Search Results (56)

This study investigates the time-periodic electroosmotic flow and solute transport of Maxwell fluid in a parallel microchannel with modulated surface charges. The Poisson–Boltzmann equation and the linearized momentum equations are solved using a superposition-based analytical approach. The influences of oscillation intensity, fluid elasticity, and electrokinetic parameters on the velocity and concentration distributions are examined. The results show that wall-potential modulation combined with a time-periodic electric field generates recirculating motion and oscillatory velocity patterns. Moderate oscillation strengthens both flow and solute transport, whereas stronger oscillation weakens transport efficiency. This work provides a quantitative analysis the interplay between oscillatory electroosmotic flow and solute transport in Maxwell fluid and clarifies the role of oscillation strength in controlling solute dispersion. Full article

Theoretical models of polyelectrolyte systems with cross-linked polymer networks are often simplified to linear differential equations by means of the linearized Poisson–Boltzmann approximation, whose validity is traditionally limited to cases where the electrostatic potentials are small. However, the limits of applicability of the linear theory remain debatable in many cases. Moreover, the Poisson–Boltzmann equation is, in principle, not applicable to the description of non-equilibrium systems, particularly those through which an electric current flows. In the present work, a direct comparison is carried out between the exact solution and the approximate solution (i.e., the solution obtained within the framework of the linearization procedure) of the equations describing the contact region between a cross-linked polyelectrolyte network and a low-molecular-mass salt solution. This makes it possible to determine the conditions under which the linear model is applicable, including for the analysis of promising systems in the field of organic electronics. The conclusions obtained in this work are based on basic electrostatics equations and transport equations of low-molecular-mass ions. The proposed approach also makes it possible to obtain a generalized linear differential equation that is not subject to a Boltzmann distribution approximation and is valid for polyelectrolyte systems rather far from thermodynamic equilibrium and even carrying steady electric currents. Full article

Electric impedance spectrum (EIS) is attracting attention in many areas of science, ranging from electrochemistry and material science to medical diagnosis. Interestingly, theoretical description often stops at material constants and specific physical mechanisms are represented by equivalent circuit elements, which is also motivated by the common use of various bridge methods. This specifically applies to biological samples, which exhibit a rich variety of responses to the electric field. Here, we present a step further from the description that utilizes equivalent circuit elements. We demonstrate how alteration of the mesoscopic structure affects the EIS in a biological sample: a cucumber under thermal treatment that comprises a cooling and warming phase. As the freezing temperature of water is exceeded during the cycle, the cucumber becomes frosted, which leads to unrecoverable changes in the internal structure, with no change of chemical composition. The experimental evidence is complemented by theoretical analysis, based on a novel approach to modeling non-stationary problems, derived from the stationary Poisson–Boltzmann equation. We demonstrate a qualitative agreement between the theoretical and the experimental results, and discuss the procedure for tuning the model. We also demonstrate that, of the temperature variations of the position of the beta dispersion, the one related to the mesoscopic structure, can be used to assess the ionic strength of the material, determine the microscopic diffusion constant, or reflect the changes in mesoscopic structure, depending on experimental protocol. Full article

Despite the increased interest in neuromorphic materials—a physical implementation of neural networks that could overcome the so-called von Neumann architecture’s limitations—most studies have been performed on the basis of systems specially constructed for this purpose. It has previously been shown that analogues of neural networks can spontaneously arise in solutions of hydrophilic polymers, but these systems involved molecules of different natures or required direct interaction between macromolecular clusters. The present paper proposes a theory that indicates the possibility of an analogue of neural network formation even in a single-component solution of a relatively weak polyacid. A model is suggested based on the account of heterogeneous distribution of polymer ionogenic groups within the volume leading to the fluctuations of electric fields and, as a result, to the local changes in the degree of ionisation of functional groups. Theoretical description of the system shows how it was reduced to a solution of the analogue based on the Poisson–Boltzmann equation. The results obtained showed that it is just fluctuations in the distribution of charges that provide the collective response of the system to external influences and serve as an argument in favour of analogy of such a solution within a neural network. The results are discussed in the context of a potential simple hydrophilic polymer system as a prototypical neuromorphic and evolving material that is relevant for organic electronics, metamaterials, and studies on prebiological evolution. Full article

