Y-Al diffusion layers can be transformed to corrosion-resistant YAlSixOy layers under corrosive atmosphere. Eventually, based on experimental results, the corrosion-resistant mechanism is analyzed: chemical potential gradient caused by preferential oxidation of Y-Al prompts the immigration of Y-Al from matrix to surface, gradually forming a continuous Y/Al-silicate layer on the surface and thus can hinder the further corrosion of H2O, O2.

Rigorous Models for Vapor Diffusion in Polymers with Immobilization and Chemical Potential Gradients.

Two key phenomena─immobilization and concentration-dependent mixing free energies─simultaneously alter the sorption thermodynamics and diffusion of vapors in materials. This interrelation is leveraged to fit a unified model simultaneously capturing both sorption dynamics and the equilibrium isotherms. This transport model incorporates quasi-equilibrated immobilization reactions and considers Fick's law rigorously in terms of chemical potential gradients rather than concentration gradients. Five material case studies are discussed with varying characteristics, including fillers that provide sites for surface sorption, pores for capillary condensation, and apparent clustering or pooling at high vapor concentrations. Each case study illustrates that intrinsic diffusivity is constant, while the effective diffusivity changes predictably because of immobilization or changing free energies of mixing.

Modeling oxygen transport in Cr doped UO2 fuel with the TAF-ID during power transients

This paper proposes an efficient coupling between an oxygen redistribution model and the Thermodynamics for Advanced Fuels-International Database (TAF-ID) to describe the behavior of fission products, actinides, and dopant in a uranium dioxide matrix. The formulation of oxygen migration in the fuel is a function of the oxygen (and uranium) chemical potential gradient. The proposed formulation does not require the introduction of the Soret term and relies solely on the known mobilities of uranium and oxygen in the fuel. This coupling is applied to the simulation of a power ramp on a chromia-doped fuel rod using the PLEIADES/ALCYONE fuel performance code. The simulations successfully reproduce most of the available experimental observations on the fission products (Cs, Mo, Ru) and on the chromium dopant.

(Battery Student Slam 8 Award Winner) Multi-Clustered Lithium Diffusion in Single-Crystalline NMC Battery Particles

Understanding the diffusion dynamics of lithium within solid-state electrodes is pivotal for developing high-performance batteries. In this context, layered oxides were utilized as a promising cathode material due to their high energy density and fast intraparticle lithium diffusivity. Despite advancements in material composition, coating, and doping, the understanding of intraparticle lithium diffusion has long been described by Fick's law. Conventionally, lithium diffusion is assumed to generate a monotonic lithium concentration gradient within solid-solution single-crystalline battery materials during cycling. This raises fundamental questions about diffusion in layered oxides; (1) Can the diffusion of Li in solids be interpreted as Fickian diffusion, similar to diffusion in gases or liquids, even though it involves structural and phase evolution throughout the battery cycle? and, (2) Does the fast diffusivity (10-11-10-9 cm2/s) support the homogenization of Li?In this study, we address these questions surrounding lithium diffusion in layered oxide by utilizing operando scanning transmission X-ray microscopy. We revealed the formation of mobile Li-dense/-dilute nano-domains within individual single-crystalline LiNi1/3Mn1/3Co1/3O2 (scNMC) during battery cycles. We term this phenomenon ‘multi-clustered lithium diffusion’, distinguishing our findings from the conventionally suggested Fickian diffusion model in solid-solution materials. These domains persist for at least 4 hours during relaxation, accompanied by locally residing strained domains, as confirmed by Bragg coherent diffraction imaging (BCDI), within a single particle. We believe these domains arise due to the compensation of localized chemical potential gradients that are generated by the sustained presence of strain within the battery particles during cycling.While maintaining integrity of Li-dense/-dilute domain at various C-rates, STXM result further show that Li-dilute domains maintain during the discharging. Given the lower concentration of Li at insertion boundaries, which could lower the surface charge transfer impedance of the system, Li-dilute domains facilitate lithium transport by functioning as low-resistance pathways. Through a comprehensive analysis of electrical impedance spectroscopy (EIS), STXM imaging and finite element analysis (FEA), we showed that controlling the local domain fraction is crucial for controlling the overpotential during subsequent charging. Our study introduces new insights into nanoscale solid-state diffusion, thereby enabling the fabrication of high-performance batteries. Figure 1

