arXiv subjects

Elena F. Silkina

Publications and source records attributed to Elena F. Silkina.

13 recordsLinked to original sources

arXiv2026

Surface Charge--Potential Relation for Spherical Particles in Electrolyte Solutions

Predicting the relationship between surface charge density and electrostatic potential for spherical particles remains a fundamental challenge in colloid science. Because the governing non-linear Poisson--Boltzmann equation lacks a general exact analytical solution, researchers typically rely on numerical calculations or various semi-empirical approximations. In this paper, we overcome these limitations by developing a dual-asymptotic framework that provides explicit, closed-form expressions for this surface charge--potential relationship across the entire spectrum of particle curvature. For weakly curved systems, where the Debye length $λ_D$ is much smaller than the particle radius $R$ ($λ_D/R \ll 1$), a formal mathematical derivation rigorously establishes the Ohshima--Healy--White formula as an exact regular perturbation expansion. Conversely, for highly curved spheres ($R/λ_D \ll 1$), we employ singular perturbation analysis using the scaled particle radius as the small parameter. This approach provides a first-principles mathematical justification for the spherical Debye--Hückel theory, proving that its leading-order expansion remains asymptotically exact within the full non-linear Poisson--Boltzmann framework due to the geometric deactivation of non-linearity. Crucially, we map the exact limits of this geometric regulation, demonstrating how non-linear screening re-emerges as the particle radius increases, with the breakdown threshold governed by the interplay between curvature and surface charge density.

cond-mat.soft↗

arXiv2026

Diffusioosmosis of electrolyte solutions in axisymmetric channels

We present a theory of a flow of salt solutions in long axisymmetric channels induced by concentration and pressure drops between their ends. The consideration is restricted to thin, compared to the local radius, electrostatic diffuse layers, but remains valid even when the concentration drop is quite large. We show that the magnitude of the diffusio-osmotic fluid flow rate $Q_{DO}$ in the cylinder is the same as in the slit of equal to its diameter thickness, but channels of variable cross-sections could either retard or enhance it, depending on their geometry. The application of the pressure drop $Δp \neq 0$ results in an extra contribution $Q_{P}$ to the total flow rate of fluid $Q$, but does not affect $Q_{DO}$. We calculate the curves $Δp (Q)$ for several axisymmetric channels and conclude that they are nearly linear, with the sensitive to the shape slopes. This leads to the possibility of introducing a simple, but rather accurate, cylinder approximation, where the radius of the imaginary cylinder is related to a hydrodynamic resistivity of the real channel and can be easily determined, if its geometry is known. We also derive an equation relating the ionic flux with the total flow rate of fluid and demonstrate that both the sign and magnitude of ionic flux could be tuned by using the appropriate channel shape. Our analysis provides a framework for interpreting experimental and numerical data, as well as may guide the design of micro- and nanofluidic devices.

physics.flu-dyn↗

arXiv2026

Tuning diffusioosmosis of electrolyte solutions by hydrostatic pressure

When two reservoirs of a distinct salinity are connected by channels or pores, a fluid flow termed diffusio-osmotic is generated. This article investigates the flow emerging in an uniformly charged long slit whose thickness exceeds the local Debye screening length. Attention is focussed on the role of hydrostatic pressure drop $Δp$ in establishing diffusioosmosis at a finite concentration difference. For a thick slit we recover the known formula for a local diffusio-osmotic slip over a single wall, which is determined by the surface potential, salt concentration and its gradient. An equation for the global fluid flow rate $\mathcal{Q}$ is presented as a sum of the diffusio-osmotic and pressure-driven contributions. Although the diffusio-osmotic term itself remains unaffected by $Δp$, the nonlinear concentration and surface potential profiles along the slit, and consequently, the local slip velocity are dramatically modified. We present an equation relating the local concentration to $\mathcal{Q}$ and employ it to derive an expression describing the surface potential variation in the slit. Since $\mathcal{Q}$ can easily be tuned by $Δp$, the variety of possible concentration and surface potential profiles becomes very rich. Our theory provides a simple explanation of recent flow rate measurements and shows that experimental data provide rather direct information about concentration and surface potential profiles in the uniformly charged slit. The relevance of our results for sensing the salt dependence of surface potentials is discussed briefly.

