Prediction of Ethanol Content and Total Extract Using Densimetry and Refractometry
Prediction of Ethanol Content and Total Extract Using Densimetry and Refractometry
Plugatar, Yurij;Johnson, Joel B.;Timofeev, Ruslan;Korzin, Vadim;Kazak, Anatoliy;Nekhaychuk, Dmitry;Borisova, Elvira;Rotanov, Gennady
2023-04-07 00:00:00
beverages Article Prediction of Ethanol Content and Total Extract Using Densimetry and Refractometry 1 2 3 1 4 , Yurij Plugatar , Joel B. Johnson , Ruslan Timofeev , Vadim Korzin , Anatoliy Kazak * , 5 6 7 Dmitry Nekhaychuk , Elvira Borisova and Gennady Rotanov Nikitsky Botanical Gardens—National Scientific Center of the Russian Academy of Sciences, 298648 Yalta, Russia School of Health, Medical and Applied Sciences, Central Queensland University, North Rockhampton, QLD 4701, Australia Magarach All-Russia National Research Institute for Viticulture and Wine-Making, 298600 Yalta, Russia Humanitarian Pedagogical Academy, V.I. Vernadsky Crimean Federal University, 295007 Simferopol, Russia Sevastopol Branch, Plekhanov Russian University of Economics, 117997 Moscow, Russia Faculty of Economics, Russian University of Cooperation, 141014 Moscow, Russia Institute of City Development, Sevastopol State University, 299053 Sevastopol, Russia * Correspondence: kazak@cfuv.ru or kazak_a@mail.ru Abstract: This study investigated the interrelationships between the parameters of density, optical refraction, the volume fraction of ethanol and the total extract, using model solutions and samples of wine materials. The regularities of changes in refractometer readings in the process of alcoholic fermentation have been studied. The functional dependence of the value of the volume fraction of ethanol in the finished wine products on the density and scale of refractometer values has been established. A technique is proposed for controlling the process of alcoholic fermentation of grape must, based on the use of refractometry. Finally, we present an algorithm to calculate the composition (volume fraction of ethanol, mass concentration of the total extract) of the fermentation product from its physical properties (density, refractive index), the coefficient of determination was R = 0.975. Citation: Plugatar, Y.; Johnson, J.B.; Keywords: densimetry; refractometry; process control; ethanol content; sugar content; refractive index Timofeev, R.; Korzin, V.; Kazak, A.; Nekhaychuk, D.; Borisova, E.; Rotanov, G. Prediction of Ethanol Content and Total Extract Using 1. Introduction Densimetry and Refractometry. To determine the concentration of sugars (extract) in the wort before fermentation, Beverages 2023, 9, 31. https:// as well as monitoring the decrease in their concentration during alcoholic fermentation doi.org/10.3390/beverages9020031 in winemaking, a densimetric (hydrometric) method based on the linear dependence of Academic Editor: António the wort density on the concentration of sugars is used. The density of freshly squeezed Manuel Jordão grape must before fermentation uniquely, with an accuracy of 5 g/dm , determines the mass concentration of sugars [1]. During alcoholic fermentation, the density of the wort Received: 17 February 2023 decreases in proportion to the amount of fermented sugars. To estimate the concentration Revised: 17 March 2023 of sugars during fermentation by the densimetric method, it is necessary to know the initial Accepted: 30 March 2023 density of the wort before fermentation. The relationship between the wort density and the Published: 7 April 2023 mass concentration of sugars is shown by the formula [2]: p p C = C (1) 0.453 Copyright: © 2023 by the authors. Licensee MDPI, Basel, Switzerland. where C and C are the determined and initial concentration of sugars in the wort, g/dm , This article is an open access article p and p are the initial and desired density of the wort (in kg/m ), and 0.453 is a coefficient distributed under the terms and showing the decrease in the density of the wort during the fermentation of 1 g/dm conditions of the Creative Commons of sugar. Attribution (CC BY) license (https:// Previously, we proposed and justified a method for determining the volume fraction creativecommons.org/licenses/by/ of ethanol and the mass concentration of the extract in grape wines by measuring the 4.0/). Beverages 2023, 9, 31. https://doi.org/10.3390/beverages9020031 https://www.mdpi.com/journal/beverages Beverages 2023, 9, 31 2 of 12 refractive index and density of the product, with further calculation of the composition indicators based on a developed mathematical model [3]. However, due to their complexity, the previously reported algorithms and models cannot be the basis for creating a draft guidance document (on methods for determining the volume fraction of ethanol), followed by its metrological certification and introduction into the register of methods of analysis generally accepted for the industry. This publication aims to fill this gap in two ways: 1. Establish patterns of changes in refractometer readings during the fermentation of grape must and develop a way to control the fermentation process by registering changes in Brix refractometer readings; 2. To develop a rapid, non-destructive method for determining the volume fraction of ethanol in liquid homogeneous products of grape winemaking, based on measuring the density and refractive index. This will be conducted using a device suitable for implementation in production conditions (i.e., using standard laboratory equipment that would be available at a winery’s laboratory) and based on a clear algorithm of actions and calculations that ensures sufficient accuracy and unambiguity of the determined result. 