Self-consistent sharp interface theory of active condensate dynamics

Biomolecular condensates help organize the cell cytoplasm and nucleoplasm into spatial compartments with different chemical compositions. A key feature of such compositional patterning is the local enrichment of enzymatically active biomolecules which, after transient binding via molecular interactions, catalyze reactions among their substrates. Thereby, biomolecular condensates provide a spatial template for nonuniform concentration profiles of substrates. In turn, the concentration profiles of substrates, and their molecular interactions with enzymes, drive enzyme fluxes which can enable novel nonequilibrium dynamics. To analyze this generic class of systems, with a current focus on self-propelled droplet motion, we here develop a self-consistent sharp interface theory. In our theory, we diverge from the usual bottom-up approach, which involves calculating the dynamics of concentration profiles based on a given chemical potential gradient. Instead, reminiscent of control theory, we take the reverse approach by deriving the chemical potential profile and enzyme fluxes required to maintain a desired condensate form and dynamics. The chemical potential profile and currents of enzymes come with a corresponding power dissipation rate, which allows us to derive a thermodynamic consistency criterion for the passive part of the system (here, reciprocal enzyme-enzyme interactions). As a first-use case of our theory, we study the role of reciprocal interactions, where the transport of substrates due to reactions and diffusion is, in part, compensated by redistribution due to molecular interactions. More generally, our theory applies to mass-conserved active matter systems with moving phase boundaries. Published by the American Physical Society 2024

Examining basic theorems and plane waves in the context of thermoelastic diffusion using a multi-phase-lag model with temperature dependence

This study employs a novel mathematical formulation of temperature-dependent thermoelastic diffusion with multi-phase delays (TDMT). The TDMT model, which is assumed, is obtained by converting the fundamental rules of Fourier’s and Fick’s laws into higher order time derivatives of the heat flow vector, the temperature gradient, diffusing mass flux, and the chemical potential gradient. Fundamental theorems such as energy, uniqueness, reciprocity theorems, and variational criterion are established using the fundamental equations for the assumed model TDMT. The reciprocity theorem is applied to a particular scenario by using instantaneous concentrated body forces, heat sources, chemical potential sources, and moving heat sources as examples. It is noted that both the variational criterion and these theorems depend on the field variables’ susceptibility as well as the fluctuations in the higher order temporal derivatives’ parameters. Additionally, the assumed model’s two-dimensional (2D) plane wave propagation is described. Three longitudinal waves are identified: the longitudinal (P) wave, the thermal (T) wave, the chemical potential (CP) wave, and the linked transverse (SV) wave. Wave properties (phase velocity and attenuation coefficient) are calculated numerically and shown visually. A few special examples are also investigated and compared with the established findings. The framework for additional research into basic issues in thermoelastic continua under various physical field variables is provided by this work. Numerous applications in material science, geomechanics, soil dynamics, and the electronic sector can be made of the current findings.

Influence of heat flow due to concentration gradient on unsteady MHD heat and mass transform dissipative flow with spanwise fluctuating temperature

This study investigates the influence of heat flow due to a concentration gradient on unsteady Newtonian free convective magnetohydrodynamic heat and mass transform dissipative fluid flow over a heated normal porous plate in the presence of radiation absorption and chemical reaction. The plate temperature is assumed to fluctuate in a spanwise cosinusoidal manner over a time and exhibit heat generation with suction velocity. The analysis employs the multiple regular perturbation method to evaluate the governing equations under stipulated boundary conditions. The outcomes are visually depicted to assess the impact of various parameters on the system dynamics. Graphical representations illustrate the physical significance of various parameters on velocity, temperature, and concentration. Additionally, skin friction, mass transfer rate, and heat transfer coefficients are presented in tabular form. The significant findings indicate that velocity, temperature, and skin friction are directly proportional to parameters such as radiation absorption, heat generation, and heat flux due to a chemical potential gradient, whereas Sherwood and concentration are inversely proportional to the Schmidt number and chemical reaction. The outcomes obtained in this study have been cross-referenced with existing scientific literature, demonstrating strong concordance. This alignment provides confidence in the numerical results.

Detailed characterizations of proton permeability properties through commercial Nafion® films under various acidic electrolytes

Nafion® film has been widely used as a representative cationic ion exchange membrane for electrochemical systems including water splitting. However, detailed H+ permeability properties have been poorly understood thus far. We here attempt to relate the H+ permeability with the material properties of Nafion® films. For that, four samples representing two casting types were selected to study the H+ permeability. We conducted the pretreatment to see the effect of the new alignment of the water clusters on the H+ permeability. Although the studied membranes show individual transport features, we observed the increased H+ permeability from 0.05 to 0.5 M concentrations in acidic electrolytes. Such a feature is caused by the increased chemical-potential gradient along with the osmotic de-swelling. We also found that a H+ diffusion channel is associated with the ionic cluster size of the films, which can explain the higher H+ permeability after the pretreatment. Lastly, the individual H+ permeability was obtained when measuring at different electrolytes, revealing that the H+ permeability is strongly influenced by the anionic mobility rather than the acidic dissociation constants. Our results provide a fundamental understanding of the H+ transports through the commercial Nafion® membrane, which gives a guideline for the rational design of ion exchange membranes.