Electric field-assisted local functionalization of materials is a resist-free technique generally applied at the nanoscale, which has been understood within the paradigm of the water meniscus. Using a home-made prototype the authors applied this technique at scales compatible with the biosensor industry (tens of microns). However, interpreting these results requires a different paradigm. The expansion of the oxidized region over time in two-dimensional materials under a localized electric field is modeled from first physical principles. Boltzmann statistics is applied to the oxyanion incorporation at the perimeter of the oxidized zone, and a new general relation between oxide radius and time is formulated. It includes the reduction in the energy barrier due to the field effect and its dependence on the oxide radius. To gain insight into this dependence whatever the layers structure, 2D material involved, or electrical operating conditions, simple structures based on multilayer stacks representing the main constituents are proposed, where the Poisson equation is solved using finite element calculations. This enables to derive energy barriers for oxyanion incorporation at varying spot radii which are consistent with those resulting from fitting experimental data. The reasonable agreement obtained provides researchers with a new tool to predict the evolution of local functionalization of 2D layers as a function of the following fabrication parameters: time, applied voltage, and relative humidity, solely based on materials properties. Full article

The driving force behind protein translocation across the cell membrane is not yet fully understood. In bacteria, there is an electrochemical potential across the cell membrane, which can interact with charged residues in the translocation substrate. In this study, the protonation states of lysine and glutamate, serving as test residues in a peptide translocating across the bacterial channel SecYEG, are investigated by applying Poisson–Boltzmann continuum electrostatic free energy calculations and Monte Carlo titrations to snapshots of molecular dynamics (MD) simulations. A clear shift in protonation probability towards the uncharged state is found for both test residues as they move deeper into the channel. Thus, charge neutralization occurs irrespective of whether the original charge of the test residue is positive (lysine) or negative (glutamate). Electrostatic interactions of acidic and basic residues of SecYEG with the peptide cancel out. The main determinants of the test residue’s protonation state are the dielectric properties of its surroundings and interactions with non-titrating charges in the channel. Crucially, the membrane protein—including its water-filled pore—is assigned a low dielectric constant. The results are discussed in the context of the limitations inherent to continuum electrostatics and MD simulations with fixed protonation states. Full article

Solvents represent the quiet majority in biomolecular systems, yet modeling their influence with both speed and ri:gor remains a central challenge. This study maps the state of the art in implicit solvent theory and practice, spanning classical continuum electrostatics (PB/GB; DelPhi, APBS), modern nonpolar and cavity/dispersion treatments, and quantum–continuum models (PCM, COSMO/COSMO-RS, SMx/SMD). We highlight where these methods excel and where they falter, namely, around ion specificity, heterogeneous interfaces, entropic effects, and parameter sensitivity. We then spotlight two fast-moving frontiers that raise both accuracy and throughput: machine learning-augmented approaches that serve as PB-accurate surrogates, learn solvent-averaged potentials for MD, or supply residual corrections to GB/PB baselines, and quantum-centric workflows that couple continuum solvation methods, such as IEF-PCM, to sampling on real quantum hardware, pointing toward realistic solution-phase electronic structures at emerging scales. Applications across protein–ligand binding, nucleic acids, and intrinsically disordered proteins illustrate how implicit models enable rapid hypothesis testing, large design sweeps, and long-time sampling. Our perspective argues for hybridization as a best practice, meaning continuum cores refined by improved physics, such as multipolar water, ML correctors with uncertainty quantification and active learning, and quantum–continuum modules for chemically demanding steps. Full article

The present work analyzes the combined viscoelectric and steric effects on electroosmotic flow in a soft channel with polyelectrolyte coating. The structured channel surface, which controls the electric potential, creates two different flow regions: the electrolyte flow within the permeable polyelectrolyte layer (PEL) and the bulk electrolyte. Thus, this study discusses the interaction of various electrostatic effects to predict the electroosmotic flow field. The nonlinear governing equations describing the fluid flow are the modified Poisson–Boltzmann equation for the electric potential distribution, the mass conservation equation, and the modified Navier–Stokes equations for the flow field, which are solved numerically using a one-dimensional (1D) scheme. The results indicate that the flow enhances when increasing the electric potential magnitude across the channel cross-section via the rise in different dimensionless parameters, such as the PEL thickness, the steric factor, and the ratio of the electrokinetic parameter of the PEL to that of the electrolyte layer. This research demonstrates that the PEL significantly enhances control over electroosmotic flow. However, it is crucial to consider that viscoelectric effects at high electric fields and the friction generated by the grafted polymer brushes of the PEL can reduce these benefits. Full article

