scholarly journals Extraction Process of Intracellular Substance

2010 ◽  
Vol 4 (2) ◽  
pp. 163-166
Author(s):  
Vasil Dyachok ◽  
Keyword(s):  
Mathematical Model ◽  
Plant Material ◽  
Extraction Process ◽  
Anatomical Structure ◽  
Process Conditions ◽  
Intercellular Spaces ◽  
Process Implementation ◽  
Kinetic Coefficients ◽  
The Mathematical Model ◽  
Kinetics Of

In this study the mathematical model of the extraction process from plant material is developed, taking into account the anatomical structure of plant material, namely the presence of cellular and intercellular spaces. The solution of the model enables to determine its kinetic coefficients Dc, Dt, process conditions, and predict the kinetics of the extraction process implementation in practice.

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.

An enhanced composting process with bioaugmentation: Mathematical modelling and process optimization

2021 ◽  
pp. 0734242X2110337
Author(s):  
Tea Sokač ◽  
Anita Šalić ◽  
Dajana Kučić Grgić ◽  
Monika Šabić Runjavec ◽  
Marijana Vidaković ◽  
...  
Keyword(s):  
Mathematical Model ◽  
Model Simulation ◽  
Process Conditions ◽  
Air Flow Rate ◽  
Optimal Process ◽  
Composting Process ◽  
Different Types ◽  
Adiabatic Reactor ◽  
The Mathematical Model ◽  
Good Agreement

In this paper, two different types of biowaste composting processes were carried out – composting without and with bioaugmentation. All experiments were performed in an adiabatic reactor for 14 days. Composting enhanced with bioaugmentation was the better choice because the thermophilic phase was achieved earlier, making the composting time shorter. Additionally, a higher conversion of substrate (amount of substrate consumed) was also noticed in the process enhanced by bioaugmentation. A mathematical model was developed and process parameters were estimated in order to optimize the composting process. Based on good agreement between experimental data and the mathematical model simulation results, a three-level-four-factor Box-Behnken experimental design was employed to define the optimal process conditions for further studies. It was found that the air flow rate and the mass fraction of the substrate have the most significant effect on the composting process. An improvement of the composting process was achieved after altering the mentioned variables, resulting in shorter composting time and higher conversion of the substrate.

scholarly journals Experimental studies of iron transformations kinetics and autocatalysis during its physicochemical removal from underground water

2021 ◽  
Author(s):  
S. Yu Martynov ◽  
V. L. Poliakov
Keyword(s):  
Experimental Data ◽  
Mathematical Model ◽  
Experimental Studies ◽  
Underground Water ◽  
Model Parameters ◽  
Kinetic Coefficients ◽  
Transfer Equations ◽  
The Mathematical Model ◽  
Autocatalytic Effect ◽  
Forms Of Iron

Abstract The mathematical model of physicochemical iron removal from groundwater was developed. It consists of three interrelated compartments. The results of the experimental research provide information in support of the first two compartments of the mathematical model. The dependencies for the concentrations of the adsorbed ferrous iron and deposited hydroxide concentrations are obtained as a result of the exact solution of the system of the mass transfer equations for two forms of iron in relation to the inlet surface of the bed. An analysis of the experimental data of the dynamics of the deposit accumulation in a small bed sample was made, using a special application that allowed to select the values of the kinetic coefficients and other model parameters based on these dependencies. We evaluated the autocatalytic effect on the dynamics of iron ferrous and ferric forms. The verification of the mathematical model was carried out involving the experimental data obtained under laboratory and industrial conditions.

scholarly journals Kinetics of Extraction of Dioscine from Vegetable Raw Materials in Vibrocavitation Homogenizer

2020 ◽  
Vol 9 (2) ◽  
pp. 77-81 ◽  
Author(s):  
E. V. Flisyuk ◽  
S. S. Belokurov ◽  
I. A. Narkevich ◽  
A. N. Shikov ◽  
O. M. Flisyuk ◽  
...  
Keyword(s):  
Mass Transfer ◽  
Plant Material ◽  
Raw Materials ◽  
Extraction Process ◽  
Rotor Speed ◽  
Plant Materials ◽  
Periodic Action ◽  
Initial Stage ◽  
Working Volume ◽  
Kinetics Of