physics.flu-dyn↗

arXiv2025

Diffusioosmosis of electrolyte solutions in uniformly charged channels

When the concentration of electrolyte solution varies along the channel the forces arise that drag the fluid toward the higher or lower concentration region inducing a flow termed diffusio-osmotic. This article investigates a flow that emerges in channels with constant density of surface charge σ and thin compared to their thickness electrostatic diffuse layers. An equation for the fluid flow rate Q is derived and used to describe analytically the flux of ions, and local potentials and concentrations. This equation, which allows to treat the diffusio-osmotic problems without tedious and time consuming computations, clarifies that the global flow rate is controlled only by the surface charge and concentration drop between the channel ends, and indicates that there always exist two different values of σ that correspond to a particular Q. Our theory provides a simple explanation of the directions of the fluid flow rate and ionic flux depending on the surface charge and diffusivity of ions, predicts a non-linear concentration distribution along the channel caused by convection, and relates it to the local potential changes by a compact formula. We also present and interpret the variations of the diffusio-osmotic velocity profiles and the apparent slip velocity along the channel and show that the latter is highly non-uniform and could even becomes alternating. The relevance of our results for diffusio-osmotic experiments and for some electrochemistry and membrane science issues is discussed briefly.

cond-mat.soft↗

arXiv2025

Enhanced zeta potentials caused by surface ion mobilities

The electro-hydrodynamics near conducting walls is revisited. Attention is focused on the impact of an explicit diffuse Stern layer, which permittivity and viscosity differ from the bulk values, on the velocity of an electro-osmotic plug flow. To solve this problem we propose an approach of mapping the flow in the Stern layer to the surface dividing the Stern and diffuse layer, where an effective electro-hydrodynamic slip boundary condition is imposed. The latter implies that an effective surface charge is responding to the applied field and characterized by a mobility parameter $μ\geq 1$. We derive analytic equations for $μ$ and demonstrate that it is determined only by electrostatic properties of the electric double layer. These equations are then used to calculate electrokinetic (zeta) potentials of surfaces. We show that the zeta potential generally exceeds the surface one, which implies an amplification of the electro-osmotic flow. This effect is most pronounced if the hydrodynamic slip length is large and/or in concentrated solutions.

physics.flu-dyn↗

arXiv2024

Surface potentials of conductors in electrolyte solutions

When we place conducting bodies in electrolyte solutions, their surface potential $Φ_s$ appears to be much smaller in magnitude than the intrinsic one $Φ_0$ and normally does not obey the classical electrostatic boundary condition of a constant surface potential expected for conductors. In this paper, we demonstrate that an explanation of these observations can be obtained by postulating that diffuse ions condense at the "wall" due to a reduced permittivity of a solvent. For small values of $Φ_0$ the surface potential responds linearly. On increasing $Φ_0$ further $Φ_s$ augments nonlinearly and then saturates to a constant value. Analytical approximations for $Φ_s$ derived for these three distinct modes show that it always adjusts to salt concentration, which is equivalent to a violation of the constant potential condition. The latter would be appropriate for highly dilute solutions, but only if $Φ_0$ is small. Surprisingly, when the plateau with high $Φ_s$ is reached, the conductor surface switches to a constant charge density condition normally expected for insulators. Our results are directly relevant for conducting electrodes, mercury drops, colloidal metallic particles and more.

cond-mat.soft↗

arXiv2023

Electrophoresis of ions and electrolyte conductivity: from bulk to nanochannels

When electrolyte solutions are confined in micro- and nanochannels their conductivity is significantly different from those in a bulk phase. Here we revisit the theory of this phenomenon by focusing attention on the reduction in the ion mobility with the concentration of salt and a consequent impact to the conductivity of a monovalent solution, from bulk to confined in a narrow slit. We first give a systematic treatment of electrophoresis of ions and obtain equations for their zeta potentials and mobilities. The latter are then used to obtain a simple expression for a bulk conductivity, which is valid in a concentration range up to a few molars and more accurate than prior analytic theories. By extending the formalism to the electrolyte solution in the charged channel the equations describing the conductivity in different modes are presented. They can be regarded as a generalization of prior work on the channel conductivity to a more realistic case of a nonzero reduction of the zeta potential and electrophoretic mobility of ions with salt concentration. Our analysis provides a framework for interpreting measurements on the conductivity of electrolyte solutions in the bulk and in narrow channels.

cond-mat.soft↗

arXiv2023

Slippery and mobile hydrophobic electrokinetics: from single walls to nanochannels

We discuss how the wettability of solid walls impacts electrokinetic properties, from large systems to a nanoscale. We show in particular how could the hydrophobic slippage, coupled to confinement effects, be exploited to induce novel electrokinetic properties, such as a salt-dependent giant amplification of zeta potential and conductivity, and a much more efficient energy conversion. However, the impact of slippage is dramatically reduced if some surface charges migrate along the hydrophobic wall under an applied field.

cond-mat.soft↗

arXiv2022

Transport of ions in hydrophobic nanotubes

The theory of electrokinetic ion transport in cylindrical channels of a fixed surface charge density is revisited. Attention is focused on impact of the hydrophobic slippage and mobility of adsorbed surface charges. We formulate generalised Onsager relations for a cylinder of an arbitrary radius and then derive exact expressions for the mean electro-osmotic mobility and conductivity. To employ these expressions we perform additional electrostatic calculations, with the special focus on the non-linear electrostatic effects. Our theory provides a simple explanation of a giant enhancement of the electrokinetic mobility and conductivity of hydrophobic nanotubes by highlighting the role of appropriate electrostatic and hydrodynamic length scales and their ratios. We also propose a novel interpretation of zeta potentials of cylindrical channels.

