scholarly journals Mathematical model on surface reaction diffusion in the presence of front chemical reaction

2013 ◽  
Vol 57 (1) ◽  
pp. 215-221 ◽  
Author(s):  
D.V. Permikin ◽  
V.S. Zverev
Keyword(s):  
Mathematical Model ◽  
Chemical Reaction ◽  
Surface Reaction ◽  
Reaction Diffusion

Modeling the Electrical Double Layer to Understand the Reaction Environment in a CO2 Electrocatalytic System

2019 ◽  
Author(s):  
Divya Bohra ◽  
Jehanzeb Chaudhry ◽  
Thomas Burdyny ◽  
Evgeny Pidko ◽  
wilson smith
Keyword(s):  
Electric Field ◽  
Double Layer ◽  
Electrical Double Layer ◽  
Surface Reaction ◽  
Catalyst Surface ◽  
Local Reaction ◽  
Reaction Diffusion ◽  
Alkali Metal Cations ◽  
Applied Potential ◽  
Critical Aspect

<p>The environment of a CO<sub>2</sub> electroreduction (CO<sub>2</sub>ER) catalyst is intimately coupled with the surface reaction energetics and is therefore a critical aspect of the overall system performance. The immediate reaction environment of the electrocatalyst constitutes the electrical double layer (EDL) which extends a few nanometers into the electrolyte and screens the surface charge density. In this study, we resolve the species concentrations and potential profiles in the EDL of a CO<sub>2</sub>ER system by self-consistently solving the migration, diffusion and reaction phenomena using the generalized modified Poisson-Nernst-Planck (GMPNP) equations which include the effect of volume exclusion due to the solvated size of solution species. We demonstrate that the concentration of solvated cations builds at the outer Helmholtz plane (OHP) with increasing applied potential until the steric limit is reached. The formation of the EDL is expected to have important consequences for the transport of the CO<sub>2</sub> molecule to the catalyst surface. The electric field in the EDL diminishes the pH in the first 5 nm from the OHP, with an accumulation of protons and a concomitant depletion of hydroxide ions. This is a considerable departure from the results obtained using reaction-diffusion models where migration is ignored. Finally, we use the GMPNP model to compare the nature of the EDL for different alkali metal cations to show the effect of solvated size and polarization of water on the resultant electric field. Our results establish the significance of the EDL and electrostatic forces in defining the local reaction environment of CO<sub>2</sub> electrocatalysts.</p>

scholarly journals Nanofluid flow containing carbon nanotubes with quartic autocatalytic chemical reaction and Thompson and Troian slip at the boundary

2020 ◽  
Vol 10 (1) ◽  
Author(s):  
Muhammad Ramzan ◽  
Jae Dong Chung ◽  
Seifedine Kadry ◽  
Yu-Ming Chu ◽  
Muhammad Akhtar
Keyword(s):  
Mathematical Model ◽  
Carbon Nanotubes ◽  
Drag Force ◽  
Chemical Reaction ◽  
Slip Velocity ◽  
Volume Fraction ◽  
Surface Drag ◽  
Nanofluid Flow ◽  
Velocity Parameter ◽  
The Impact

Abstract A mathematical model is envisioned to discourse the impact of Thompson and Troian slip boundary in the carbon nanotubes suspended nanofluid flow near a stagnation point along an expanding/contracting surface. The water is considered as a base fluid and both types of carbon nanotubes i.e., single-wall (SWCNTs) and multi-wall (MWCNTs) are considered. The flow is taken in a Dacry-Forchheimer porous media amalgamated with quartic autocatalysis chemical reaction. Additional impacts added to the novelty of the mathematical model are the heat generation/absorption and buoyancy effect. The dimensionless variables led the envisaged mathematical model to a physical problem. The numerical solution is then found by engaging MATLAB built-in bvp4c function for non-dimensional velocity, temperature, and homogeneous-heterogeneous reactions. The validation of the proposed mathematical model is ascertained by comparing it with a published article in limiting case. An excellent consensus is accomplished in this regard. The behavior of numerous dimensionless flow variables including solid volume fraction, inertia coefficient, velocity ratio parameter, porosity parameter, slip velocity parameter, magnetic parameter, Schmidt number, and strength of homogeneous/heterogeneous reaction parameters are portrayed via graphical illustrations. Computational iterations for surface drag force are tabulated to analyze the impacts at the stretched surface. It is witnessed that the slip velocity parameter enhances the fluid stream velocity and diminishes the surface drag force. Furthermore, the concentration of the nanofluid flow is augmented for higher estimates of quartic autocatalysis chemical.

