scholarly journals Calculation of the equilibrium pH in a multiple-buffered aqueous solution based on partitioning of proton buffering: a new predictive formula

2009 ◽  
Vol 296 (6) ◽  
pp. F1521-F1529 ◽  
Author(s):  
Minhtri K. Nguyen ◽  
Liyo Kao ◽  
Ira Kurtz
Keyword(s):  
Mathematical Model ◽  
Aqueous Solution ◽  
Polynomial Equation ◽  
Acid Base ◽  
Ph Values ◽  
Quartic Polynomial ◽  
New Equation ◽  
The Mathematical Model ◽  
Proton Load ◽  
Hasselbalch Equation

Upon the addition of protons to an aqueous solution containing multiple buffers, the final H+concentration ([H+]) at equilibrium is determined by the partitioning of added H+among the various buffer components. In the analysis of acid-base chemistry, the Henderson-Hasselbalch equation and the Stewart strong ion formulation can only describe (rather than predict) the equilibrium pH following a proton load since these formulas calculate the equilibrium pH only when the reactant concentrations at equilibrium11 The term “equilibrium” refers to the steady state proton and reactant concentrations when the buffering of excess protons by the various buffers is complete. are already known. In this regard, it is simpler to directly measure the equilibrium pH rather than measure the equilibrium reactant concentrations to calculate the equilibrium pH. As these formulas cannot predict the final equilibrium [H+] following a proton load to a multiple-buffered aqueous solution, we developed a new quantitative approach for predicting the equilibrium [H+] that is based on the preequilibrium22 The term “preequilibrium” refers to the initial proton and reactant concentrations immediately upon addition of protons and before the buffering of excess protons by the various buffers. concentrations of all buffers in an aqueous solution. The mathematical model used to derive our equation is based on proton transfer buffer equilibria without requiring the incorporation of electroneutrality considerations. The model consists of a quartic polynomial equation that is derived based solely on the partitioning of H+among the various buffer components. We tested the accuracy of the model using aqueous solutions with various buffers and measured the equilibrium pH values following the addition of HCl. Our results confirmed the accuracy of our new equation ( r2= 1; measured pH vs. predicted pH), indicating that it quantitatively accounts for the underlying acid-base phenomenology.

scholarly journals Approximation of weak solution for the problem of a pH-gradient creation in isoelectrofocusing

2014 ◽  
Vol 470 (2171) ◽  
pp. 20140290
Author(s):  
L. V. Sakharova ◽  
E. V. Shiryaeva ◽  
M. Yu. Zhukov
Keyword(s):  
Mathematical Model ◽  
Aqueous Solution ◽  
Weak Solution ◽  
Differential Equations ◽  
Electric Field ◽  
Small Parameter ◽  
General Model ◽  
Smooth Functions ◽  
Piecewise Continuous ◽  
The Mathematical Model

The mathematical model describing the stationary natural pH -gradient arising under the action of an electric field in an aqueous solution of ampholytes is constructed and investigated. The model is a part of a more general model of the isoelectrofocusing process. Investigation is based on the approximation of a weak solution by the piecewise continuous non-smooth functions. The method can be used for solving classes of problems for ordinary differential equations with a small parameter at the highest derivatives and the turning points.

The Computer Simulation of the Acid-Base Titration

2013 ◽  
Vol 634-638 ◽  
pp. 20-24
Author(s):  
Xue Zheng Huang ◽  
Yang Tao Liu ◽  
Lei Zhang
Keyword(s):  
Analytical Chemistry ◽  
Mathematical Model ◽  
Ph Value ◽  
Visual Basic ◽  
Acid Base ◽  
Basic Language ◽  
Acid Base Titration ◽  
Visual Basic Language ◽  
The Mathematical Model ◽  
Titration Solution

The mathematical model on acid-base titration was established by using analytical chemistry theory; therefore the author designed a program to solve the model by using of Visual Basic language. The program can not only calculate the pH Value of the acid-base titration solution, choose the appropriate indicator, calculate the endpoint error and judge the feasibility of the titration, but also can draw the curve of the acid-base titration.

A COMPREHENSIVE SIMULATOR OF THE HUMAN PULMONARY SYSTEM: VALIDATION WITH DETERMINATION OF TOTALCO2AND DIAGNOSIS OF ACID-BASE ABNORMALITIES

2009 ◽  
Vol 17 (01) ◽  
pp. 153-171
Author(s):  
MOHAMMAD REZA BIGDELI ◽  
SOHRAB HAJIZADEH ◽  
BEHZAD BANIEGHBAL ◽  
MOHAMMAD REZA MASJDI
Keyword(s):  
Mathematical Model ◽  
Physicochemical Properties ◽  
Comprehensive Model ◽  
Acid Base ◽  
System Validation ◽  
Steady State Responses ◽  
Fluid Compartments ◽  
The Mathematical Model ◽  
State Responses

