A Mathematical Model for the Growth of Anodic TiO2Nanotubes under Higher Current Density

2017 ◽  
Vol 164 (13) ◽  
pp. E401-E407 ◽  
Author(s):  
Siwei Zhao ◽  
Sitong Lu ◽  
Huimin Cui ◽  
Dongliang Yu ◽  
Shaoyu Zhang ◽  
...  
Keyword(s):  
Mathematical Model ◽  
Current Density

scholarly journals A mathematical model of the current density distribution in electrochemical cells

2011 ◽  
Vol 76 (6) ◽  
pp. 805-822 ◽  
Author(s):  
Konstantin Popov ◽  
Predrag Zivkovic ◽  
Nebojsa Nikolic
Keyword(s):  
Mathematical Model ◽  
Density Distribution ◽  
Current Distribution ◽  
Current Density ◽  
Current Density Distribution ◽  
Theoretical Explanation ◽  
Electrochemical Kinetics ◽  
Complete Analysis ◽  
Electrochemical Cells ◽  
Corner Effects

An approach based on the equations of electrochemical kinetics for the estimation of the current density distribution in electrochemical cells is presented. This approach was employed for a theoretical explanation of the phenomena of the edge and corner effects. The effects of the geometry of the system, the kinetic parameters of the cathode reactions and the resistivity of the solution are also discussed. A procedure for a complete analysis of the current distribution in electrochemical cells is presented.

Electrochemical Model for Ionic Liquid Electrolytes in Lithium Batteries

2015 ◽  
Author(s):  
Kisoo Yoo ◽  
Prashanta Dutta ◽  
Soumik Banerjee
Keyword(s):  
Mathematical Model ◽  
Ionic Liquid ◽  
Lithium Ion Battery ◽  
Current Density ◽  
Lithium Batteries ◽  
Specific Capacity ◽  
Lithium Ion ◽  
High Concentration ◽  
Load Current ◽  
Liquid Electrolytes

A mathematical model is developed for transport of ionic components to study the performance of ionic liquid based lithium batteries. The mathematical model is based on a univalent ternary electrolyte frequently encountered in ionic liquid electrolytes used for lithium batteries. Owing to the very high concentration of components in ionic liquid, the transport of lithium ions are described by the mutual diffusion phenomena using Maxwell-Stefan diffusivity. The model is used to study a lithium ion battery where the cations and anions of ionic liquid are mppy+ and TFSI-. The electric performance results predicted by the model are in good agreement with experimental data. We also studied the effect of load current density on the performance of lithium ion battery using this model. Numerical results indicate that low rate of lithium ion transport causes lithium depleted zone in the porous cathode regions as the load current density increases. This lithium depleted region is responsible for lower specific capacity in lithium-ion cells. The model presented in this study can be used for optimum design of ionic liquid electrolytes for lithium-ion and lithium-air batteries.

scholarly journals A multi-factorial mathematical model for the selection of electropolishing parameters with a view to reducing the environmental impact

2021 ◽  
Vol 11 (1) ◽  
Author(s):  
Paweł Lochyński ◽  
Sylwia Charazińska ◽  
Maciej Karczewski ◽  
Edyta Łyczkowska-Widłak
Keyword(s):  
Mathematical Model ◽  
Weight Loss ◽  
Stainless Steel ◽  
Current Density ◽  
Quality Parameters ◽  
Important Goal ◽  
Process Duration ◽  
Metal Processing ◽  
Selection Of

AbstractElectrochemical metal processing is a process that generates harmful pollution. An important goal often disregarded by researchers is not only the achievement of the best possible quality of electropolished surface, but also minimising the load of metal ions in the wastewater generated in the process. The conducted experiments on the electropolishing of stainless steel in laboratory conditions, varied time, temperature and current density conditions, as well as process bath contamination (ranging from 0 to 6% Fe mass) allowed us to develop a multi-factorial mathematical model. This model offers the possibility of being able to select the process parameters recommended for achieving the desired effects. It takes into account such surface quality parameters as roughness and gloss, process duration and current density that determine power consumption, as well as the weight loss of the electropolished element that influence the rate of contamination in processing baths and wastewater. The study presents the composition of a passive film of stainless steel after the electropolishing process at the initial and final stages of the process bath’s exploitation. The results obtained from XPS tests were then correlated with the results of corrosion tests and resistance to pitting corrosion in the environment of 0.1 M NaCl.

scholarly journals Mathematical Modeling of the Effect of Pulsed Electric Field on the Specific Permselectivity of Ion-Exchange Membranes

Membranes ◽  
2021 ◽  
Vol 11 (2) ◽  
pp. 115
Author(s):  
Andrey Gorobchenko ◽  
Semyon Mareev ◽  
Victor Nikonenko
Keyword(s):  
Mathematical Model ◽  
Electric Field ◽  
Current Density ◽  
Mass Transfer Rate ◽  
Pulsed Electric Field ◽  
Concentration Profiles ◽  
Average Current Density ◽  
Diffusion Layers ◽  
Specific Permeability ◽  
Average Current