2. Materials and Methods 2.1. Materials The material for the study was the white must of Sabash and Muscat grapes harvested 3 3 in 2018 with a sugar content of 150 g/dm to 300 g/dm . A total of 8 wort samples were available. In clarified wort, sulphated to 75 mg/dm , density, mass concentration of sugars and mass fraction of dissolved substances in terms of sucrose were determined by densimetry and refractometry. 2.2. Fermentation Process and Monitoring Fermentation of the samples was carried out using the yeast strain 47-K. After the appearance of signs of fermentation, the fermentation process was monitored at intervals of 2–3 days according to the following indicators: Density—by the areometric method Mass concentration of sugars—by the Bertrand method according to Magwaza and Opara [4] The volume fraction of ethanol—by distillation according to Iland et al. [5] and Gayda et al. [6] Refractive index according to the Brix readings of a URL-1 (LLC “Spektro Lab”, Ukraine) refractometer at a temperature of (20 0.5) C [7] 2.3. Production and Measurements of Model Solutions Model solutions were produced by mixing varying amounts of wine materials of various types and wine distillates and water. The use of model solutions made it possible to obtain sufficient accuracy and unambiguity in determining the volume fraction of ethanol based on refractometry and densimetry data. The model solutions were prepared with a volume fraction of ethanol from 0 to 30% and a total extract concentration from 0 to 3 3 350 g/dm in increments of 3% vol. by volume fraction of ethanol and 10–25 g/dm by extract. In the obtained model solutions, the refractive index (in Brix) was measured by the refractometric method [8], density by the areometric method, and the total extract mass concentration according to Iland et al. [5]. Preliminary metrological certification of the non-destructive express method for determining the volume fraction of ethyl alcohol for wines and wine drinks prepared on the basis of grape winemaking products, based on measuring the density and refractive index of liquid media was carried out according to Taylor [9]. Beverages 2023, 9, 31 3 of 12 2.4. Data Analysis Mathematical processing of experimental data and metrological evaluation of the method were carried out using Microsoft Excel with an analysis package—Visual Basic for Applications (VBA) and a solution search module. The experimental data obtained from the model solutions were processed using two- dimensional interpolation methods by Newton polynomials [10–12] in order to construct a regular, tabulated function of the volume fraction of ethanol depending on the density and the refractometer readings. 3. Results and Discussion 3.1. Background Refractometry can also be used to determine the volume fraction of ethanol in water- alcohol solutions with between 0 and 50% vol. ethanol [13,14]. In the case of ethanol solutions, the volume the solution occupies has a non-linear relationship with its concen- tration; consequently, the density function of water-alcohol solutions also has a non-linear character. In the process of alcoholic fermentation of wort, there is a decrease in the concen- tration of reducing sugars with a concomitant increase in the concentration of ethanol. Two molecules of ethanol and two molecules of carbon dioxide are formed from one hexose molecule. Taking into account the molecular weights of hexose and ethanol, it is therefore theoretically possible to obtain 0.5114 g (0.6479 cm ) of pure ethanol from 1 g of sugar. However, the actual yield of ethanol is always lower than this due to the influence of various factors, principally the formation of fermentation by-products, the entrainment of alcohol with carbon dioxide, and the use of a portion of the sugars in yeast biomass accumulation. A value of 0.6 cm of ethanol formed from 1.0 g of sugars is commonly used in technological calculations [2,15]; this is a normative value, rather than reflecting the actual alcohol output at each current time. If we consider the process simplistically, it can be assumed that for each unit of reduction in the wort sugar concentration, a certain volume of alcohol is formed, which should theoretically lead to a linear change in the refractive index of the wort during fermentation in proportion to the amount of sugar fermented. One of the main components of grape wine and its processing products is endogenous natural ethanol, which is formed during the fermentation of must and pulp, as well as exogenous ethanol, obtained artificially from sugar-containing food raw materials and used in the production of liqueur wines and wine drinks. The certified method (Method OIV-MA-AS312-01A) for determining the concentration of ethanol in the wine industry is distillation of a certain volume of product, followed by determination of the density of the distillate [5]. The use of this method is mandatory in case of disputes with manufacturers or suppliers of products, and is also indispensable for determining the ethanol content in products with a heterogeneous structure, for example, pressing, yeast precipitation, when rationing in winemaking, etc. However, in most cases, the winemaker deals