The Gaseous Hydrogen Transport Capacity in Nanopores Coupling Bulk Flow Mechanisms and Surface Diffusion: Integration of Profession and Innovation

Due to its unique chemical structure, hydrogen energy inherently has a high calorific value without reinforcing global warming, so it is expected to be a promising alternative energy source in the future. In this work, we focus on nanoconfined hydrogen flow performance, a critical issue in terms of geological hydrogen storage. For nanopores where the pore scale is comparable to hydrogen’s molecular size, the impact on hydrogen molecules exerted by the pore surface cannot be neglected, leading to the molecules near the surface gaining mobility and slipping on the surface. Furthermore, hydrogen adsorption takes place in the nanopores, and the way the adsorption molecules move is completely different from the bulk molecules. Hence, the frequently applied Navier–Stokes equation, based on the no-slip boundary condition and overlooking the contribution of the adsorption molecules, fails to precisely predict the hydrogen flow capacity in nanopores. In this paper, hydrogen molecules are classified as bulk molecules and adsorption molecules, and then models for the bulk hydrogen and the adsorption hydrogen are developed separately. In detail, the bulk hydrogen model considers the slip boundary and rarefaction effect characterized by the Knudsen number, while the flow of the adsorption hydrogen is driven by a chemical potential gradient, which is a function of pressure and the essential adsorption capacity. Subsequently, a general model for the hydrogen flow in nanopores is established through weight superposition of the bulk hydrogen flow as well as the adsorption hydrogen, and the key weight coefficients are determined according to the volume proportion of the identified area. The results indicate that (a) the surface diffusion of the adsorption molecules dominates the hydrogen flow capacity inside nanopores with a pore size of less than 5 nm; (b) improving the pressure benefits the bulk hydrogen flow and plays a detrimental role in reducing surface diffusion at a relatively large pressure range; (c) the nanoconfined hydrogen flow conductance with a strong adsorption capacity (PL = 2 MPa) could reach a value ten times greater than that with a weak adsorption capacity (PL = 10 MPa). This research provides a profound framework for exploring hydrogen flow behavior in ultra-tight strata related to adsorption phenomena.

Swelling kinetics of mixtures of soybean phosphatidylcholine and glycerol dioleate

Lipid-based drug delivery systems offer the potential to enhance bioavailability, reduce dosing frequency, and improve patient adherence. In aqueous environment, initially dry lipid depots take up water and form liquid crystalline phases. Variation of lipid composition, depot size and hydration-induced phase transitions will plausibly affect the diffusion in and out of the depot. Lipid depots of soybean phosphatidylcholine (SPC) and glycerol dioleate (GDO) mixtures were hydrated for varying time durations in a phosphate-buffered saline (PBS) buffer and then analyzed with Karl Fischer titration, magnetic resonance imaging (MRI) and gravimetrically. Mathematical modeling of the swelling process using diffusion equations, was used to estimate the parameters of diffusion. Both composition of lipid mixture and depot size affect swelling kinetics… The diffusion parameters obtained in Karl Fischer titration and MRI (with temporal and spatial resolution respectively) are in good agreement. Remarkably, the MRI results show a gradient of water content within the depot even after the end of diffusion process. Apparently contradicting the first Fick’s law in its classical form, these results find an explanation using the generalized Fick’s law that considers the gradient of chemical potential rather than concentration as the driving force of diffusion.

A design of solar-driven thermochemical reactor integrated with heat recovery for continuous production of renewable fuels

To cope with the increasingly serious energy crisis and environmental problems, the transformation from traditional energy to renewable energy is urgent. Solar-driven thermochemical conversion of CO2 and H2O into renewable fuels technology provides a favorable path for alternative energy. However, the temperature/pressure swing required for the reduction and oxidation steps during thermochemical process incurs irreversible energy losses and severe material stresses. Moreover, the two-step redox cycle mode cannot achieve a continuous fuel production in the reactor. To address these issues, this study proposes a novel design of thermochemical reactor integrated with heat recovery for continuous production of renewable fuels. In this design, an oxygen-conducting ceria membrane is employed to conduct oxygen ions, electrons and vacancies induced by the oxygen chemical potential gradient to achieve an isothermal and continuous splitting of CO2 and H2O. At the fuel production side, a counter-flow and tube-in-tube alumina reticulate porous ceramic filling heat exchange design is developed to recover the sensible heat of gas products and excessive reactants. In addition, a comprehensive model is developed by coupling the computational dynamics of flow, radiation, conduction and convection, and is solved by the Monte Carlo method coupled with ANSYS FLUENT software through User-defined Functions. Results indicate that the integrating membrane reactor/heat recovery design can not only realize continuous production of renewable fuels, but also recover sensible heat of gas products, which is beneficial for conversion of solar energy to chemical energy. Optimizing heat recovery design can help reactor achieve a solar-to-fuel efficiency of 10.58%. Moreover, if the theoretical CO2 conversion rate could be achieved, the solar-to-fuel efficiency of reactor can reach as high as 40.43%, which means that such a reactor design has a huge potential in conversion of solar energy into renewable fuels.

