Related papers: Thin layer analysis of a non-local model for the d…
The Poisson-Nernst-Planck (PNP) system is a standard model for describing ion transport. In many applications, e.g., ions in biological tissues, the presence of thin boundary layers poses both modelling and computational challenges. In this…
We show that finite-size violations of local electroneutrality in confined electrolytes are governed by the topology of the confining domain, yielding a universal hierarchy of deviations across spherical, cylindrical, and planar geometries.…
Within the Poisson-Boltzmann (PB) approach electrolytes in contact with planar, spherical, and cylindrical electrodes are analyzed systematically. The dependences of their capacitance $C$ on the surface charge density $\sigma$ and the ionic…
We consider a class of models for nonlinearly elastic surfaces in this work. We have in mind thin, highly deformable structures modeled directly as two-dimensional nonlinearly elastic continua, accounting for finite membrane and bending…
Boundary integral equations are an efficient and accurate tool for the numerical solution of elliptic boundary value problems. The solution is expressed as a layer potential; however, the error in its evaluation grows large near the…
We study the role of the electrical double layer (EDL) in the formation of the quasistatic electrical conductivity of suspensions of nanosized particles. A suspension is viewed as a system of hard-core--penetrable-shell particles. The…
In this thesis we study the lateral electrostatic interaction between a pair of non-identical, moderately charged colloidal particles trapped at an electrolyte interface in the limit of short inter-particle separations. Using a simplified…
We study the boundary layer solution to singular perturbation problems involving Poisson-Boltzmann (PB) type equations with a small parameter $\epsilon$ in general bounded smooth domains (including multiply connected domains) under the…
We study the electro-hydrodynamics of the Debye screening layer that arises in an aqueous binary solution near a planar insulating wall when applying a spatially modulated AC-voltage. Combining this with first order perturbation theory we…
We consider a set of identical mobile point-like charges (counter-ions) confined to a domain with curved hard walls carrying a uniform fixed surface charge density, the system as a whole being electroneutral. Three domain geometries are…
A Poisson-Boltzmann approach is used to determine the double-layer integral and differential capacitances in a finite-length situation for an electrolytic cell. By means of simple analytical calculations, it is shown how these quantities…
In this thesis, the electrostatic interaction between two chemically identical colloids, both carrying constant surface potential is studied in the limit of short inter-particle separation at the interface of two immiscible fluids. Using an…
The interfacial nature of the electric double layer (EDL) assumes that electrode surface morphology significantly impacts the EDL properties. Since molecular-scale roughness modifies the structure of EDL, it is expected to disturb the…
The structure and thickness of the electrical double layer (EDL) at carbon electrodes strongly influence electrochemical performance, yet remain poorly understood in super-concentrated aqueous electrolytes. Here we combine classical and…
In electrochemical systems, the structure of electrical double layers (EDLs) near electrode surfaces is crucial for energy conversion and storage functions. While the electrodes in real-world systems are usually heterogeneous, to date the…
For a wide class of noninteracting tight-binding models in one dimension we present an analytical solution for all scattering and edge states on a half-infinite system. Without assuming any symmetry constraints we consider models with…
The structure of cylindrical double layers is studied using a modified Poisson Boltzmann theory and the density functional approach. In the model double layer, the electrode is a cylindrical polyion that is infinitely long, impenetrable,…
The ongoing scientific interest in the properties and structure of electric double layers (EDLs) stems from their pivotal role in (super)capacitive energy storage, energy harvesting, and water treatment technologies. Classical density…
Asymmetric valences in a binary electrolyte can significantly affect the performance of systems such as reverse electrodialysis cells, batteries, and supercapacitors. To generate a theoretical understanding of this effect, we consider a…
Understanding the electrodes' surface morphology influence on the ions' distribution is essential for designing the supercapacitors with enhanced energy density characteristics. We develop a model for the structure of electrolytes near the…