We develop a unified analytical framework that systematically connects kinetic theory, optimal transport, and entropy dissipation through the novel integration of hypocoercivity methods with geometric structures. Building upon but distinctly extending classical hypocoercivity approaches, we demonstrate how geometric control, via commutators and curvature-like structures in probability spaces, resolves degeneracies inherent in kinetic operators. Centered around the Boltzmann and Fokker–Planck equations, we derive sharp exponential convergence estimates under minimal regularity assumptions, improving on prior methods by incorporating Wasserstein gradient flow techniques. Our framework is further applied to the study of hydrodynamic limits, collisional relaxation in magnetized plasmas, the Vlasov–Poisson system, and modern data-driven algorithms, highlighting the central role of entropy as both a physical and variational tool across disciplines. By bridging entropy dissipation, optimal transport, and geometric analysis, our work offers a new perspective on stability, convergence, and structure in high-dimensional kinetic models and applications. Full article

This study analyzes the impact of slip-dependent zeta potential on the heat transfer characteristics of nanofluids in cylindrical microchannels with consideration of thermal radiation effects. An analytical model is developed, accounting for the coupling between surface potential and interfacial slip. The linearized Poisson–Boltzmann equation, along with the momentum and energy conservation equations, is solved analytically to obtain the electrical potential field, velocity field, temperature distribution, and Nusselt number for both slip-dependent (SD) and slip-independent (SI) zeta potentials. Subsequently, the effects of key parameters, including electric double-layer (EDL) thickness, slip length, nanoparticle volume fraction, thermal radiation parameters, and Brinkman number, on the velocity field, temperature field, and Nusselt number are discussed. The results show that the velocity is consistently higher for the SD zeta potential compared to the SI zeta potential. Meanwhile, the temperature for the SD case is higher than that for the SI case at lower Brinkman numbers, particularly for a thinner EDL. However, an inverse trend is observed at higher Brinkman numbers. Similar trends are observed for the Nusselt number under both SD and SI zeta potential conditions at different Brinkman numbers. Furthermore, for a thinner EDL, the differences in flow velocity, temperature, and Nusselt number between the SD and SI conditions are more pronounced. Full article

Electrically conductive membranes (ECMs) were prepared by coating porous ethylenediamine-modified polyacrylonitrile (PAN-EDA) UF membranes with an ultrathin layer of platinum (Pt) nanoparticles through magnetron sputtering. These ECMs were used in electrofiltration to study the removal of brilliant blue dye from an aqueous solution under positive electrical potentials (0–2.5 V). Negative electrical potentials (−1.0–−2.5 V) were also investigated to regenerate the membrane by desorbing the dye from the ECM surface. At +0 V, the EC PAN-EDA membrane adsorbed the dye due to its intrinsic positive charge. Application of −2.0 V resulted in a maximum of 39% desorption of the dye. A modified Poisson-Boltzmann (MPB) model showed that −2.0 V created a repulsive force within the first 24 nm of the membrane matrix, which had a minimal effect on dye ions adsorbed deeper within the membrane, thus limiting the electro-desorption efficiency to 39%. Moreover, increasing positive potentials from +0.5 V to +2.5 V led to increased dye electro-adsorption by 9.5 times, from 132 mg/m² to 1112 mg/m² at pH 8 (equivalent to the membrane’s isoelectric point). The MBP simulations demonstrated that increasing electro-adsorption loadings are related to increasing attractive force, indicating electro-adsorption induced by attractive force is the dominant mechanism and the role of other mechanisms (e.g., electrochemical oxidation) is excluded. At pH 5, electro-adsorption further increased to 1390 mg/m², likely due to the additional positive charge of the membrane (zeta potential = 9.2 mV) compared to pH 8. At pH 8, complete desorption of the dye from the ECM surface was achieved with a significant repulsive force at −2.0 V. However, as pH decreased from 8 to 5, the desorption efficiency decreased by 3.9% due to the membrane’s positive charge. These findings help elucidate the mechanisms of electro-adsorption and desorption on ECMs using dye as a model for organic compounds like humic acids. Full article

In this paper, we investigate the electro-osmotic flow (EOF) and mass transfer of a Newtonian fluid propelled by a pressure gradient and alternating current (AC) electric field in a parallel microchannel with sinusoidal roughness and modulated charged surfaces. The two-wall roughness is described by in-phase or out-of-phase sine functions with a small amplitude δ. By employing the method of perturbation expansion, the semi-analytical solutions of the Poisson–Boltzmann (P–B) equation based on the Debye–Hückel approximation and the modified Navier–Stokes (N–S) equation are obtained. The numerical solution of the concentration equation is obtained by the finite difference method. The effects of sinusoidal roughness, modulated charged surface, and the AC electric field on the potential field, velocity field, and concentration field are discussed. Under the influence of the modulated charged surface and sinusoidal roughness, vortices are generated. The velocity oscillates due to the effect of the AC electric field. The results indicate that solute diffusion becomes enhanced when the oscillation Reynolds number is below a specific critical value, and it slows down when the oscillation Reynolds number exceeds this critical value. Full article

