Numerical solution of the mathematical model of internal-diffusion kinetics of adsorption

1993 ◽  
Vol 66 (2) ◽  
pp. 2149-2155
Author(s):  
I. P. Gavrilyuk ◽  
P. F. Zhuk ◽  
L. N. Bondarenko
Keyword(s):  
Mathematical Model ◽  
Numerical Solution ◽  
Internal Diffusion ◽  
Diffusion Kinetics ◽  
Kinetics Of Adsorption ◽  
The Mathematical Model ◽  
Kinetics Of

Some inverse problems of internal-diffusion kinetics of adsorption

1993 ◽  
Vol 66 (4) ◽  
pp. 2387-2390 ◽  
Author(s):  
I. P. Gavrilyuk ◽  
P. F. Zhuk ◽  
L. N. Bondarenko
Keyword(s):  
Inverse Problems ◽  
Internal Diffusion ◽  
Diffusion Kinetics ◽  
Kinetics Of Adsorption ◽  
Kinetics Of

Simulation of ion exchange interaction kinetics in the clinoptylolite - ammonium ion system

2021 ◽  
Vol 6 (4) ◽  
pp. 233-237
Author(s):  
Vira Sabadash ◽  
◽  
Jaroslaw Gumnitsky ◽  
Sofia Omelyanova ◽  
◽  
...  
Keyword(s):  
Mathematical Model ◽  
Mass Transfer ◽  
Ion Exchange ◽  
Rate Constants ◽  
Internal Diffusion ◽  
Ammonium Ion ◽  
Ammonium Ions ◽  
Kinetics Of Adsorption ◽  
Interaction Kinetics ◽  
Kinetics Of

The kinetics of adsorption of ammonium ions under dynamic conditions has been studied. A mathematical model of the process was built. The mass transfer coefficient was calculated depending on the intensity of the change of location. It was established that ion exchange occurs in external and internal diffusion regions. The rate constants of ion exchange for the region of external and internal diffusion were calculated.

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.

scholarly journals Mathematical Modeling of Pollution Transfer in Open Channel

2019 ◽  
pp. 49-50
Author(s):  
Petro Martyniuk ◽  
Oksana Ostapchuk ◽  
Vitalii Nalyvaiko
Keyword(s):  
Mathematical Modeling ◽  
Mathematical Model ◽  
Numerical Solution ◽  
Boundary Problem ◽  
Water Flow ◽  
Numerical Experiments ◽  
Open Channel ◽  
Computational Algorithm ◽  
The Mathematical Model

The problem of pollution transfer by water flow in open channel was considered. The mathematical model of the problem was constructed. The numerical solution of the onedimensional boundary problem was obtained. The computational algorithm for solving the problem was programmed to implement. A series of numerical experiments with their further analysis was conducted.

Studi Perpindahan Panas Material pada Sistem Koordinat Segitiga

2017 ◽  
Vol 1 ◽  
pp. 114
Author(s):  
Imam Basuki ◽  
C Cari ◽  
A Suparmi
Keyword(s):  
Heat Transfer ◽  
Mathematical Model ◽  
Heat Conduction ◽  
Partial Differential Equations ◽  
Finite Difference ◽  
Finite Difference Method ◽  
Numerical Solution ◽  
Difference Method ◽  
The Finite Difference Method ◽  
The Mathematical Model

<p class="Normal1"><strong><em>Abstract: </em></strong><em>Partial Differential Equations (PDP) Laplace equation can be applied to the heat conduction. Heat conduction is a process that if two materials or two-part temperature material is contacted with another it will pass heat transfer. Conduction of heat in a triangle shaped object has a mathematical model in Cartesian coordinates. However, to facilitate the calculation, the mathematical model of heat conduction is transformed into the coordinates of the triangle. PDP numerical solution of Laplace solved using the finite difference method. Simulations performed on a triangle with some angle values α and β</em></p><p class="Normal1"><strong><em> </em></strong></p><p class="Normal1"><strong><em>Keywords:</em></strong><em>  heat transfer, triangle coordinates system.</em></p><p class="Normal1"><em> </em></p><p class="Normal1"><strong>Abstrak</strong> Persamaan Diferensial Parsial (PDP) Laplace  dapat diaplikasikan pada persamaan konduksi panas. Konduksi panas adalah suatu proses yang jika dua materi atau dua bagian materi temperaturnya disentuhkan dengan yang lainnya maka akan terjadilah perpindahan panas. Konduksi panas pada benda berbentuk segitiga mempunyai model matematika dalam koordinat cartesius. Namun untuk memudahkan perhitungan, model matematika konduksi panas tersebut ditransformasikan ke dalam koordinat segitiga. Penyelesaian numerik dari PDP Laplace diselesaikan menggunakan metode beda hingga. Simulasi dilakukan pada segitiga dengan beberapa nilai sudut  dan  </p><p class="Normal1"><strong> </strong></p><p class="Normal1"><strong>Kata kunci :</strong> perpindahan panas, sistem koordinat segitiga.</p>