with homogeneous liquid products in the winemaking process, such as wort, wine material, mistelle, etc., all of which have the properties of a true solution. Consequently, it would be beneficial to promptly obtain information about the content of ethanol in these products without conducting an extended analysis. A separate problem is the need to determine the volume fraction of ethanol when the volume of the sample is limited, or the sample is unique and it is undesirable to conduct destructive analysis (e.g., distillation. In this case, instrumental (non-destructive) methods of analyzing the composition of products based on various principles have come to the fore [1,2,16,17]. However, there are some problems of ensuring repeatability, accuracy and reproducibility of the results, as well as questions of compliance between the results obtained and those found using the method for determining the strength of alcohol by volume OIV-MA-AS312-01A [5]. In addition, the use of some techniques such as infrared spectroscopy (IR spectrometry), nuclear magnetic resonance spectroscopy (NMR spectroscopy), and gas and liquid chromatography, is not practical for many winery laboratories, due to the high equipment costs and ongoing operating expenses. Beverages 2023, 9, 31 4 of 12 Refractometry and densimetry—measurement of refractive index and density of matter, are among the oldest methods of analysis of binary mixtures. The combination of refractometric methods with the measurement of other physical properties (density), makes it possible to determine the composition of products and biological objects. Despite the rapid development of analytical equipment, methods for determining the concentration of substances based on the measurement of their density and refractive index are still in demand, due to their simplicity and reliability. The methods of refractometry and densimetry adopted in winemaking and given in Haynes [18], due to the presence of dissolved substances in wine, require certain sample preparation in order to use them in the direct determination of ethanol concentration. Although there are no particular difficulties when measuring the density of the initial wort, during fermentation the wort is largely saturated with carbon dioxide, which causes a number of problems related to the exact determination of its density. These include the presence of gas bubbles in the liquid phase, the adsorption of gas bubbles on the surface of the hydrometer (which can cause an apparent decrease in the density of the liquid), foaming, and interference from suspended material or yeast cells. To neutralize these effects, it is possible to partially degas the sample before determining its density, remove gas bubbles by rotating the hydrometer, or use larger hydrometers. However, these processes can complicate the operational monitoring of the fermentation process. An alternative to the densimetric method for determining the concentration of sugars in the wort before fermentation is the refractometric method [1], which can be applied to samples of around 0.1 mL volume. Studies of the possibilities of refractometry for monitor- ing the fermentation process of wort were conducted by A.S. Vecherom as early as 1958 [19]; however, despite the rather detailed studies conducted, this problem is far from being fully resolved in terms of its application in enochemical practice. According to the concepts un- derlying the refractometric methods of analysis, in ideal systems (formed without changing the volume and polarizability of components), the dependence of the refractive index (n) of the mixture on the composition is close to rectilinear if the composition is expressed in volume fractions (percentages) [16]. This fact underlies refractometric methods for deter- mining dissolved substances in vegetable and fruit processing products [17], as well as assessing the mass concentration of extract and sugars in grape must before fermentation, along with the densimetric method [20]. The volume occupied by a unit of mass of most soluble substances in solution including the substances in grape must, does not depend on its concentration, which explains its linear relationship with the solution density. 3.2. Determination of the Dynamics of Changes in the Readings of the Refractometer Scale during Alcoholic Fermentation From the studies carried out, it was found that in the process of alcoholic fermentation of grape must, the refractometer readings on the Brix scale decreased in proportion to the decrease in its density (Figure 1). Regression analysis performed on the experimental data gave the following empirical formula for expressing the relationship between these values: r = (0.0342 B + 6.049) B + 969.72 + 0.66 B 0.086 B (2) 0 0 0 where r is the wort density, kg/m ; B is the initial (before fermentation) indication of the refractometer reading, B is the refractometer reading during fermentation. At B = B , we obtain an expression for the wort density (kg/m ) before the start of alcoholic fermentation based on the Brix readings of the refractometer: r = 969.72 + 6.709 B 0.05158 B (3) 0 0 0 Beverages 2023, 9, 31 5 of 12 Then for the mass concentration of the extract before fermentation, g/dm , the follow- ing expression can be written: 2 3 969.72 B + 6.709 B 0.05158 B p 10 B 0 0 0 0 0 E = = (4) 1000 100 These expressions (Formulas (2)–(4) for the density and concentration of the extract are determined