Search Results (130)

The negative differential resistance (NDR) effect provides nonlinear control over ionic current and has important potential in ion sensing and information storage. A multiphys-ics numerical model is established using COMSOL Multiphysics 6.3, coupling the Poisson−Nernst−Planck and Navier−Stokes equations to investigate the effects of solution concentration gradient, pore length, pore diameter, and surface charge density on NDR effect. The results indicate that the NDR effect occurs only in the negative voltage range, where concentration gradient diffusion competes with electric field driven migration. The characteristic voltage window stabilizes between −0.2 V and −0.5 V, and the total current reaches a local extremum near −0.2 V. Electromigration dominates in this range and sup-presses Cl⁻ ion diffusion, while K⁺ transport is less affected, resulting in decreased total ionic current. Under baseline conditions, the total current decreases by 26.19%, from −0.42 nA to −0.31 nA. Increasing the concentration gradient, shortening the pore length, enlarging the pore diameter, and reducing the surface charge density enhance local vortices or maintain Cl⁻ diffusion pathways, thereby strengthening NDR characteristics. This study reveals the regulation mechanisms of NDR effect by solution conditions, macropore structures, and surface properties, providing theoretical guidance for tunable ionic current devices. Full article

Diffusion against a concentration gradient, also called uphill transport, has been reported for magnesium and sulfate ions in solutions of NaCl and Mg${\mathrm{SO}}_4$ in reverse electrodialysis (RED). Here we derive transport equations for such systems and explain the observed uphill transport using non-equilibrium thermodynamics (NET). A set of Nernst–Planck equations was reformulated into a set of flux equations with neutral salt driving forces. By applying the condition of entropy production invariance to the sets of variables, we show how an ideal ion selectivity model provides Onsager coupling coefficients for the ion transport. These coupling coefficients can predict and explain the observed uphill transport of magnesium and sulfate. A linear fitting scheme is developed to fit the transport coefficients to experimental data for the ideal ion selectivity model and for a more general model. The results show that even the simplest ideal ion selectivity model captures the uphill transport, and the phenomenon occurs due to diffusional ion exchange, as in Donnan dialysis. Under open-circuit conditions, deviations are large, and the simplest model is no longer sufficient; co-ion leakage corrections are essential. The results provide a basis for future modelling of RED processes; in particular, one can determine and optimise the process efficiency, as the model gives direct access to the process’s local entropy production. Osmosis is identified as a potential source of error. Full article

This study presents a first-principles dynamic model for the electrochemical production of lithium hydroxide (LiOH) in a bench-scale cation exchange membrane (CEM) cell. Its distinguishing feature is a single, dynamically coupled description of the whole cell, in which the lumped Ordinary Differential Equation (ODE) dynamics of the anodic and cathodic chambers are coupled to a spatially resolved Nernst–Planck (PDE) model of membrane ion transport. The model resolves the transient induction period of ion crossover and captures the association kinetics of Li⁺ and ${\mathrm{OH}}^{-}$, cathodic water reduction, and the back-migration and neutralization of ${\mathrm{OH}}^{-}$ at the anode, with the local electric field represented by a non-linear potential gradient. Solved by the Method of Lines and reduced through symbolic treatment of the Robin boundary conditions to a consistent ODE system, it yields a numerically robust framework for this stiff, strongly coupled problem. Two process-level results emerge: the membrane strongly attenuates cross-chamber disturbances, largely decoupling the anode and cathode, and it reaches a quasi-steady state far faster than the bulk chambers—a separation of time scales expected to widen at larger volume-to-surface-area ratios. These insights inform scale-up strategies and multiscale control architectures for the cell. Full article

Aqueous humor (AH) is a watery fluid continuously circulating through the posterior and anterior chambers of the human eye and is essential to maintain a healthy intraocular pressure in the eyeball and keep the eye clean from waste products of metabolism and external agents. This paper presents a stationary compartment model of AH dynamics consisting of three integrated modules (M): M1 for AH production, M2 for AH passive flow and M3 for AH drainage. M1 is a zero-dimensional (0D) reduction of the velocity-extended Poisson-Nernst-Planck model and simulates solute transfer and fluid movement across the cellular structure of the ciliary epithelium (CE). M2 is the electric equivalent representation of Poiseuille flow across the series of two linear hydraulic resistors. M3 is a 0D reduction of the Darcy equations for a porous medium and simulates AH flow across the parallel between a nonlinear and a linear resistor. Compared to existing compartment approaches, the present model integrates at the macroscopic scale the multi-physical description of the human eye at the cellular scale. Numerical simulations suggest that (1) sodium channels in the CE are essential for maintaining proper AH dynamics; and (2) increased episcleral vein pressure reduces AH drainage, potentially explaining the development of secondary open-angle glaucoma. These insights advance the understanding of the mechanisms regulating AH dynamics and offer new perspectives for patient-specific therapies. Full article