The application of pulsed electric field (PEF) in electrodialysis has been proven to be efficient for a number of effects: increasing mass transfer rate, mitigation of scaling and fouling, reducing water splitting. Recently, the improvement of the membrane permselectivity for specific counterions was discovered experimentally by the group of Laurent Bazinet (N. Lemay et al. J. Memb. Sci. 604, 117878 (2020)). To better understanding the effect of PEF in electrodialysis, simulations were performed using a non-stationary mathematical model based on the Nernst–Planck and Poisson equations. For the first time, it was not only the condition used when the current density is specified but also the condition when the voltage is set. A membrane and two adjacent diffusion layers are considered. It is shown that when applying the regime used by Lemay et al. (the same current density in conventional continuous current (CC) mode and during the pulses in PEF mode), there is a significant gain in specific permselectivity. It is explained by a reduction in the membrane concentration polarization in PEF mode. In the CC mode of electrodialysis, increasing current density leads to a loss in specific permselectivity: concentration profiles in the diffusion layers and membrane are formed in such a way that ion diffusion reduces the migration flux of the preferentially transferred ion and increases that of the poorly transferred ion. In PEF mode, the concentration profiles are partially restored during the pauses when the current is zero. However, if a different condition is used than the condition applied by Lemay et al., that is, when the same average current density is applied in both the PEF and CC modes, there is no gain in specific permeability. It is shown that within the framework of the applied mathematical model, the specific selectivity depends only on the average current density and does not depend on the mode of its application (CC or PEF mode).

Study on AC Stray Current Corrosion Law of Buried Steel Pipelines

2012 ◽  
Vol 263-266 ◽  
pp. 448-451 ◽  
Author(s):  
Xin Hua Wang ◽  
Guo Yong Yang ◽  
Hai Huang ◽  
Zhenhua Chen ◽  
Li Mei Wang
Keyword(s):  
Mathematical Model ◽  
Experimental Study ◽  
Current Density ◽  
Transmission Lines ◽  
Buried Pipelines ◽  
Safe Operation ◽  
Stray Current ◽  
Soil Resistivity ◽  
Ac Current ◽  
The Impact

AC stray current can cause AC corrosion and destroy the safe operation of buried pipelines, which comes mainly from nearby high voltage transmission lines and AC electric railway. The research and evaluation lags far behind DC stray current at home and abroad, besides, the AC current density measuring procedures are complex. Through experimental study of different parameters on the impact of the AC current density established a mathematical model of damaged area, soil resistivity, pipe-to-soil potential and coating resistivity. With it can indirectly get the AC current density, which improve efficiency by simplifying the measuring procedures. Also, provide a basis for harmfulness evaluation of AC stray current by studying the impact of AC current density on the corrosion rate.

scholarly journals A Refined Mathematical Model of Physical Processes in a Conductor at a High-Current Pulse Discharge

2021 ◽  
Vol 60 (3) ◽  
pp. 124-132
Author(s):  
Yevgen Bajda ◽  
Michael Pantelyat
Keyword(s):  
Mathematical Model ◽  
Cross Section ◽  
Current Density ◽  
Thermal Stresses ◽  
Pulse Discharge ◽  
Circular Cross Section ◽  
Nonuniform Heating ◽  
Physical Processes ◽  
Short Term ◽  
The Cross

A novel mathematical model describing physical processes during the flow of an aperiodic pulse current with amplitude of 100 kA along a conductor with a circular cross-section is proposed and investigated. It is shown how a short-term electric discharge of an aperiodic shape affects the distribution of the current density in the cross-section of the conductor, causing its nonuniform heating and the appearance of significant thermal forces as well as mechanical stresses and strains. Based on the developed mathematical model, the relation-ship between electromagnetic, thermal and mechanical phenomena is shown, allowing a deeper understanding of the multiphysics processes taking place. The maximum values of the current density are calculated, which on the surface of the conductor reach values of 47 kA/mm2, while the temperature rise of a copper conductor with a diameter of 2.44 mm is no more than 80ºC at high temperature gradients, which causes the appearance of thermal stresses that have value (40–50)% of the value of the short-term strength limit of electrical copper. Utilization of this model allows to more accurately determine the required conductor cross-section based on the characteristics of electromagnetic, thermal and mechanical pro-cesses. It is shown that the simplified model (the condition for the uniform distribution of the current over the cross-section) gives significantly underestimated values of temperatures and does not take into account temperature deformations.

scholarly journals Electromagnetic analysis of single/multiple grounding rods

2018 ◽  
Vol 31 (3) ◽  
pp. 487-500
Author(s):  
Vesna Arnautovski-Toseva ◽  
Leonid Grcev
Keyword(s):  
Mathematical Model ◽  
Integral Equation ◽  
Current Density ◽  
Wide Frequency Range ◽  
Electromagnetic Analysis ◽  
Mixed Potential ◽  
Electromagnetic Modeling ◽  
Frequency Range ◽  
The Mathematical Model

This paper presents electromagnetic modeling of multiple driven grounding rods in homogeneous/two-layer soil. The mathematical model is formulated by mixed potential integral equation (MPIE) on the basis of Sommerfield integrals. Several configurations of multiple driven rods located in homogeneous or two-layer soil are analyzed. The authors are focused on the calculation of the current density along the rods in wide frequency range from 100Hz to 1MHz.

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