This study examines the behavior of single-walled carbon nanotubes (SWCNTs) suspended in a water-based ionic solution, driven by the combined mechanisms of electroosmosis and peristalsis through ciliated media. The inclusion of nanoparticles in ionic fluid expands the range of potential applications and allows for the tailoring of properties to suit specific needs. This interaction between ionic fluids and nanomaterials results in advancements in various fields, including energy storage, electronics, biomedical engineering, and environmental remediation. The analysis investigates the influence of a transverse magnetic field, thermal radiation, and mixed convection acting on the channel walls. The novel physical outcomes include enhanced propulsion efficiency due to SWCNTs, understanding the influence of thermal radiation on fluid behavior and heat exchange, elucidation of the interactions between SWCNTs and the nanofluid, and recognizing implications for microfluidics and biomedical engineering. The Poisson–Boltzmann ionic distribution is linearized using the modified Debye–Hückel approximation. By employing real-world approximations, the governing equations are simplified using long-wavelength and low-Reynolds-number approximation. Conducting sensitivity analyses or exploring the impact of higher-order corrections on the model’s predictions in recent literature might alter the results significantly. This acknowledges the complexities of the modeling process and sets the groundwork for further enhancement and investigation. The resulting nonlinear system of equations is solved through regular perturbation techniques, and graphical representations showcase the variation in significant physical parameters. This study also discusses pumping and trapping phenomena in the context of relevant parameters. Full article

The transition zone (TZ) of hydrocarbon reservoirs is an integral part of the hydrocarbon pool which contains a substantial fraction of the deposit, particularly in carbonate petroleum systems. Consequently, knowledge of its thickness and petrophysical properties, viz. its pore size distribution and wettability characteristic, is critical to optimizing hydrocarbon production in this zone. Using classical formation evaluation techniques, the thickness of the transition zone has been estimated, using well logging methods including resistivity and Nuclear Magnetic Resonance, among others. While hydrocarbon fluids’ accumulation in petroleum reservoirs occurs due to the migration and displacement of originally water-filled potential structural and stratigraphic traps, the development of their TZ integrates petrophysical processes that combine spontaneous capillary imbibition and wettability phenomena. In the literature, wettability phenomena have been shown to also be governed by electrostatic phenomena. Therefore, given that reservoir rocks are aggregates of minerals with ionizable surface groups that facilitate the development of an electric double layer, a definite theoretical relationship between the TZ and electrostatic theory must be feasible. Accordingly, a theoretical approach to estimating the TZ thickness, using the electrostatic theory and based on the electric double layer theory, is attractive, but this is lacking in the literature. Herein, we fill the knowledge gap by using the interfacial electrostatic theory based on the fundamental tenets of the solution to the Poisson–Boltzmann mean field theory. Accordingly, we have used an existing model of capillary rise based on free energy concepts to derive a capillary rise equation that can be used to theoretically predict observations based on the TZ thickness of different reservoir rocks, using well-established formation evaluation methods. The novelty of our work stems from the ability of the model to theoretically and accurately predict the TZ thickness of the different lithostratigraphic units of hydrocarbon reservoirs, because of the experimental accessibility of its model parameters. Full article

Self-gravitating fluid instabilities are analysed within the framework of a post-Newtonian Boltzmann equation coupled with the Poisson equations for the gravitational potentials of the post-Newtonian theory. The Poisson equations are determined from the knowledge of the energy–momentum tensor calculated from a post-Newtonian Maxwell–Jüttner distribution function. The one-particle distribution function and the gravitational potentials are perturbed from their background states, and the perturbations are represented by plane waves characterised by a wave number vector and time-dependent small amplitudes. The time-dependent amplitude of the one-particle distribution function is supposed to be a linear combination of the summational invariants of the post-Newtonian kinetic theory. From the coupled system of differential equations for the time-dependent amplitudes of the one-particle distribution function and gravitational potentials, an evolution equation for the mass density contrast is obtained. It is shown that for perturbation wavelengths smaller than the Jeans wavelength, the mass density contrast propagates as harmonic waves in time. For perturbation wavelengths greater than the Jeans wavelength, the mass density contrast grows in time, and the instability growth in the post-Newtonian theory is more accentuated than the one of the Newtonian theory. Full article