Introduction. In recent years, substances extracted from plant materials have been widely used in the pharmaceutical, cosmetic and food industries. Such substances are used as solutions, dry extracts for the manufacture of medicines, dietary supplements, cosmetic creams, food additives in various forms – tablets, capsules, solutions, granular powders. The extraction of valuable substances from plant materials is carried out using the extraction process, which is carried out by various methods and in apparatuses of various designs. Earlier, a comparative study of the extraction of dioscin from fenugreek by various methods was carried out: in devices with a stirrer, in an ultrasonic field, supercritical, fluid CO2 extraction, and in a vibro-cavitation homogenizer. It is shown that the most effective method is the extraction carried out in a vibrocavitation homogenizer.Aim.To analyze the kinetics of the extraction of dioscin from fenugreek seeds, to determine the optimal values of the required degree of grinding of the raw materials, working temperature, the concentration of ethyl alcohol in the solution and the rotational speed of the rotor of the vibrocavitation homogenizer. Determine the effective mass transfer coefficient responsible for the intensity of mass transfer inside the particles.Materials and methods. An experimental study of the extraction of valuable components from plant materials was carried out in a laboratory unit with a vibrocavitation homogenizer of periodic action. As raw materials were used seeds of hay fenugreek, ecotype of Morocco, acquired in the company Fitokasa, Casablanca (Morocco), which we used for research. Commodity analysis showed that raw materials comply with the requirements of the State Pharmacopoeia XIVth edition. As extractants, aqueous solutions of ethanol with an alcohol concentration of 40, 50, 60, 70, 80, and 90 %. The analysis of the kinetics of the process was based on the following ideas. Extraction begins with the surface of the particles of plant material. As the extracted component moves into the volume of the solution, the extractant penetrates into the internal pores of the particles, and the surface on which the extractant and the extracted component interact is gradually shifted into the individual particles. In this case, the resistance to mass transfer in the region between the specified surface and the outer surface of the particle increases over time.Results and discussion. An analysis of the results shows that the rotor speed significantly intensifies the process. In addition, the influence of the rotor speed is most pronounced at the initial stage of the process, when the surface layers of particles of plant material are extracted. It was also found that the resistance to mass transfer inside particles increases significantly as it approaches the final stage of the process, and with an increase in the rotor speed, it increases, especially at the initial stage of the process, which is associated with the intensity of cavitation and the weakening of its effect as the process deepens inward particles.Conclusions. The obtained dependences are necessary to determine the duration of the extraction process in a batch mode, or the average residence time of seeds in the working volume when organizing the process in a continuous mode.

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.

Effect of Global Ventilation to Perfusion Ratio, for Normal Lungs, on Desflurane and Sevoflurane Elimination Kinetics

2021 ◽  
Author(s):  
James E. Baumgardner ◽  
Moritz Kretzschmar ◽  
Alf Kozian ◽  
Thomas Hachenberg ◽  
Thomas Schilling ◽  
...  
Keyword(s):  
Mathematical Model ◽  
Time Constant ◽  
Practical Importance ◽  
Elimination Kinetics ◽  
Retention Equation ◽  
Pressure Part ◽  
Inhaled Anesthetic ◽  
The Mathematical Model ◽  
Kinetics Of ◽  
Normal Lungs

Background Kinetics of the uptake of inhaled anesthetics have been well studied, but the kinetics of elimination might be of more practical importance. The objective of the authors’ study was to assess the effect of the overall ventilation/perfusion ratio ( .VA/.Q  ), for normal lungs, on elimination kinetics of desflurane and sevoflurane. Methods The authors developed a mathematical model of inhaled anesthetic elimination that explicitly relates the terminal washout time constant to the global lung  .VA/.Q   ratio. Assumptions and results of the model were tested with experimental data from a recent study, where desflurane and sevoflurane elimination were observed for three different  .VA/.Q   conditions: normal, low, and high. Results The mathematical model predicts that the global  .VA/.Q   ratio, for normal lungs, modifies the time constant for tissue anesthetic washout throughout the entire elimination. For all three  .VA/.Q   conditions, the ratio of arterial to mixed venous anesthetic partial pressure Part/Pmv reached a constant value after 5 min of elimination, as predicted by the retention equation. The time constant corrected for incomplete lung clearance was a better predictor of late-stage kinetics than the intrinsic tissue time constant. Conclusions In addition to the well-known role of the lungs in the early phases of inhaled anesthetic washout, the lungs play a long-overlooked role in modulating the kinetics of tissue washout during the later stages of inhaled anesthetic elimination. The  .VA/.Q  ratio influences the kinetics of desflurane and sevoflurane elimination throughout the entire elimination, with more pronounced slowing of tissue washout at lower  .VA/.Q   ratios. Editor’s Perspective What We Already Know about This Topic What This Article Tells Us That Is New

Modelling the Wear Process of Inhomogeneous Bodies

2005 ◽  
Author(s):  
I. G. Goryacheva
Keyword(s):  
Mathematical Model ◽  
Phase Composition ◽  
Contact Mechanics ◽  
Two Phase ◽  
Wear Process ◽  
Substrate Interface ◽  
Inhomogeneous Bodies ◽  
The Mathematical Model ◽  
Kinetics Of ◽  
Local Hardening

The approaches of contact mechanics are used to evaluate the evolution of the contact characteristics in wear process of inhomogeneous bodies (coated bodies, two-phase composition, bodies with inclusions, etc.). The mathematical model is formulated and used to study the kinetics of the wear process depending on the parameters of inhomogeneity such as size and density of inclusions, waviness at the coating-substrate interface, local hardening parameters, etc.

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