We fabricated a chemoresistive sensor based on indium–tin oxide (ITO) nanoparticle detection layer printed on a polyethylene terephthalate (PET). The ITO sensor operates on a mechanism that detects substances through resistance change induced by electrochemical potential variations on the sensor surface, which correspond to changes in analyte concentration governed by the Nernst equation. In this study, we confirmed broad-spectrum detection capabilities of the ITO sensor by successfully detecting 31 kinds of substances and demonstrated by achieving a low limit of detection that fully satisfies the environmental protection limit (EPL) for effluents, also alongside an error margin of within 5% for all 31 substances. In addition, the possibility of selective detection was confirmed by presenting the response of the ITO sensor according to pH changes, concentration, and type of substance as a two-dimensional scattering pattern. Thus, this study demonstrates that ITO based on chemoresistive sensors can achieve real-time monitoring of various underwater substances with high sensitivity and broad detection capabilities. Full article

This work numerically reveals a novel strategy to modulate two ionic conductance state in a nanochannel via pressure-dependent fluidic motion inside the channel. Steady and transient simulations based on Poisson–Nernst–Planck–Stokes equations demonstrate that the two states with distinct ionic conductance and ion selectivity can be reversibly switched by external pressure, with a characteristic time of ~100 μs. Furthermore, the two conductance states are found to depend on the transversal electric field, which gives rise to two distinct intrachannel fluidic flow patterns, namely laminar flow and vortex flow, respectively. This finding suggests the potential of pressure-controlled ionic conductance switching for applications in nanofluidic ionic circuits, flow-regulated sensing, and integrated micro/nanoscale devices. It also provides insights into nonlinear ionic current–voltage behaviors. Full article

Exogenous application of plant hormones has been considered a short-term and effective strategy to alleviate deleterious effects of water stress on plants. However, whether exogenous gibberellic acid (GA₃) directly enhances nitrogen accumulation and thereby alleviates drought stress in soybean (Glycine max (Linn.) Merr.) remains to be investigated. This study set three water treatments (75% CK, 50% MD, 25% SD), with half of the plants at each level sprayed with 10⁻⁶ mol·L⁻¹ GA₃, measuring growth, photosynthesis, nitrogen content, water status, and electrophysiological parameters and calculating cellular metabolic electronic energy (ΔG_B) based on Nernst equation. The results showed that drought reduced soybean nitrogen accumulation, photosynthesis, growth and yield. GA₃ increased soybean nitrogen accumulation, improving photosynthesis and yield under CK, which enhanced the consumption of intracellular stored energy and reduced ΔG_B. Under MD, GA₃ improved leaf water status, promoted soybean nitrogen accumulation and photosynthesis and reduced ΔG_B by allocating more energy to drought resistance; it could therefore mitigate the moderate drought stress on plants. ΔG_B negatively correlated with total nitrogen content and yield, indicating that ΔG_B was a potential indicator associated with nitrogen accumulation, which can guide the optimization of GA₃ spraying strategies. Further studies on GA₃ application details are necessary to improve the soybean yields under drought conditions. Full article

The escalating accumulation of pharmaceutical micropollutants in global water systems represents a significant challenge to current circular economy frameworks, highlighting a critical gap in the management of environmental persistence. Although advanced remediation technologies are often proposed to mitigate this crisis, their engineering optimization is frequently compromised by a reliance on empirical approximations rather than precise physicochemical constants. Addressing this fundamental deficit, this study executes a rigorous determination of mass transfer properties for two ubiquitous contaminants: Butylparaben and Triclosan. Utilizing a high-precision electrolytic conductance method under infinite dilution, we investigated transport dynamics across varying temperature gradients (305.15–319.15 K). Experimental data were subjected to advanced mathematical modeling, where the Modified Robinson–Stokes (MRS) quadratic model significantly outperformed classical linear approaches ($R^2>0.98$), accurately capturing non-ideal solute–solvent interactions. The derived limiting molar conductivities facilitated the calculation of infinite dilution diffusion coefficients via the Nernst–Haskell equation, yielding values of $0.99\times {10}^{-8}$ m²/s for Butylparaben and $0.98\times {10}^{-8}$ m²/s for Triclosan. Furthermore, Stokes–Einstein analysis quantified the hydrodynamic radii, elucidating the steric mechanisms governing the sluggish migration of bulky chlorinated ethers compared to single-ring esters. These precise transport parameters are not merely theoretical values; they are essential inputs for developing accurate computational fate models and designing regenerable separation processes, thereby providing the hard physics required to engineer solutions for the perpetual pollution era. Full article