Mathematical Model for a Lithium-Ion Battery with a SiO/Graphite Blended Electrode Based on a Reduced Order Model Derived Using Perturbation Theory

Silicon oxide (SiO) is a promising anode material for high-energy lithium-ion batteries, as it is made from low-cost precursors, has a potential close to that of Li, and has high theoretical specific capacity. However, the applications of SiO are limited by the intrinsic low electrical conductivity, large volume change, and low coulombic efficiency, which often lead to poor cycling performance. A common strategy to address these shortcomings is to blend SiO with graphite active materials to form a composite anode for better capacity retention. In this work, we derive a reduced order model (ROM1) using perturbation theory. We employ the multi-site, multi-reaction (MSMR) framework of a composite porous electrode blend consisting of two lithium-host materials, SiO and graphite. The ROM1 model employs a single-particle model (SPM) approach as the leading-order solution and involves the numerical analysis of a single, nonlinear partial differential equation for each host material that describes diffusion by means of irreversible thermodynamics, wherein chemical-potential gradients are the driving forces for the diffusion. The first-order correction treats losses other than that of the SPM.

Applications of Ni and Ag metallizations at the solder/Cu interfaces in advanced high-power automobile interconnects: An electromigration study

An advanced Pb-free solder interconnect, Cu line/Cu pillar/Ni/Sn1.8Ag/Ag/Cu lead frame/Sn3Ag0.5Cu/Au/Ni(P)/Cu trace, using the flip-chip quad flat no‑lead (FCQFN) packaging technology was designed for high-power automobile applications. An electromigration study revealing the Ni and Ag metallization effects on the interfacial reaction was investigated. Current stressing was conducted at a 2 A direct current at 160 °C until the defined 200 %-electrical-resistance-rise failure occurrence. Electromigration induced a two-stage electrical resistance increase mode in the advanced automobile test vehicle with a mechanism transition time of 585 h, as evidenced by the in situ resistance monitoring. Phase transformation from the constituent phases into the predominant (Cu,Ni)6Sn5 and Cu3Sn intermetallic compounds (IMCs) at the interfaces was proposed to explain the rapid resistance rise in the early-stage electromigration. Void formation and coalescence due to the Kirkendall effect and volume shrinkage during the phase transformation were proposed to explain the following steady resistance increase after the critical current stressing time. Furthermore, the phase transformation and growth of the IMCs behaved divergently at different interfaces and electron flow directions. The rapid phase transformation occurred in the downstream Sn1.8Ag solder interconnect due to the accelerated Ni metallization dissolution and formed a complete IMC joint. The anisotropic diffusion driven by the competitive or synergetic effect between the electron wind force and chemical potential gradient was proposed to explain the asymmetric microstructures after the electromigration experiment. The application of Ag metallization benefited the flip-chip soldering process, and the layer-type Ag3Sn IMC served as a diffusion barrier against Sn/Cu interdiffusion at the solder/Cu lead frame interface during the solid-state electromigration. In contrast, the Ni metallization was designed as a diffusion barrier to hinder interdiffusion and the undesirable Cu3Sn growth at the solder/Cu interface. The findings presented in this study could benefit the solder interconnect design with an appropriate metallization combination against undesirable electromigration failure.

A Dual-Cation Exchange Membrane Electrolyzer for Continuous H2 Production from Seawater.