for B in the range of (10–30) B. Thus, knowing the Brix readings of the re- fractometer before fermentation and, consequently, the sugar content in the initial wort, for example, using special tables given in dos Santos et al. [1] and Pretorius et al. [20], as well as the density of the wort before and during fermentation, calculated by Formulas (2) and (3), respectively, it is possible to control the sugar content according to the indications of the refractometer readings using Formula (1). It should be noted that when measuring the refractive index, the wort sample should be filtered through a syringe filter. Without this, foreign inclusions (suspensions, yeast cells) in the wort can settle on the refractometer prism and blur the boundary between light and Beverages 2023, 9, x FOR PEER REVIEW 5 of 13 shadow when taking readings. It is possible to dispense with pre-filtration of the sample, but in this case, the refractometer prism should be rotated so that foreign particles do not settle on it under the influence of gravity, if technically possible. Figure 1. The relationship between grape must density and Brix readings during the process of Figure 1. The relationship between grape must density and Brix readings during the process of al- coholic fermentation for alcoholic fermentation diff for erent initia different l su initial gar content in sugar content the muin st.the must. Regression analysis performed on the experimental data gave the following empiri- Thus, as a result of control in the process of fermentation of grape must, the degree of cal formula for expressing the relationship between these values: fermentation of sugars, the values of the coefficients of the yield of alcohol from a unit of fermented sugars (cm /g) were determined by the refractometric method. These data are r = (0.0342 × B0 + 6.049) × B + 969.72 + 0.66 × B0 − 0.086 × B0 (2) presented in Figure 2. where r is the wort density, kg/m ; B0 is the initial (before fermentation) indication of the At the first stage of fermentation, the alcohol yield coefficient increases to a certain refractometer reading, B is the refractometer reading during fermentation. local maximum of 0.6, then decreases slightly and increases again towards the end of At B = B0, we obtain an expression for the wort density (kg/m ) before the start of fermentation. This change in the alcohol yield coefficient is a cumulative characteristic, since alcoholic fermentation based on the Brix readings of the refractometer: it summarizes the yield that was obtained at the previous stages of the fermentation process. r0 = 969.72 + 6.709 × B0 − 0.05158 × B0 (3) To achieve a value of 0.6 and higher (see, for example, the curve at the initial sugar concentration of 264 g/dm in Figure 2) with an amount of fermented sugars between Then for the mass concentration of the extract before fermentation, g/dm , the follow- 50–100 g/dm , the rate of ethanol formation in the fermentation interval of grape must sug- ing expression can be writt en: ars from 30–50 g/dm should significantly exceed the rate of sugar assimilation (Figure 2). 𝑝 × 10 ×𝐵 969.72 × 𝐵 + 6.709 × 𝐵 − 0.05158 × 𝐵 (4) The accumulation 𝐸 = of ethanol =is caused by the consumption of metabolites accumulated by 1000 100 yeast cells, following the well-documented biochemical processes in the cell. These expressions (Formulae (2)–(4) for the density and concentration of the extract are determined for B0 in the range of (10–30) °B. Thus, knowing the Brix readings of the refractometer before fermentation and, consequently, the sugar content in the initial wort, for example, using special tables given in dos Santos et al. [1] and Pretorius et al. [20], as well as the density of the wort before and during fermentation, calculated by Formulae (3) and (2), respectively, it is possible to control the sugar content according to the indications of the refractometer readings using Formula (1). It should be noted that when measuring the refractive index, the wort sample should be filtered through a syringe filter. Without this, foreign inclusions (suspensions, yeast cells) in the wort can sett le on the refractometer prism and blur the boundary between light and shadow when taking readings. It is possible to dispense with pre-filtration of the sample, but in this case, the refractometer prism should be rotated so that foreign particles do not sett le on it under the influence of gravity, if technically possible. Thus, as a result of control in the process of fermentation of grape must, the degree of fermentation of sugars, the values of the coefficients of the yield of alcohol from a unit Beverages 2023, 9, x FOR PEER REVIEW 6 of 13 of fermented sugars (cm /g) were determined by the refractometric method. These data Beverages 2023, 9, 31 6 of 12 are presented in Figure 2. Figure 2. The change in the alcohol yield ratio from a unit of sugars depending on the amount of Figure 2. The change in the alcohol yield ratio from a unit of sugars depending on the amount of fermented sugars for musts with varying initial sugar concentrations. fermented sugars for musts with varying initial sugar concentrations. The analysis of experimental data also showed that, despite the significantly smaller At the first stage of fermentation, the alcohol yield coefficient increases to a certain amount of alcohol formed at the first stage of fermentation, the decrease in density was local maximum of 