Designing structure-preserving numerical schemes for the generalized Poisson-Nernst-Planck (PNP) system is challenging due to its inherent strong nonlinearity and coupling. In this paper, we propose a class of efficient, unconditional energy-stable schemes based on the Stabilized Scalar Auxiliary Variable (S-SAV) framework combined with the finite element method. We construct both first-order (BE-S-SAV) and second-order (BDF2-S-SAV) fully discrete schemes. A distinguishing feature of our approach is the use of a linear decomposition strategy, which decouples the complex nonlinear system into a sequence of linear, constant-coefficient elliptic equations at each time step. This significantly reduces computational complexity by avoiding expensive nonlinear iterations. We provide rigorous theoretical proofs demonstrating that the proposed schemes are unconditionally energy stable and strictly preserve mass conservation. Numerical experiments satisfy the theoretical analysis, confirming optimal convergence rates and demonstrating robust preservation of mass conservation and modified energy stability in the tested regimes. Full article

This study concerns the simulation of copper electrodeposition and related phenomenological and technological aspects as influenced by electrode geometry and electrolyte flow velocity. A multiphysics simulation approach was employed, integrating mathematical models accounting for electrochemical deposition and hydrodynamic behavior. Ionic transport is described by the Nernst-Planck equations, electrode kinetics by Butler–Volmer expressions, and fluid flow by the Navier–Stokes equations. Simplified 2D and 3D models were developed to investigate industrial frame plating electrodeposition processes. The results indicate that the fluid direction of the solution in relation to the position of the substrate within the electrodeposition cell enables the distribution of the thickness of the coating to be optimized. Numerical simulation can be used to guide the choice of the orientation of cathodes to be electroplated inside the electroplating tank, to take into consideration agitation direction, and to achieve the best deposit uniformity. Full article

We introduce a hybridizable discontinuous Galerkin (HDG) scheme for solving the Poisson–Nernst–Planck (PNP) equations. The log-density formulation as introduced by Metti et al. in their paper “Energetically stable discretizations for charge transport and electrokinetic models. J. Comput. Phys. 2016, 306, 1-18” is utilized to ensure the positivity of the densities of the charged particles. We further prove that our fully discrete scheme is energy stable and mass conserving. Numerical simulations are provided to demonstrate the accuracy of the scheme in one and two spatial dimensions. A derivation of an HDG-DG space–time scheme is given, with implementation and convergence analysis left to future work. Full article

This paper presents the first theoretical investigation of the effect of a variable equilibrium coefficient on the steady-state transport of a binary electrolyte in a desalination channel cross-section of the electrodialyzer. To address this problem, we developed a new mathematical model in the form of a boundary value problem for an extended system of stationary Nernst–Planck–Poisson equations. We obtained a numerical solution to this problem using the finite element method. Analysis of this solution revealed that the channel cross-section has a complex structure: it is divided into seven regions dominated by different processes, and, consequently, the solution to the boundary value problem behaves differently in each of them. Existing models of the diffusion layer or channel cross-section typically assume a constant equilibrium coefficient. In this paper, we demonstrated that in the channel cross-section, the velocity change corresponding to the equilibrium constant is related not only to the field strength but also to the magnitude of the space charge. In the space-charge region, in the boundary layers near the ion-exchange membranes, intense dissociation of water molecules occurs, and the higher the equilibrium coefficient, the more intense this dissociation is. We have shown that an internal boundary layer (recombination region) arises deep within the solution, associated with the recombination reaction of H+ and OH− ions. In this study, we found that with increasing equilibrium coefficient, fluxes increase, while with increasing fluxes, the electric field strength decreases proportionally, and equilibrium is reached. We demonstrate that by calibrating a single fitting parameter in the model, the simulation results can be matched to experimental data with high accuracy. Thus, our proposed model and its numerical solution provide a completely new understanding of the ion transport process in electromembrane systems, taking into account the influence of the dissociation/recombination reaction of water molecules. Full article

