Simulation of solubility by the example of a sugar solution

2019 ◽  
pp. 660-664
Author(s):  
Denis V. Arapov ◽  
Vladimir A. Kuritsyn ◽  
Sergey G. Tikhomirov ◽  
Vladimir V. Denisenko
Keyword(s):  
Mathematical Model ◽  
Mass Concentration ◽  
Sugar Solution ◽  
Pure Solvent ◽  
Solubility Equation ◽  
Solubility Model ◽  
Industrial Solutions

A method to expand solubility equation for pure sugar solutions to a generalized solubility model has been developed. The proposed approach can be used to calculate the solubility of a substance in an impure solvent with the known equation of its solubility in a pure solvent. A generalized mathematical model of solubility of sucrose in pure and industrial solutions has been obtained. The adequacy of the model was tested on 6 samples of impure solutions, including a water-ethanol-sucrose mixture. The solubility of sucrose in ethanol for a mass concentration from 1.0 to 99.0% of ethanol in the solution is calculated.

scholarly journals SIMULATION OF HEAT TRANSPORT AT THE COOLING OF THE SUGAR SOLUTION IN A RECUPERATION EXCHANGER

2015 ◽  
Vol 55 (3) ◽  
pp. 140-145 ◽  
Author(s):  
Tomáš Brestovič ◽  
Mária Čarnogurská ◽  
Miroslav Příhoda ◽  
Michal Kubík
Keyword(s):  
Mathematical Model ◽  
Heat Transport ◽  
Sugar Solution ◽  
Cooling Process ◽  
Cooling Performance ◽  
The Real ◽  
Operation Temperature ◽  
The Individual

<p>The paper describes a mathematical model of the cooling process of a highly concentrated sugar solution in an exchanger with a specifically shaped heat exchanging surface of the cooling panels. An analysis of the individual parts of the stum cooling line is made, dealing with the cooling performance of the cooling panels located in the stum tanks, whose volume is 3230 litres or 1430 litres. One of the monitored parameters is the cooling performance of the JN30 aggregate. The article also deals with an appropriateness of the aggregate for cooling the stum of the total volume 78.21 m<sup>3</sup>, from the real operation temperature to 0 °C during 48 hours.</p>

scholarly journals INFLUENCE OF THE CONCENTRATION OF ELECTROLYTES ON THE ELECTRIFICATION AND THE RATE OF DIFFUSION OF WATER THROUGH COLLODION MEMBRANES

1919 ◽  
Vol 2 (2) ◽  
pp. 173-200 ◽  
Author(s):  
Jacques Loeb
Keyword(s):  
Initial Rate ◽  
Pressure Effect ◽  
Critical Concentration ◽  
Pure Water ◽  
Preceding Paper ◽  
Gas Pressure ◽  
Sugar Solution ◽  
Opposite Charge ◽  
Pure Solvent ◽  
Solutions Of Electrolytes