0.6, then decreases slightly and increases again towards the end of fer- proportional to the decrease in the mass concentration of sugars determined according to mentation. This change in the alcohol yield coefficient is a cumulative characteristic, since Magwaza and Opara [4]. Furthermore, the increments were equal in the middle and at the it summarizes the yield that was obtained at the previous stages of the fermentation pro- end of fermentation, which indicates that the nature of the resulting fermentation products cess. at the stage of the fermentation and accumulation of yeast biomass is somewhat different To achieve a value of 0.6 and higher (see, for example, the curve at the initial sugar than in the middle and end of fermentation. It also suggests that these fermentation concentration of 264 g/dm in Figure 2) with an amount of fermented sugars between 50– products do not contribute to the change in the distillation density when determining the 100 g/dm , the rate of ethanol formation in the fermentation interval of grape must sugars volume fraction of ethanol according to Iland et al. [5]. from 3 The 0–5average 0 g/dm sho value uldand signi 95% ficaconfidence ntly exceed the interval rate for of sug theayield r assimi of la alcohol tion (Ffr igom ure 2) the . Th unit e accum mass of ulation sugars of ethano in the prl is ocess caused by t of alcoholic he consumption of fermentation of clarified metabo wort lites using accum yeast ulated by strain y 47-K, east cell obtained s, followi onn the g the w basisel of l-d pr ocu ocessing mented bi experimental ochemical processes data, is given in the cell in Table . 1. The analy In the processing sis of experimen of grape tal d wines, ata also show there may ed that, d be a need espite the sig to calculatenthe ificant Brix ly sm readings aller amount of alcohol formed at the of the refractometer, when a certain first st mass agconcentration e of fermentati of on, the decrease i sugars is reached, n densi for example, ty was in order to prepare wines with an interrupted process of alcoholic fermentation (table proportional to the decrease in the mass concentration of sugars determined according to semi-dry, semi-sweet, as well as liqueur wines). Magwaza and Opara [4]. Furthermore, the increments were equal in the middle and at the end of fermentation, which indicates that the nature of the resulting fermentation prod- Table 1. The dependence of the alcohol yield ratio on the amount of fermented sugars for grape must ucts at the stage of the fermentation and accumulation of yeast biomass is somewhat dif- with an initial mass concentration of sugars between 160–270 g/dm . ferent than in the middle and end of fermentation. It also suggests that these fermentation products do not contribute to the change in the distillation density when determining the Alcohol Yield Coefficient, cm /g (Mean 95% Amount of Discarded Sugars, g/dm volume fraction of ethanol according to Iland et al. [5]. Confidence Interval) The average value and 95% confidence interval for the yield of alcohol from the unit 30 0.40 0.12 mass of sugars in the process of alcoholic fermentation of clarified wort using yeast strain 50 0.54 0.10 47-K, obtained on the basis of processing experimental data, is given in Table 1. 80 0.58 0.04 150 0.56 0.03 >200 0.60 0.01 Analysis of the structure of Formula (2) showed that it can be represented as a linear function of the form: r = Kx(B ) B + Lx(B ) (5) 0 0 Beverages 2023, 9, 31 7 of 12 i.e., for a given initial value of B , the density dependence on the Brix readings of the refractometer is linear. On the other hand, there is a linear relationship between the decrease in wort density during fermentation and the mass concentration of fermented sugars according to Formula (1). Based on this, we can write: p p B B 0 0 = (6) 0.453 X where X is the change in the refractometer readings with a decrease in the mass concentra- tion of sugars by 1 g/dm . Then, for the mass concentration of sugars (extract) during fermentation, we can write: B B 1 C = C =C (B B ) (7) 0 0 0 X(B ) X(B ) 0 0 where C and C are the mass concentration of sugars (extract) during fermentation and before fermentation, respectively (in gdm ); B and B are the Brix readings of the refrac- tometer before and during fermentation (in Brix); and 1/X(B ) is the proportionality coefficient between the decrease in the mass concentration of sugars and the change in the refractometer readings. 3.3. Example Calculation We will now demonstrate the obtained regularities for technological calculations. As one example, the initial Brix reading for a particular wort was 25.2 Brix (25.2% by weight). After stopping fermentation by chilling, followed by filtration, the refractometer reading was 10 Brix. From this, we can determine the concentration of the total extract and sugars before fermentation, after stopping fermentation, and the amount of ethanol formed. We determine the concentration of the extract E before fermentation according to the Formula (4). 