Ion channels are protein pores that regulate ionic flow across cell membranes, enabling vital processes such as nerve signaling. They often conduct multiple ionic species simultaneously, leading to complex nonlinear transport phenomena. Because experimental techniques provide only indirect measurements of ion channel currents, mathematical models—particularly Poisson–Nernst–Planck (PNP) equations—are indispensable for analyzing the underlying transport mechanisms. In this work, we examine ionic transport through a one-dimensional steady-state PNP model of a narrow membrane channel containing multiple cation species of different valences. The model incorporates a small fixed charge distribution along the channel and imposes relaxed electroneutrality boundary conditions, allowing for a slight charge imbalance in the baths. Using singular perturbation analysis, we first derive approximate solutions that capture the boundary-layer structure at the channel—reservoir interfaces. We then perform a regular perturbation expansion around the neutral reference state (zero fixed charge with electroneutral boundary conditions) to obtain explicit formulas for the steady-state ion fluxes in terms of the system parameters. Through this analytical approach, we identify several critical applied potential values—denoted $V_k^a$ (for each cation species k), $V^b$, and $V^c$—that delineate distinct transport regimes. These critical potentials govern the sign of the fixed charge’s influence on each ion’s flux: depending on whether the applied voltage lies below or above these thresholds, a small positive permanent charge will either enhance or reduce the flux of each ion species. Our findings thus characterize how a nominal fixed charge can nonlinearly modulate multi-ion currents. This insight deepens the theoretical understanding of nonlinear ion transport in channels and may inform the interpretation of current–voltage relations, rectification effects, and selective ionic conduction in multi-ion channel experiments. Full article

The transport of chloride ions in concrete is often affected by electric fields, and its concentration distribution is generally evaluated using the Nernst–Planck equation. The Nernst–Planck theory can only effectively predict the mass electromigration in ideal porous media. However, under an electric field, cementitious materials still have a certain binding ability to chloride ions. This causes the transport model to have significant prediction errors, and the specific value of the electromigration coefficient cannot be accurately measured. This article systematically investigated the transfer rate of chloride ions in cementitious material under different current densities. An analytical solution of the Nernst–Planck equation containing an independent electromigration coefficient was presented, and its value was quantitatively measured and discussed. The results indicated that the relationship between the electromigration and the apparent diffusion coefficient of chloride ions needs to be fitted in segments corresponding to various electric voltage intensities; but the electromigration coefficient shows a highly linear relationship with the pure effective diffusion coefficient. This work can provide assistance and valuable data support for the evaluation of mass transport in non-ideal porous media, such as cementitious materials, using the Nernst–Planck theory. Full article

Modeling ion transport through membrane channels is crucial for understanding cellular processes, and Poisson–Nernst–Planck (PNP) equations provide a fundamental continuum framework for such ionic fluxes. We investigate a quasi-one-dimensional steady-state PNP system for two oppositely charged ion species, focusing on how large permanent charges within the channel and realistic boundary conditions impact ion transport. In contrast to classical models that impose ideal electroneutrality at the channel ends (a simplification that eliminates boundary layers near the membrane interfaces), we adopt relaxed neutral boundary conditions that allow small charge imbalances at the boundaries. Using asymptotic analysis treating the large permanent charge as a singular perturbation, we derive explicit first-order expansions for each ionic flux, incorporating boundary layer parameters $(\sigma ,\rho )$ to quantify slight deviations from electroneutrality. This analysis enables a qualitative characterization of individual cation and anion flux behaviors. Notably, we identify two critical transmembrane potentials, $V_{1c}$ and $V_{2c}$, at which the cation and anion fluxes, respectively, vanish, signifying flux-reversal thresholds that delineate distinct monotonic regimes in the flux-voltage response; these critical values depend on the permanent charge magnitude and the boundary layer parameters. We further show that both ionic fluxes exhibit saturation: as the applied voltage becomes extreme, each flux approaches a finite limiting value, with the saturation level modulated by the degree of boundary charge imbalance. Moreover, allowing even small boundary charge deviations reveals non-intuitive discrepancies in flux behavior relative to the ideal electroneutral case. For example, in certain parameter regimes, a large permanent charge that enhances an ionic current under strict electroneutral conditions will instead suppress that current under relaxed-neutral conditions (and vice versa). This new analytical framework exposes subtle yet essential nonlinear dynamics that classical electroneutral assumptions would otherwise obscure. It provides deeper insight into the interplay between large fixed charges and boundary-layer effects, emphasizing the importance of incorporating such realistic boundary conditions to ensure accurate modeling of ion transport through membrane channels. Numerical simulations are performed to provide more intuitive illustrations of our analytical results. Full article