Direct seawater splitting (DSS) offers an aspirational route toward green hydrogen (H2) production but remains challenging when operating in a practically continuous manner, mainly due to the difficulty in establishing the water supply-consumption balance under the interference from impurity ions. A DSS system is reported for continuous ampere-level H2 production by coupling a dual-cation exchange membrane (CEM) three-compartment architecture with a circulatory electrolyte design. Monovalent-selective CEMs decouple the transmembrane water migration from interferences of Mg2+, Ca2+, and Cl- ions while maintaining ionic neutrality during electrolysis; the self-loop concentrated alkaline electrolyte ensures the constant gradient of water chemical potential, allowing a specific water supply-consumption balance relationship in a seawater-electrolyte-H2 sequence to be built among an expanded current range. Even paired with commercialized Ni foams, this electrolyzer (model size: 2 × 2 cm2) continuously produces H2 from flowing seawater with a rate of 7.5 mL min-1 at an industrially relevant current of 1.0 A over 100 h. More importantly, the energy consumption can be further reduced by coupling more efficient NiMo/NiFe foams (≈6.2 kWh Nm-3 H2 at 1.0 A), demonstrating the potential to further optimize the continuous DSS electrolyzer for practical applications.

Phase-field lattice Boltzmann model with singular mobility for quasi-incompressible two-phase flows.

In this paper, a lattice Boltzmann for quasi-incompressible two-phase flows is proposed based on the Cahn-Hilliard phase-field theory, which can be viewed as an improved model of a previous one [Yang and Guo, Phys. Rev. E 93, 043303 (2016)2470-004510.1103/PhysRevE.93.043303]. The model is composed of two LBE's, one for the Cahn-Hilliard equation(CHE) with a singular mobility, and the other for the quasi-incompressible Navier-Stokes equations(qINSE). Particularly, the LBE for the CHE uses an equilibrium distribution function containing a free parameter associated with the gradient of chemical potential, such that the variable (and even zero) mobility can be handled. In addition, the LBE for the qINSE uses an equilibrium distribution function containing another free parameter associated with the local shear rate, such that the large viscosity ratio problems can be handled. Several tests are first carried out to test the capability of the proposed LBE for the CHE in capturing phase interface, and the results demonstrate that the proposed model outperforms the original LBE model in terms of accuracy and stability. Furthermore, by coupling the hydrodynamic equations, the tests of double-stationary droplets and droplets falling problems indicate that the proposed model can reduce numerical dissipation and produce physically acceptable results at large time scales. The results of droplets falling and phase separation of binary fluid problems show that the present model can handle two-phase flows with large viscosity ratio up to the magnitude of 10^{4}.

A Phase-Field Regularized Cohesion Model for Hydrogen-Assisted Cracking

Hydrogen-assisted cracking (HAC) usually causes premature mechanical failure of the material and results in structural damage in hydrogen environments. A phase-field regularized cohesion model (PF-CZM) was proposed to address hydrogen-assisted cracking. It incorporated the hydrogen-enhanced decohesion mechanism to decrease the critical energy release rate to address damage initiation and progression in a chemo-mechanical coupled environment. This model is based on coupled mechanical and hydrogen diffusion responses, driven by chemical potential gradients, and the introduction of hydrogen-related fracture energy degradation laws. The coupling problem is solved by an implicit time integral, in which hydrogen concentration, displacement and phase-field order parameters are the main variables. Three commonly used loading regimes (tension, shear, and three-point bending) were provided for comparing crack growth. Specifically, (i) hydrogen-dependent fracture energy degradation, (ii) mechanical–chemical coupling, and (iii) the diffusion coefficient D is influenced by both the phase field and the chemical field. By considering these factors, the PF-CZM model provided a variational framework by coupling mechanical loading with concentration diffusion for studying the complex interplay between a chemo-mechanical coupled environment and material damage, thereby enhancing our understanding of hydrogen-assisted cracking phenomena.

Ion-concentration gradients induced by synaptic input increase the voltage depolarization in dendritic spines

The vast majority of excitatory synaptic connections occur on dendritic spines. Due to their extremely small volume and spatial segregation from the dendrite, even moderate synaptic currents can significantly alter ionic concentrations. This results in chemical potential gradients between the dendrite and the spine head, leading to measurable electrical currents. In modeling electric signals in spines, different formalisms were previously used. While the cable equation is fundamental for understanding the electrical potential along dendrites, it only considers electrical currents as a result of gradients in electrical potential. The Poisson-Nernst-Planck (PNP) equations offer a more accurate description for spines by incorporating both electrical and chemical potential. However, solving PNP equations is computationally complex. In this work, diffusion currents are incorporated into the cable equation, leveraging an analogy between chemical and electrical potential. For simulating electric signals based on this extension of the cable equation, a straightforward numerical solver is introduced. The study demonstrates that this set of equations can be accurately solved using an explicit finite difference scheme. Through numerical simulations, this study unveils a previously unrecognized mechanism involving diffusion currents that amplify electric signals in spines. This discovery holds crucial implications for both numerical simulations and experimental studies focused on spine neck resistance and calcium signaling in dendritic spines.