scholarly journals Drying kinetics of Chinese garlic (Allium tuberosum) and its effect on color

2020 ◽  
Vol 42 ◽  
pp. e8
Author(s):  
Paula De Almeida Rios ◽  
Ednilton Tavares De Andrade ◽  
Kátia Soares Moreira ◽  
Filipe Da Silva De Oliveira ◽  
Bárbara Lemes Outeiro Araújo
Keyword(s):  
Experimental Data ◽  
Mathematical Model ◽  
Air Temperature ◽  
Linear Regression Analysis ◽  
Drying Kinetics ◽  
Allium Tuberosum ◽  
Thin Slices ◽  
The Mathematical Model ◽  
Quasi Newton ◽  
Kinetics Of

Dehydrated garlic is an important component both for culinary and medicinal purposes. However, there is a scarcity of studies that characterizes its drying kinetics. Thus, the objective of this work was to study the drying kinetics of Chinese garlic (Allium tuberosum), as well as to analyze the color effect resulting from each treatment. The garlic bulbs were cut into thin slices with a width of 2 and 3 mm, subjected to the drying air temperature of 35, 45, 55 and 70 °C in a mechanical dryer of a fixed layer with forced convection. Was performed a non-linear regression analysis by the Quasi-Newton method, for adjustment to 11 mathematical models to the experimental data of drying. The Midilli equation was the mathematical model that best characterized all the drying temperatures, for the experimental data. The diffusion coefficient presented values between 1.46 x 10-11 and 7.32 x 10-11 m2.s-1. The increase of the drying air temperature caused the dimming of the samples with a reduction of the L* coordinate and reduction of the yellow of the samples according to the coordinate results h*. The temperature of 70 °C was detrimental to the maintenance of the Chinese garlic coloration. 

scholarly journals МАТЕМАТИЧЕСКАЯ МОДЕЛЬ И МЕТОД РАСЧЕТА ДИНАМИКИ СУШКИ И ТЕРМОДЕСТРУКЦИИ БИОМАССЫ

2018 ◽  
Vol 82 (1) ◽  
Author(s):  
Наталья Николаевна Сороковая ◽  
Дмитрий Николаевич Коринчук
Keyword(s):  
Mathematical Model ◽  
Mass Transfer ◽  
Thermal Decomposition ◽  
Numerical Method ◽  
Heat And Mass Transfer ◽  
The Body ◽  
Physical Factors ◽  
Deformation Equation ◽  
The Mathematical Model ◽  
Kinetics Of