2 3 969.72 25.2 + 6.709 25.2 0.05158 25.2 E = 278 g/dm (8) The mass concentration of sugars in the wort before fermentation is determined from Table 2, which will be 252 g/dm . The concentration of the total extract and sugars is determined from the Formula (7), which for our case, at = 15.56 (Table 2), has the form for the mass concentration of extract: E = 278.7 (25.2 10) 15.56 = 278.7 236.5 = 42.2 g/dm (9) And the mass concentration of sugars: C = 252 (25.2 10) 15.56 = 252 236.5 = 15.5 g/dm (10) The alcohol concentration, taking into account the variability of the alcohol yield coefficient from the sugar unit, will be: (C C) 0.6 = (252 15.5) (0.06 + 0.001) = (14.2 + 0.3) = 14.5 % vol. (11) 0 Beverages 2023, 9, 31 8 of 12 Table 2. The dependence of the initial mass concentration of sugars in the grape must (C ) and the value of the coefficient (B ) on the initial mass fraction of dry substances in the grape must B . 0 0 B C B C B C 0 0 0 0 0 0 10.0 82 14.16 16.8 155 14.76 23.6 233 15.41 10.2 84 14.17 17.0 158 14.78 23.8 235 15.43 10.4 86 14.19 17.2 160 14.80 24.0 238 15.44 10.6 88 14.21 17.4 162 14.81 24.2 240 15.46 10.8 90 14.23 17.6 164 14.83 24.4 242 15.48 11.0 92 14.24 17.8 167 14.85 24.6 245 15.50 11.2 94 14.26 18.0 169 14.87 24.8 247 15.52 11.4 97 14.28 18.2 171 14.89 25.0 249 15.54 11.6 99 14.29 18.4 173 14.91 25.2 252 15.56 11.8 101 14.31 18.6 176 14.93 25.4 254 15.58 12.0 103 14.33 18.8 178 14.94 25.6 256 15.60 12.2 105 14.35 19.0 180 14.96 25.8 259 15.62 12.4 107 14.36 19.2 182 14.98 26.0 261 15.64 12.6 109 14.38 19.4 185 15.00 26.2 263 15.66 12.8 112 14.40 19.6 187 15.02 26.4 266 15.68 13.0 114 14.42 19.8 189 15.04 26.6 268 15.71 13.2 116 14.43 20.0 192 15.06 26.8 270 15.73 13.4 118 14.45 20.2 194 15.08 27.0 273 15.75 13.6 120 14.47 20.4 196 15.10 27.2 275 15.77 13.8 122 14.49 20.6 198 15.11 27.4 277 15.79 14.0 125 14.51 20.8 201 15.13 27.6 280 15.81 14.2 127 14.52 21.0 203 15.15 27.8 282 15.83 14.4 129 14.54 21.2 205 15.17 28.0 284 15.85 14.6 131 14.56 21.4 208 15.19 28.2 287 15.87 14.8 133 14.58 21.6 210 15.21 28.4 289 15.89 15.0 135 14.59 21.8 212 15.23 28.6 292 15.91 15.2 138 14.61 22.0 215 15.25 28.8 294 15.93 15.4 140 14.63 22.2 217 15.27 29.0 296 15.95 15.6 142 14.65 22.4 219 15.29 29.2 299 15.97 15.8 144 14.67 22.6 221 15.31 29.4 301 15.99 16.0 147 14.69 22.8 224 15.33 29.6 303 16.01 16.2 149 14.70 23.0 226 15.35 29.8 306 16.03 16.4 151 14.72 23.2 228 15.37 30.0 308 16.06 16.6 153 14.74 23.4 231 15.39 3.4. Determination of the Volume Fraction of Ethanol As another outcome of the experimental work, calculated values of the volume fraction of ethanol were obtained depending on the density of the product in the range of 970 kg/m 3 3 to 1130 kg/m in increments of 10 kg/m and the Brix readings of the refractometer in the range from 4.0 to 31.0% by weight, in increments of 1.0. The results of these studies are shown in Table 3. The dashes in the table show cells with a negative value for the volume fraction of ethanol or for the mass concentration of the extract, which are devoid of physical meaning. We have established the relationship between the mass concentration of the extract and the mass concentration of sugars in the wort. This allowed us to apply our approaches to determining the mass concentration of the total extract by the refracto–densimetric method to assess the mass concentration of residual sugars and the volume fraction of ethanol. Based on mathematical modeling of the composition (volume fraction of ethanol and mass concentration of sugars as part of the extract) and physical properties (refractive index and density) of the wort, tabular functions of the values of the volume fraction of ethyl alcohol in the fermenting wort on the density and readings of the sugar scale of the refractometer were developed. The results of these studies are shown in Table 3 and Figure 3. Beverages 2023, 9, 31 9 of 12 Table 3. The volume fraction of ethanol depending on the density of the product r and the Brix readings of the refractometer B at 20 C. Density, kg/m B, % 970 980 990 1000 1010 1020 1030 1040 1050 1060 1070 1080 1090 1100 1110 1120 1130 mass 4.0 - 12.48 8.79 5.11 1.43 2.25 - - - - - - - - - - - 5.0 - 13.96 10.27 6.59 2.91 0.77 - - - - - - - - - - - 6.0 - 15.44 11.75 8.07 4.39 0.71 2.96 - - - - - - - - - - 7.0 20.61 16.92 13.23 9.55 5.87 2.19 1.48 - - - - - - - - - - 8.0 22.09 18.40 14.71 11.03 7.35 3.67 0.00 - - - - - - - - - - 9.0 23.56 19.88 16.19 12.51 8.83 5.15 1.48 2.19 - - - - - - - - - 10.0 25.04 21.35 17.67 13.98 10.31 6.63 2.96 0.71 - - - - - - - - - 11.0 26.61 22.92 19.24 15.56 11.88 8.20 4.53 0.86 2.81 - - - - - - - - 12.0 28.08 24.40 20.71 17.03 13.36 9.68 6.01 2.34 1.33 - - - - - - - - 13.0 29.65 25.97 22.28 18.60 14.93 11.25 7.58 3.91 0.24 - - - - - - - - 14.0 31.22 27.54 23.85 20.17 16.50 12.82 9.15 5.48 1.82 1.85 - - - - - - - 15.0 32 29.10 25.42 21.74 18.07 14.39 10.72 7.05 3.39 0.28 - - - - - - - 16.0 - 30.67 26.99 23.31 19.04 15.96 12.29 8.62 4.96 1.29 2.37 - - - - - - 17.0 - 32.23 28.55 24.88 21.20 17.53 13.86 10.19 6.53 2.86 0.80 - - - - - - 18.0 - - 30.12 26.44 22.77 19.10 15.43 11.76 8.09 4.43 0.77 2.89 - - - - - 19.0 - - 31.78 28.10 24.43 20.76 17.09 13.42 9.76 6.10 2.44 1.22 - - - - - 20.0 - - - 29.66 25.99 22.32 18.65 14.99 11.32 7.66 4.00 0.34 3.31 - - - - 21.0 - - - 31.32 27.65 23.98 20.31 16.65 12.98 9.32 5.66 2.01 1.65 - - - - 22.0 - - - 32.98 29.31 25.64 21.97 18.31 14.64 10.98 7.32 3.67 0.01 - - - - 23.0 - - - - 30.96 27.29 23.63 19.96 16.30 12.64 8.98 5.33 1.67 - - - - 24.0 - - - - 32.61 28.95 25.28 21.62 17.96 14.30 10.64 6.99 3.33 0.32 - - - 25.0 - - - - - 30.60 26.94 23.27 19.61 15.95 12.30 8.64 4.99 1.34 2.31 - - 26.0 - - - - - 32.25 28.59 24.93 21.27 17.61 13.95 10.30 6.65 2.99 0.65 - - 27.0 - - - - - - 30.29 26.62 22.97 19.31 15.65 12.00 8.35 4.70 1.05 - - 28.0 - - - - - - 31.98 28.32 24.66 21.01 