On a Robust and Efficient Numerical Scheme for the Simulation of Stationary 3-Component Systems with Non-Negative Species-Concentration with an Application to the Cu Deposition from a Cu-(β-alanine)-Electrolyte

Mathematical Modeling of the Limiting Current Density from Diffusion-Reaction Systems

The limiting current density is one of to the most important indicators in electroplating for the maximal current density from which a metal can be deposited effectively from an electrolyte. Hence, it is an indicator of the maximal deposition speed and the homogeneity of the thickness of the deposited metal layer. For these reasons, a major interest in the limiting current density is given in practical applications. Usually, the limiting current density is determined via measurements. In this article, a simple model to compute the limiting current density is presented, basing on a system of diffusion–reaction equations in one spatial dimension. Although the model formulations need many assumptions, it is of special interest for screenings, as well as for comparative work, and could easily be adjusted to measurements.

Stabilization of the Computation of Stability Constants and Species Distributions from Titration Curves

Thermodynamic equilibria and concentrations in thermodynamic equilibria are of major importance in chemistry, chemical engineering, physical chemistry, medicine etc. due to a vast spectrum of applications. E.g., concentrations in thermodynamic equilibria play a central role for the estimation of drug delivery, the estimation of produced mass of products of chemical reactions, the estimation of deposited metal during electro plating and many more. Species concentrations in thermodynamic equilibrium are determined by the system of reactions and to the reactions’ associated stability constants. In many applications the stability constants and the system of reactions need to be determined. The usual way to determine the stability constants is to evaluate titration curves. In this context, many numerical methods exist. One major task in this context is that the corresponding inverse problems tend to be unstable, i.e., the output is strongly affected by measurement errors, and can output negative stability constants or negative species concentrations. In this work an alternative model for the species distributions in thermodynamic equilibrium, based on the models used for HySS or Hyperquad, and titration curves is presented, which includes the positivity of species concentrations and stability constants intrinsically. Additionally, in this paper a stabilized numerical methodology is presented to treat the corresponding model guaranteeing the convergence of the algorithm. The numerical scheme is validated with clinical numerical examples and the model is validated with a Citric acid–Nickel electrolyte. This paper finds a stable, convergent and efficient methodology to compute stability constants from potentiometric titration curves.