In previous models, heart-lung-blood interactions and their physicochemical properties have not been considered in comprehensive simulators and an integrated mathematical model has not been presented. The aim of the present study is to combine different phenomena involved in the cardiopulmonary function, which are often considered separately. In this study, the variables that constitute a comprehensive model; which includes physicochemical reactions of O2and CO2in the blood and fluid compartments, V/Q, pH , body temperature and diffusion limitation in the adult human and its ability to provide realistic response under different physiological and pathophysiological conditions; have been evaluated. The new biological system model consists of two subsystems: physicochemical properties of blood and physiological subsystem models. Based on the mentioned parameters, comprehensive simulator model has been suggested as following: [Formula: see text] According to the literature, all patients [COPD (20) and asthma (20)] showed acid-base imbalances. The mathematical model has been validated by diagnosis of acid-base abnormalities via calculating the total CO2and T40HCO3in physiological and pathophysiological conditions, and then the results compared to literature experimental data. Our comprehensive model provides results consistent with dynamic and steady state responses measured in subjects undergoing physiological and pathophysiological conditions. This might enable us to deepen our understanding of the cardiopulmonary system as a whole.

DETERMINATION OF PERFORMANCE INDICATORS OF THE TRUCK KrAZ-6510TE

2020 ◽  
pp. 19-26
Author(s):  
Olexandr Pavlenko ◽  
Serhii Dun ◽  
Maksym Skliar
Keyword(s):  
Mathematical Model ◽  
Surface Friction ◽  
Building Structures ◽  
Maximum Torque ◽  
Military Equipment ◽  
Military Vehicles ◽  
Force Magnitude ◽  
Vehicle Mobility ◽  
The Mathematical Model

In any economy there is a need for the bulky goods transportation which cannot be divided into smaller parts. Such cargoes include building structures, elements of industrial equipment, tracked or wheeled construction and agricultural machinery, heavy armored military vehicles. In any case, tractor-semitrailer should provide fast delivery of goods with minimal fuel consumption. In order to guarantee the goods delivery, tractor-semitrailers must be able to overcome the existing roads broken grade and be capable to tow a semi-trailer in off-road conditions. These properties are especially important for military equipment transportation. The important factor that determines a tractor-semitrailer mobility is its gradeability. The purpose of this work is to improve a tractor-semitrailer mobility with tractor units manufactured at PJSC “AutoKrAZ” by increasing the tractor-semitrailer gradeability. The customer requirements for a new tractor are determined by the maximizing the grade to 18°. The analysis of the characteristics of modern tractor-semitrailers for heavy haulage has shown that the highest rate of this grade is 16.7°. The factors determining the limiting gradeability value were analyzed, based on the tractor-semitrailer with a KrAZ-6510TE tractor and a semi-trailer with a full weight of 80 t. It has been developed a mathematical model to investigate the tractor and semi-trailer axles vertical reactions distribution on the tractor-semitrailer friction performances. The mathematical model has allowed to calculate the gradeability value that the tractor-semitrailer can overcome in case of wheels and road surface friction value and the tractive force magnitude from the engine. The mathematical model adequacy was confirmed by comparing the calculations results with the data of factory tests. The analysis showed that on a dry road the KrAZ-6510TE tractor with a 80 t gross weight semitrailer is capable to climb a gradient of 14,35 ° with its coupling mass full use condition. The engine's maximum torque allows the tractor-semitrailer to overcome a gradient of 10.45° It has been determined the ways to improve the design of the KrAZ-6510TE tractor to increase its gradeability. Keywords: tractor, tractor-semitrailer vehicle mobility, tractor-semitrailer vehicle gradeability.

EXPERIMENTAL STUDIES OF CAR PROPERTIES ON A PHYSICAL MODEL

2019 ◽  
pp. 10-16
Author(s):  
Oleksii Timkov ◽  
Dmytro Yashchenko ◽  
Volodymyr Bosenko
Keyword(s):  
Mathematical Model ◽  
Remote Control ◽  
Physical Model ◽  
Model Experiment ◽  
Experimental Studies ◽  
Electrical Energy ◽  
Short Term ◽  
Motor Current ◽  
Memory Card ◽  
The Mathematical Model

The article deals with the development of a physical model of a car equipped with measuring, recording and remote control equipment for experimental study of car properties. A detailed description of the design of the physical model and of the electronic modules used is given, links to application libraries and the code of the first part of the program for remote control of the model are given. Atmega microcontroller on the Arduino Uno platform was used to manage the model and register the parameters. When moving the car on the memory card saved such parameters as speed, voltage on the motor, current on the motor, the angle of the steered wheel, acceleration along three coordinate axes are recorded. Use of more powerful microcontrollers will allow to expand the list of the registered parameters of movement of the car. It is possible to measure the forces acting on the elements of the car and other parameters. In the future, it is planned to develop a mathematical model of motion of the car and check its adequacy in conducting experimental studies on maneuverability on the physical model. In addition, it is possible to conduct studies of stability and consumption of electrical energy. The physical model allows to quickly change geometric dimensions and mass parameters. In the study of highway trains, this approach will allow to investigate the various layout schemes of highway trains in the short term. It is possible to make two-axle road trains and saddle towed trains, three-way hitched trains of different layout. The results obtained will allow us to improve not only the mathematical model, but also the experimental physical model, and move on to further study the properties of hybrid road trains with an active trailer link. This approach allows to reduce material and time costs when researching the properties of cars and road trains. Keywords: car, physical model, experiment, road trains, sensor, remote control, maneuverability, stability.