17.35 13.70 10.05 6.40 2.75 0.90 - 29.0 - - - - - - - 30.07 26.41 22.75 19.10 15.45 11.80 8.15 4.50 0.85 2.79 30.0 - - - - - - - 31.81 28.15 24.50 20.84 17.19 13.54 9.89 6.25 2.60 1.04 31.0 - - - - - - - - 29.89 26.24 22.59 18.94 15.29 11.64 7.99 4.35 0.70 To calculate the intermediate data of the table, it is advisable to use a bilinear interpo- lation formula for a function given in equidistant nodes, which has the form: F(p,B) = b + b (p p ) + b (B B ) + b (p p ) (B B ) (12) 1 2 0 3 0 4 0 0 where: b = , 1 00 b = ( )/(p p ), 2 10 00 1 0 b = ( )/(B B ), 3 01 00 1 0 b = ( + )/(p p ) (B B ) 4 00 10 01 11 1 0 1 0 Thus, in order to find the volume fraction of ethanol by the density of the product and the Brix readings of the refractometer, it is necessary to measure the density of the product and take refractometer readings of the product at 20 C, and then use Formula (12), in combination with the data from Table 3. 3.5. Example Calculation Let us illustrate this with a practical example (Table 4). Table 4. The data position in Table 3 for calculating alcohol according to Formula (12) (practical example). P = 990 P = 1000 0 1 . . . . . . . . . . . . . . . B = 7.0 . . . = 18.60 = 14.93 . . . 0 00 10 B = 8.0 . . . = 20.17 = 16.50 . . . 0 01 11 . . . . . . . . . . . . . . . Beverages 2023, 9, 31 10 of 12 To calculate the coefficients b , b , b and b : 1 2 3 4 b = = 18.6 1 00 a a 14.93 18.6 10 00 b = = = 0.367 p p 1010 1000 1 0 a a 20.17 18.6 01 00 b = = = 1.57 B B 14 13 1 0 a a a a 18.6 14.93 20.17+16.5 00 10 01 11 b = = = 0.0 (p p )(B B ) (1010 1000)(14 13) 1 0 1 0 The numerical values of the coefficients b , b , b , b are substituted in, as well as the 1 2 3 4 experimentally obtained values of the density p and the Brix readings of the refractometer B. From Formula (12), the desired value of the volume fraction of ethanol can then be calculated: F(p,B) = b + b (p p ) + b (B B ) + b (p p ) (B B ) Beverages 2023, 9, x FOR PEER REVIEW 10 of 13 1 2 0 3 0 4 0 0 = 18.6 + 0.367 (1004.5 1000) + 1.57 (13.8 13.0) (13) = 18.2045% vol. refractometer were developed. The results of these studies are shown in Table 3 and Figure A plot of two variables C and density from Table 3 with bivariate and univariate graphs is shown in Figure 3. Figure 3. The volume fraction of ethanol depending on the density (kg/m ) of the product p and the Figure 3. The volume fraction of ethanol depending on the density (kg/m ) of the product p and the Brix readings of the refractometer B at 20 °C. Brix readings of the refractometer B at 20 C. The To ca boxplot lculate t (or he i box-and-whisker ntermediate dataplot) of the ta shows ble, the it isdistribution advisable toof usthe e a bi quantitative linear inter- data C and density from Table 3 in a way that facilitates comparisons between variables or polation formula for a function given in equidistant nodes, which has the form: between levels of a variable (Figure 4). The box shows the quartiles of the dataset, with the F(p,B) = b1 + b2 × (p − p0) + b3 × (B − B0) + b4 × (p − p0) × (B − B0) (12) whiskers expanding to show the rest of the distribution. As a result of the work done, about 30 samples of wine products with a volume where: fraction of ethyl alcohol in the range of 0–20% vol. were measured. An experimentally b1 = α00, conducted verification of the conformity of the volume fraction of ethanol obtained by the b2 = (α10 − α00)/(p1 − p0), proposed method in comparison with the method of determination certified in winemaking b3 = (α01 − α00)/(B1 − B0), according to Iland et al. [5] showed that in 95% of cases the discrepancy between the b4 = (α00 − α10 − α01 + α11)/(p1 − p0) × (B1 − B0) methods does not exceed 0.1% vol. in the case of using a pycnometric method or a glass Thus, in order to find the volume fraction of ethanol by the density of the product alcohol meter type ASP-1 for measuring density, followed by finding the desired densities and the Brix readings of the refractometer, it is necessary to measure the density of the according to the density table of water-alcohol solutions [6]. The use of general-purpose product and take refractometer readings of the product at 20 °C, and then use Formula (12), in combination with the data from Table 3. 3.5. Example Calculation Let us illustrate this with a practical example (Table 4). Table 4. The data position in Table 3 for calculating alcohol according to Formula (12) (practical example). P0 = 990 P1 = 1000 … … … … … B0 = 7.0 … α00 = 18.60 α10 = 14.93 … B0 = 8.0 … α01 = 20.17 α11 = 16.50 … … … … … … Beverages 2023, 9, 31 11 of 12 hydrometers of the AON-2 type increases the discrepancy between the methods to 0.3% vol. The use of a glass alcohol meter is especially important for determining the density of table wines with a completed cycle of alcoholic fermentation, the density of which is usually lower than the density of water. Figure 4. The box-and-whisker plot of the distribution of quantitative C data and density for comparison between variables or between levels of a variable. The bar colours are a visual aid for distinguishing between different densities. 