cond-mat.soft↗

arXiv2021

Enhanced transport of ions by tuning surface properties of the nanochannel

We revisit the theory of ion transport in parallel-plate channels and also discuss how the wettability of a solid and the mobility of adsorbed surface charges impact the transport of ions. It is shown that depending on the ratio of the electrostatic disjoining pressure to the excess osmotic pressure at the walls two different regimes occur. In the thick channel regime this ratio is small and the channel effectively behaves as thick, even when the diffuse layers strongly overlap. The latter is possible for highly charged channels only. In the thin channel regime the disjoining pressure is comparable to the excess osmotic pressure at the wall, which implies relatively weakly charged walls. We derive simple expressions for the mean conductivity of the channel in these two regimes, highlighting the role of electrostatic and electro-hydrodynamic boundary conditions. Our theory provides a simple explanation of the high conductivity observed experimentally in hydrophilic channels, and allows one to obtain rigorous bounds on its attainable value and scaling with salt concentration. Our results also show that further dramatic amplification of conductivity is possible if hydrophobic slip is involved, but only in the thick channel regime provided the walls are sufficiently highly charged and the most of adsorbed charges are immobile. However, for weakly charged surfaces the massive conductivity amplification due to hydrodynamic slip is impossible in both regimes. Interestingly, in this case the moderate slip-driven contribution to conductivity can monotonously decrease with the fraction of immobile adsorbed charges. These results provide a framework for tuning the conductivity of nanochannels by adjusting their surface properties and bulk electrolyte concentrations.

cond-mat.soft↗

arXiv2021

Surface and zeta potentials of charged permeable nanocoatings

An electrokinetic (zeta) potential of charged permeable porous films on solid supports generally exceeds their surface potential, which often builds up to a quite high value itself. Recent work provided a quantitative understanding of zeta potentials of thick, compared to the extension of an inner electrostatic diffuse layer, porous films. Here, we consider porous coatings of a thickness comparable or smaller than that of the inner diffuse layer. Our theory, which is valid even when electrostatic potentials become quite high and accounts for a finite hydrodynamic permeability of the porous materials, provides a framework for interpreting the difference between values of surface and zeta potentials in various situations. Analytic approximations for the zeta potential in the experimentally relevant limits provide a simple explanation of transitions between different regimes of electro-osmotic flows, and also suggest strategies for its tuning in microfluidic applications.

physics.chem-ph↗

arXiv2020

Electro-osmotic properties of porous permeable films

Permeable porous coatings on a flat solid support significantly impact its electrostatic and electrokinetic properties. Existing work has focused on simplified cases, such as weakly charged and/or thick porous films, with limited theoretical guidance. Here, we consider the general case of coatings of any given volume charge density and obtain analytic formulas for electrostatic potential profiles, valid for any film thickness and salt concentration. They allow us to calculate analytically the difference between potentials at solid support and at interface with an outer electrolyte, that is the key parameter ascertaining the functionality of permeable coatings. Our analysis provides a framework for interpreting and predicting specific for porous films super-properties, from an enhanced ion absorption to a giant amplification of electro-osmotic flows. The results are relevant for hydrogel and zeolite coatings, porous carbon and ion-exchange resins, polyelectrolyte brushes, and more.

cond-mat.soft↗

arXiv2020

Achieving large zeta-potentials with charged porous surfaces

We discuss an electro-osmotic flow near charged porous coatings of a finite hydrodynamic permeability, impregnated with an outer electrolyte solution. It is shown that their electrokinetic (zeta) potential is generally augmented compared to the surface electrostatic potential, thanks to a large liquid slip at their surface emerging due to an electro-osmotic flow in the enriched by counter-ions porous films. The inner flow shows a very rich behavior controlled by the volume charge density of the coating, its Brinkman length, and concentration of added salt. Interestingly, even for relatively small Brinkman length the zeta-potential can, in some cases, become huge, providing a very fast outer flow in the bulk electrolyte. When the Brinkman length is large enough, the zeta-potential could be extremely high even at practically vanishing surface potential. To describe the slip velocity in a simple manner, we introduce a concept of an electro-osmotic slip length and demonstrate that the latter is always defined by the hydrodynamic permeability of the porous film, and also, depending on the regime, either by its volume charge density or the salt concentration. These results provide a framework for the rational design of porous coatings to enhance electrokineic phenomena, and for tuning their properties by adjusting bulk electrolyte concentrations, with direct applications in microfluidics.

physics.flu-dyn↗