1. When a watery solution is separated from pure water by a collodion membrane, the initial rate of diffusion of water into the solution is influenced in an entirely different way by solutions of electrolytes and of non-electrolytes. Solutions of non-electrolytes, e.g. sugars, influence the initial rate of diffusion of water through the membrane approximately in direct proportion to their concentration, and this. influence begins to show itself under the conditions of our experiments when the concentration of the sugar solution is above M/64 or M/32. We call this effect of the concentration of the solute on the initial rate of diffusion of water into the solution the gas pressure effect. 2. Solutions of electrolytes show the gas pressure effect upon the initial rate of diffusion also, but it commences at a somewhat higher concentration than M/64; namely, at M/16 or more (according to the nature of the electrolyte). 3. Solutions of electrolytes of a lower concentration than M/16 or M/8 have a specific influence on the initial rate of diffusion of water through a collodion membrane from pure solvent into solution which is not found in the case of the solutions of non-electrolytes and which is due to the fact that the particles of water diffuse in this case through the membrane in an electrified condition, the sign of the charge depending upon the nature of the electrolyte in solution, according to two rules given in a preceding paper. 4. In these lower concentrations the curves representing the influence of the concentration of the electrolyte on the initial rate of diffusion of water into the solution rise at first steeply with an increase in the concentration, until a maximum is reached at a concentration of M/256 or above. A further increase in concentration causes a drop-in the curve and this drop increases with a further increase of concentration until that concentration of the solute is reached in which the gas pressure effect begins to prevail; i.e., above M/16. Within a range of concentrations between M/256 and M/16 or more (according to the nature of the electrolyte) we notice the reverse of what we should expect on the basis of van't Hoff's law; namely, that the attraction of a solution of an electrolyte for water diminishes with an increase in concentration. 5. We wish to make no definite assumption concerning the origin of the electrification of water and concerning the mechanism whereby ions influence the rate of diffusion of water particles through collodion membranes from pure solvent to solution. It will facilitate, however, the presentation of our results if it be permitted to present them in terms of attraction and repulsion of the charged particles of water by the ions. With this reservation we may say that in the lowest concentrations attraction of the electrified water particles by the ions with the opposite charge prevails over the repulsion of the electrified water particles by the ions with the same sign of charge as that of the water; while beyond a certain critical concentration the repelling action of the ion with the same sign of charge as that of the water particles upon the latter increases more rapidly with increasing concentration of the solute than the attractive action of the ion with the opposite charge. 6. It is shown that negative osmosis, i.e. the diminution of the volume of the solution of acids and of alkalies when separated by collodion membranes from pure water, occurs in the same range of concentrations in which the drop in the curves of neutral salts occurs, and that it is due to the same cause; namely, the repulsion of the electrified particles of water by the ion with the same sign of charge as that of the water. This conclusion is supported by the fact that negative osmosis becomes pronounced when the ion with the same sign of charge as that of the electrified particles of water carries more than one charge.

Mathematical Model of an Unstable Miscible Displacement

1963 ◽  
Vol 3 (02) ◽  
pp. 155-163 ◽  
Author(s):  
E.L. Dougherty
Keyword(s):  
Mathematical Model ◽  
Porous Media ◽  
Viscosity Ratio ◽  
Miscible Displacement ◽  
Factor H ◽  
Hyperbolic Partial Differential Equations ◽  
Mixing Process ◽  
Fractional Flow ◽  
One Dimensional ◽  
Pure Solvent

DOUGHERTY, E.L., CALIFORNIA RESEARCH CORP., LA HABRA, CALIF. JUNIOR MEMBER AIME Abstract A phenomenological theory for a one-dimensional unstable miscible displacement similar in type to the Buckley-Leverett model but including the effects of mixing is proposed An equation giving the fractional flow of pure solvent through an oil phase containing dissolved solvent is derived including the effects of gravity and nonhomogeneities. Numerical integration of the resulting pair of nonlinear hyperbolic partial differential equations gives volumes of dissolved and undissolved solvent as functions of space and time. Parameters in the model which characterize mixing due to dispersion were determined from experimental data; the parameters correlated with viscosity ratio. The results indicate that the rate of dispersive mixing is proportional to volumetric flow rate Incorporated into our equations were Koval's heterogeneity factor H, which characterizes mixing due to channeling. This allowed satisfactory predictions of displacement behavior observed in horizontal floods in nonhomogeneous cores; but in most cases the values of H which we used were considerably larger than those used by Koval. Introduction It has been shown that for favorable viscosity ratios, the diffusion equation with convection satisfactorily describes the behavior of a miscible displacement in a porous media. Numerous attempts to develop a satisfactory mathematical description for the case of unfavorable viscosity ratio have been reported, but they have met with only partial success. These attempts, which are reviewed by Koval, have taken two approaches:development of a flow model akin to the Buckley-Leverett approach for immiscible displacement neglecting the effects of mixing andsimultaneous application of Darcy's Law for flow and the diffusion equation with a convection term for mass transfer. We set out to construct a mathematical model of Type 1 including, though, the effects of mixing. Based upon a set of hypotheses, we derived a pair of non-linear hyperbolic partial differential equations which describe in a one-dimensional system the combined effects of flow and mixing. To work with these equations it was necessary to develop a fractional flow formula. The combined system was integrated numerically using the method of characteristics.In our equations the mixing process is characterized by four parameters. Three of these, labeled beta, p and p, account for dispersive type mixing. The fourth is the heterogeneity factor H, proposed by Koval to account for channeling due to nonhomogeneities in the porous media. Values of the parameters which would cause agreement between theory and experiment were determined by trial-and-error for miscible floods conducted in horizontal cores of both homogeneous and heterogeneous materials. Calculations were also performed for vertical floods in homogeneous cores.The purpose of this paper isto present the details of the mathematical analysis,to present the results of the calculations,to consider what light the results shed on the mixing process in an unstable miscible displacement, andto provide a firmer foundation for the correlation technique developed by Koval for predicting the behavior of unstable miscible floods. STATEMENT OF PROBLEM The problem is to construct a mathematical model which describes in one dimension the observed behavior in an unstable miscible displacement. The approach is phenomenological in that the equations are based on assumptions which violate certain physical precepts known to apply to the displacement phenomenon. However, the assumptions do allow us to account mathematically for the more essential phenomena. The work is of value if we can quantitatively predict experimental results which heretofore could not be predicted, even though the synthetic nature of the model belies complete explanation of the observations.We assume that the system is comprised of two contiguous flowing phases. One phase, which we call free solvent, has the properties of pure solvent. We call the fraction of the pore volume occupied by this phase the solvent saturation, designated s. SPEJ P. 155^