RESEARCH OF INDICATORS OF A VEHICLE WITH A DIESEL WORKING ON DIESEL AND DIESEL GAS CYCLES USING THE MATHEMATICAL MODEL

2020 ◽  
pp. 14-19
Author(s):  
Serhii Kovbasenko ◽  
Andriy Holyk ◽  
Serhii Hutarevych
Keyword(s):  
Mathematical Model ◽  
Diesel Engine ◽  
Environmental Performance ◽  
Energy Performance ◽  
Dual Fuel ◽  
Fuel System ◽  
Compressed Natural Gas ◽  
Diesel Vehicles ◽  
Diesel Cycle ◽  
The Mathematical Model

The features of an advanced mathematical model of motion of a truck with a diesel engine operating on the diesel and diesel gas cycles are presented in the article. As a result of calculations using the mathematical model, a decrease in total mass emissions as a result of carbon monoxide emissions is observed due to a decrease in emissions of nitrogen oxides and emissions of soot in the diesel gas cycle compared to the diesel cycle. The mathematical model of a motion of a truck on a city driving cycle according to GOST 20306-90 allows to study the fuel-economic, environmental and energy indicators of a diesel and diesel gas vehicle. The results of the calculations on the mathematical model will make it possible to conclude on the feasibility of converting diesel vehicles to using compressed natural gas. Object of the study – the fuel-economic, environmental and energy performance diesel engine that runs on dual fuel system using CNG. Purpose of the study – study of changes in fuel, economic, environmental and energy performance of vehicles with diesel engines operating on diesel and diesel gas cycles, according to urban driving cycle modes. Method of the study – calculations on a mathematical model and comparison of results with road tests. Bench and road tests, results of calculations on the mathematical model of motion of a truck with diesel, working on diesel and diesel gas cycles, show the improvement of environmental performance of diesel vehicles during the converting to compressed natural gas in operation. Improvement of environmental performance is obtained mainly through the reduction of soot emissions and nitrogen oxides emissions from diesel gas cycle operations compared to diesel cycle operations. The results of the article can be used to further develop dual fuel system using CNG. Keywords: diesel engine, diesel gas engine, CNG

Glycemia monitoring

1998 ◽  
Vol 2 ◽  
pp. 23-30
Author(s):  
Igor Basov ◽  
Donatas Švitra
Keyword(s):  
Diabetes Mellitus ◽  
Mathematical Model ◽  
Numerical Methods ◽  
Differential Equations ◽  
Blood Sugar ◽  
Self Regulation ◽  
Physiological System ◽  
Non Linear ◽  
The Mathematical Model

Here a system of two non-linear difference-differential equations, which is mathematical model of self-regulation of the sugar level in blood, is investigated. The analysis carried out by qualitative and numerical methods allows us to conclude that the mathematical model explains the functioning of the physiological system "insulin-blood sugar" in both normal and pathological cases, i.e. diabetes mellitus and hyperinsulinism.

Mathematical Models of Papermaking

2001 ◽  
Vol 6 (1) ◽  
pp. 9-19 ◽  
Author(s):  
A. Buikis ◽  
J. Cepitis ◽  
H. Kalis ◽  
A. Reinfelds ◽  
A. Ancitis ◽  
...  
Keyword(s):  
Mathematical Model ◽  
Initial Value Problems ◽  
Moisture Transfer ◽  
Bound Water ◽  
Drying Process ◽  
Initial Value ◽  
First Order ◽  
Heat And Moisture ◽  
The Mathematical Model ◽  
The Web

The mathematical model of wood drying based on detailed transport phenomena considering both heat and moisture transfer have been offered in article. The adjustment of this model to the drying process of papermaking is carried out for the range of moisture content corresponding to the period of drying in which vapour movement and bound water diffusion in the web are possible. By averaging as the desired models are obtained sequence of the initial value problems for systems of two nonlinear first order ordinary differential equations. 

The mathematical modelling of corrosion in hot dip galvanized steel reinforced concrete

2011 ◽  
Vol 2 (1) ◽  
pp. 1-12
Author(s):  
A. Hegyi ◽  
H. Vermeşan ◽  
V. Rus
Keyword(s):  
Mathematical Model ◽  
Reinforced Concrete ◽  
Numerical Model ◽  
Equation System ◽  
Galvanized Steel ◽  
Steel Reinforced Concrete ◽  
Numeric Model ◽  
Physical And Mathematical Models ◽  
Physical Phenomena ◽  
The Mathematical Model

Abstract In this paper we wish to present the numerical model elaborated in order to simulate some physical phenomena that influence the general deterioration of steel, whether hot dip galvanized or not, in reinforced concrete. We describe the physical and mathematical models, establishing the corresponding equation system, the initial and boundary conditions. We have also presented the numeric model associated to the mathematical model and the numeric methods of discretization and solution of the differential equations system that describes the mathematical model.

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