Разработана математическая модель и численный метод расчета динамики тепломассопереноса, фазовых превращений и усадки при сушке коллоидных капиллярно-пористых тел цилиндрической формы в условиях равномерного обдува теплоносителем. Математическая модель строилась на базе дифференциального уравнения переноса субстанции (энергии, массы, импульса) в деформируемых системах. Проведены экспериментальные исследования кинетики обезвоживания частиц энергетической вербы в потоке воздуха с целью верификации математической модели. Обоснована возможность ее использования для расчета совместных процессов сушки и начального этапа термического разложения биомассы. С использованием ранее полученных данных по значениям энергии активации Аэф(Т) для различных видов биомассы проведено математическое моделирование динамики и кинетики высокотемпературной сушки в потоке дымовых газов энергетической вербы, которая сопровождается термодеструкцией гемиоцеллюлозы. Результаты численных экспериментов свидетельствуют об адекватности предложенного подхода, эффективности математической модели и метода ее реализации. На их основе возможно проводить исследование динамики тепломассопереноса при сушке частиц различных видов измельченной биомассы; определение температуры начала и окончания первой стадии термического разложения; момента достижения равновесного влагосодержания в зависимости от свойств материала и сушильного агента. Эти данные позволяют выбирать оптимальные с точки зрения сохранения энергии и качества высушиваемого продукта  режимные параметры процесса.         A mathematical model and a numerical method for calculating the dynamics of heat and mass transfer, phase transformations and shrinkage during the drying of colloidal capillary-porous cylindrical bodies under conditions of equitable winding by a coolant are developed. The mathematical model was based on the differential equation of substance (energy, mass, impulse) transfer in deformable systems. It includes the equations diffusion-filtration transfer of energy for the system as a whole, and the mass transfer of the liquid, vapor and air phases in the pores of the body. Expressions for the intensity of evaporation of a liquid, capillary pressure, and the diffusion coefficients are presented. The relative volume strain was found by means of an analytical solution of the thermoconcentration deformation equation. Based on the explicit three-layer counting difference scheme and the procedure splitting of algorithm  by physical factors, a numerical method for realizing this mathematical model is developed.Experimental studies of the kinetics of dehydration of energy willow particles in the airflow were carried out to verify the mathematical model. Its applicability for calculating combined processes of drying and of the initial stage of thermal decomposition of biomass is substantiated. Using the previously obtained data on the activation energy values for various types of biomass, a mathematical simulation of the dynamics and kinetics of high-temperature drying in the flue gas flow of energy willow was carried out, which is accompanied by thermal destruction of hemiocellulose. The results of numerical experiments indicate the adequacy of the proposed approach, the effectiveness of the mathematical model and the method of its implementation. On their basis, it is possible to study the dynamics of heat and mass transfer when drying particles of different types of ground biomass; determination of the temperature of the beginning and ending of the first stage of thermal decomposition; the moment when the equilibrium moisture content is reached, depending on the properties of the material and the drying agent. These data allow choosing the process parameters that are optimal in terms of energy saving and quality of the dried product.

scholarly journals In vivo imaging of the kinetics of microglial self-renewal and maturation in the adult visual cortex

2020 ◽  
Author(s):  
Monique S. Mendes ◽  
Jason Atlas ◽  
Zachary Brehm ◽  
Antonio Ladron-de-Guevara ◽  
Matthew N. McCall ◽  
...  
Keyword(s):  
Mathematical Model ◽  
Visual Cortex ◽  
Adult Brain ◽  
Self Renewal ◽  
Two Photon ◽  
And Migration ◽  
The Mathematical Model ◽  
Kinetics Of ◽  
The Brain

AbstractMicroglia are the resident immune cells in the brain with the capacity to autonomously self-renew. Under basal conditions, microglial self-renewal appears to be slow and stochastic, although microglia have the ability to proliferate very rapidly following depletion or in response to injury. Because microglial self-renewal has largely been studied using static tools, the mechanisms and kinetics by which microglia renew and acquire mature characteristics in the adult brain are not well understood. Using chronic in vivo two-photon imaging in awake mice and PLX5622 (Colony stimulating factor 1 receptor (CSF1R) inhibitor) to deplete microglia, we set out to understand the dynamic self-organization and maturation of microglia following depletion in the visual cortex. We confirm that under basal conditions, cortical microglia show limited turnover and migration. Following depletion, however, microglial repopulation is remarkably rapid and is sustained by the dynamic division of the remaining microglia in a manner that is largely independent of signaling through the P2Y12 receptor. Mathematical modeling of microglial division demonstrates that the observed division rates can account for the rapid repopulation observed in vivo. Additionally, newly-born microglia resemble mature microglia, in terms of their morphology, dynamics and ability to respond to injury, within days of repopulation. Our work suggests that microglia rapidly self-renew locally, without the involvement of a special progenitor cell, and that newly born microglia do not recapitulate a slow developmental maturation but instead quickly take on mature roles in the nervous system.Graphical Abstract(a) Microglial dynamics during control condition. Cartoon depiction of the heterogenous microglia in the visual cortex equally spaced. (b) During the early stages of repopulation, microglia are irregularly spaced and sparse. (c) During the later stages of repopulation, the number of microglia and the spatial distribution return to baseline. (d-f) We then created and ran a mathematical model that sampled the number of microglia, (d) the persistent doublets, (e) the rapid divisions of microglia and (f) the secondary divisions of microglia during the peak of repopulation day 2-day 3. The mathematical model suggested that residual microglia can account for the rapid repopulation we observed in vivo.

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