scholarly journals Development of a refractodensimetric method for determining the content of ethyl alcohol and total wine extract by a computer

2020 ◽  
Vol 10 (4) ◽  
pp. 3-11
Author(s):  
R. G. Timofeev
Keyword(s):  
Mathematical Model ◽  
Refractive Index ◽  
Ethyl Alcohol ◽  
Mass Concentration ◽  
Volume Fraction ◽  
Metrological Certification ◽  
Total Extract ◽  
Standard Equipment ◽  
Technical Specifications ◽  
Non Destructive

The work is devoted to the improvement of the methodological foundations of the refractodensimetric method of analysis as applied to liquid alcohol-containing products of grape winemaking. The regularities of changes in density and specific refraction of ethyl alcohol and substances of the extract of grapes and wine depending on their concentration based on the processing of the data of measuring the refractive index and density of various alcohol-containing products of winemaking and model solutions based on them, as well as based on the analysis of data from official densimetric and refractometric tables to determine the concentration of aqueous solutions of ethyl alcohol and total extract of the must, has been determined. The improved mathematical model of an alcoholic drink is proposed, which adequately describes the dependence of the refractive index and density of the drink on the content of ethyl alcohol and extract, based on the use of the additivity property of the specific refraction and the mass of the components of its constituents. On the basis of the proposed mathematical model of the drink, an algorithm has been developed for determining the volume fraction of ethyl alcohol and the mass concentration of the total extract for winemaking products, based on measuring the density and refractive index as the basis for the method for determining the volume fraction of ethyl alcohol and the mass concentration of the total extract. Preliminary metrological certification of the method for determining the mass concentration of the total extract and the volume fraction of ethyl alcohol in alcohol-containing products of grape winemaking has been carried out. The results of the work can be the basis for the development of a non-destructive express method for determining the volume fraction of ethyl alcohol and the mass concentration of the total extract based on the standard equipment of the laboratory of wineries, as well as the development of technical specifications for the manufacture of a portable device for determining the concentration of alcohol and extract based on the simultaneous measurement of the refractive index and density of liquid media.

Mathematical model of hit phenomena and its application to movie advertisement

2008 ◽  
Author(s):  
Ishii Akira ◽  
Yoshida Narihiko ◽  
Hayashi Takafumi ◽  
Umemura Sanae ◽  
Nakagawa Takeshi
Keyword(s):  
Mathematical Model
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