4. Conclusions As a result of this study, we can conclude that the decrease in the Brix readings of the refractometer during alcoholic fermentation of grape wort is proportional to the amount of fermented reducing sugars defined according to Magwaza and Opara [4], with increments that depend on the initial content of extractives before fermentation. Hence refractometry can be used to monitor the ethanol concentration as an alternative to the densimetric method. An experimental verification of the compliance of the value of the volume fraction of ethyl alcohol obtained by the proposed method in comparison with the method certified in winemaking showed that in 95% of cases the discrepancy between the methods does not exceed 0.1% vol. in the case of using the pycnometric method or the readings of a glass alcohol meter to measure the density, followed by finding the desired density according to the density table of water-alcohol solutions. From the experimental results, a rapid, non-destructive method was presented for determining the volume fraction of ethanol in liquid wine products the technological process and in finished products. The method can be the basis for the development of an appropriate regulatory document regulating its use in the wine industry, as well as for the development of a technical specification for the creation of a portable device for determining the concentration of ethanol in wine products, based on the simultaneous measurement of density and refractive index of liquid media. Beverages 2023, 9, 31 12 of 12 Author Contributions: Conceptualization, R.T.; Methodology, V.K.; Validation, J.B.J. and V.K.; Formal Analysis, R.T., J.B.J. and G.R.; Investigation, V.K.; Resources, A.K.; Data Curation, R.T. and A.K.; Writing—Original Draft Preparation, J.B.J., R.T. and D.N.; Writing—Review and Editing J.B.J., A.K. and E.B.; Project Administration Y.P. and V.K.; Funding Acquisition Y.P. All authors have read and agreed to the published version of the manuscript. Funding: This research received no external funding. Data Availability Statement: The full datasets are available from the corresponding author upon request. Acknowledgments: We thank our colleagues for their support of this project. Conflicts of Interest: The authors declare no conflict of interest. References 1. dos Santos, C.A.T.; Páscoa, R.N.M.J.; Lopes, J.A. A review on the application of vibrational spectroscopy in the wine industry: From soil to bottle. TrAC Trends Anal. Chem. 2017, 88, 100–118. [CrossRef] 2. Debebe, A.; Redi-Abshiro, M.; Chandravanshi, B.S. Non-destructive determination of ethanol levels in fermented alcoholic beverages using Fourier transform mid-infrared spectroscopy. Chem. Cent. J. 2017, 11, 27. [CrossRef] [PubMed] 3. Green, D.W.; Southard, M.Z. Perry’s Chemical Engineers’ Handbook; McGraw-Hill Education: New York, NY, USA, 2019. 4. Magwaza, L.S.; Opara, U.L. 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Introduction to Error Analysis, the Study of Uncertainties in Physical Measurements; University Science Books: Sausalito, CA, USA, 1997. 10. Cozzolino, D.; Cynkar, W.; Shah, N.; Dambergs, R.; Smith, P. A brief introduction to multivariate methods in grape and wine analysis. Int. J. Wine Res. 2009, 1, 123–130. [CrossRef] 11. Khodasevich, M.; Scorbanov, E.; Rogovaya, M. Application of multivariate analysis of broadband transmission spectra for calibration of physico-chemical parameters of wines. Devices Methods Meas. 2019, 10, 198–206. [CrossRef] 12. Timofeev, R. Refractodensimetric method for determining the volume fraction of ethyl alcohol in wines and winy beverages. Proc. Voronezh State Univ. Eng. Technol. 2020, 82, 104–109. [CrossRef] 13. Noiseux, I.; Long, W.; Cournoyer, A.; Vernon, M. Simple fiber-optic-based sensors for process monitoring: An application in wine quality control monitoring. Appl. Spectrosc. 2004, 58, 1010–1019. [CrossRef] [PubMed] 14. Cai, C.; Miles, R.E.H.; Cotterell, M.I.; Marsh, A.; Rovelli, G.; Rickards, A.M.J.; Zhang, Y.-H.; Reid, J.P. Comparison of Methods for Predicting the Compositional Dependence of the Density and Refractive Index of Organic-Aqueous Aerosols. J. Phys. Chem. A 2016, 120, 6604–6617. [CrossRef] [PubMed] 15. Martens, M.; Hadrich, M.J.; Nestler, F.; Ouda, M.; Schaadt, A. Combination of Refractometry and Densimetry—A Promising Option for Fast Raw Methanol Analysis. Chem. Ing. Tech. 2020, 92, 1474–1481. [CrossRef] 16. Regmi, U.; Rai, K.P.; Palma, M. Determination of organic acids in wine and spirit drinks by fourier transform infrared (FT-IR) spectroscopy. J. Food Sci. Technol. Nepal 2012, 7, 36–43. [CrossRef] 17. Fu, Q.; Wang, J.; Lin, G.; Suo, H.; Zhao, C. Short-wave near-infrared spectrometer for alcohol determination and temperature correction. J. Anal. Methods Chem. 2012, 2012, 1–7. [CrossRef] [PubMed] 18. Haynes, W.M. CRC Handbook of Chemistry and Physics; CRC Press: Boca Raton, FL, USA, 2016. 19. Peng, B.; Ge, N.; Cui, L.; Zhao, H. Monitoring of alcohol strength and titratable acidity of apple wine during fermentation using near-infrared spectroscopy. LWT-Food Sci. Technol. 2016, 66, 86–92. [CrossRef] 20. Pretorius, F.; Focke, W.W.; Androsch, R.; du Toit, E. Estimating binary liquid composition from density and refractive index measurements: A comprehensive review of mixing rules. J. Mol. Liq. 2021, 332, 115893. [CrossRef] Disclaimer/Publisher’s Note: The statements, opinions and data contained in all publications are solely those of the individual author(s) and contributor(s) and not of MDPI and/or the editor(s). MDPI and/or the editor(s) disclaim responsibility for any injury to people or property resulting from any ideas, methods, instructions or products referred to in the content.
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