SENSITIVITY ANALYSIS AND IDENTIFIABILITY OF A MATHEMATICAL MODEL OF A CHEMICAL REACTION

2021 ◽  
pp. 14-18
Author(s):  
Л.Ф. Сафиуллина
Keyword(s):  
Mathematical Model ◽  
Inverse Problem ◽  
Sensitivity Analysis ◽  
Chemical Reaction ◽  
Reaction Model ◽  
Numerical Calculations ◽  
Specific Reaction ◽  
Uniqueness Of The Solution ◽  
The Mathematical Model ◽  
Kinetics Of

В статье рассмотрен вопрос идентифицируемости математической модели кинетики химической реакции. В процессе решения обратной задачи по оценке параметров модели, характеризующих процесс, нередко возникает вопрос неединственности решения. На примере конкретной реакции продемонстрирована необходимость проводить анализ идентифицируемости модели перед проведением численных расчетов по определению параметров модели химической реакции. The identifiability of the mathematical model of the kinetics of a chemical reaction is investigated in the article. In the process of solving the inverse problem of estimating the parameters of the model, the question arises of the non-uniqueness of the solution. On the example of a specific reaction, the need to analyze the identifiability of the model before carrying out numerical calculations to determine the parameters of the reaction model was demonstrated.

On the spread of ultrafine particulate matter: A mathematical model for motor vehicle emissions and their effects as an asthma trigger

2021 ◽  
Author(s):  
Michelle N. Rosado-Pérez ◽  
Karen Ríos-Soto
Keyword(s):  
Mathematical Model ◽  
Ultrafine Particles ◽  
Motor Vehicle ◽  
Traveling Wave Solutions ◽  
Reaction Diffusion ◽  
Ambient Air ◽  
Air Pollutant ◽  
Pollutant Emissions ◽  
Motor Vehicles ◽  
Diffusion Type

Asthma is a respiratory disease that affects the lungs, with a prevalence of 339.4 million people worldwide [G. Marks, N. Pearce, D. Strachan, I. Asher and P. Ellwood, The Global Asthma Report 2018, globalasthmareport.org (2018)]. Many factors contribute to the high prevalence of asthma, but with the rise of the industrial age, air pollutants have become one of the main Ultrafine particles (UFPs), which are a type of air pollutant that can affect asthmatics the most. These UFPs originate primarily from the combustion of motor vehicles [P. Solomon, Ultrafine particles in ambient air. EM: Air and Waste Management Association’s Magazine for Environmental Managers (2012)] and although in certain places some regulations to control their emission have been implemented they might not be enough. In this work, a mathematical model of reaction–diffusion type is constructed to study how UFPs grow and disperse in the environment and in turn how they affect an asthmatic population. Part of our focus is on the existence of traveling wave solutions and their minimum asymptotic speed of pollutant propagation [Formula: see text]. Through the analysis of the model it was possible to identify the necessary threshold conditions to control the pollutant emissions and consequently reduce the asthma episodes in the population. Analytical and numerical results from this work prove how harmful the UFEs are for the asthmatic population and how they can exacerbate their asthma episodes.

scholarly journals Qualitative analysis of an autocatalytic chemical reaction model with decay

2014 ◽  
Vol 144 (2) ◽  
pp. 427-446 ◽  
Author(s):  
Jun Zhou ◽  
Junping Shi
Keyword(s):  
Steady State ◽  
Chemical Reaction ◽  
Reaction Diffusion ◽  
Steady State Solution ◽  
Reaction Model ◽  
Existence Of A Solution ◽  
Positive Steady State ◽  
Chemical Reaction Model ◽  
The One ◽  
Necessary And Sufficient

In this paper, we revisit a reaction—diffusion autocatalytic chemical reaction model with decay. For higher-order reactions, we prove that the system possesses at least two positive steady-state solutions; hence, it has bistable dynamics similar to the system without decay. For the linear reaction, we determine the necessary and sufficient condition to ensure the existence of a solution. Moreover, in the one-dimensional case, we prove that the positive steady-state solution is unique. Our results demonstrate the drastic difference in dynamics caused by the order of chemical reactions.

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