- Email: [email protected]
Concentration control in alcoholic fermentation processes from ultrasonic velocity measurements
Food Research International 37 (2004) 587–594 www.elsevier.com/locate/foodres
Concentration control in alcoholic fermentation processes from ultrasonic velocity measurements Pablo Resa *, Luis Elvira, Francisco Montero de Espinosa Instituto de Acustica (CSIC), Serrano 144, 28006 Madrid, Spain Received 25 August 2003; accepted 3 December 2003
Abstract A study of the alcoholic fermentation of several carbohydrate aqueous solutions, using an ultrasonic velocity measurement technique, is presented in this paper. It is shown that the changes occurring during the course of an alcoholic fermentation can be monitored on-line by measuring the velocity of an elastic wave propagating through the fermenting medium. During the alcoholic fermentation, carbohydrates are transformed into ethanol and carbon dioxide by the action of the yeast’s metabolism. In this work, measurements of the ultrasonic velocities and densities of the binary mixtures glucose–water, fructose–water, saccharose–water and ethanol–water were carried out. These experimental results – due to the inaccuracy of the theoretical approaches – have been satisfactorily utilised to determine the concentrations of the main components during the glucose and fructose fermentation, induced by Saccharomyces cerevisiae yeasts, and to analyse the saccharose fermentation. Ó 2004 Elsevier Ltd. All rights reserved. Keywords: Alcoholic fermentation; Density; Ultrasonic velocity; Concentration; On-line control
1. Introduction Ultrasonic based devices have being applied to control many industrial processes for a number of decades. Nowadays, these technologies are emerging as wellsuited methods to monitor food processes, fulfilling important quality requirements of non-invasiveness, non-destructiveness and easy automation (McClements, 1997; Povey & Mason, 1998). Therefore, a good knowledge of the ultrasonic wave propagation through foods is required. From the acoustical point of view, food materials are often complex media and relations between elastic and quality properties remain unknown in many cases. An ultrasonic study of the alcoholic fermentation in liquid media is presented in this paper. This process is of great importance in the elaboration of alcoholic drinks like wine or beer, but also for drug synthesis. The evolution of the fermentation reaction is usually supervised *
Corresponding author. Tel.: +34-91-561-88-06; fax: +34-91-411-76-
51. E-mail address: [email protected] (P. Resa). 0963-9969/$ - see front matter Ó 2004 Elsevier Ltd. All rights reserved. doi:10.1016/j.foodres.2003.12.012
by measuring the liquid density. Nevertheless, this kind of control is not easily achieved by a non-invasive and on-line technique. Winder, Aulik, and Rice (1970) proposed an ultrasonic method to determine alcohol and extract content in wines. They used a resonant cell to analyse these parameters. Although they did not study the fermentation process itself, an empirical relation between ultrasonic parameters and the concentrations of alcohol and soluble solids was proposed indicating that these concentrations mainly determine the speed of sound in fermenting media. Recently, Becker, Mitzscherling, and Delgado (2001, 2002) have used an ultrasonic technique to determine the density during beer fermentation. They discarded the possibility of obtaining a theoretical relation between density and ultrasonic propagation velocity, being aware of the lack of a representative model for liquid mixtures and solutions. This paper focuses on the relations between both the density and the ultrasonic velocity with the concentrations of the main components in fermenting liquids. Three different water–carbohydrate mixtures were tested (glucose, fructose and saccharose). Saccharomyces ce-
588
P. Resa et al. / Food Research International 37 (2004) 587–594
revisiae, contained in baker’s compressed yeast, was used to provoke the fermentations. Densities and ultrasonic velocities were measured in the binary mixtures of water–carbohydrate and water– ethanol, and in the fermenting media. These media are mostly constituted by a complex mixture of carbohydrates, ethanol, carbon dioxide, yeast and water. Some of the most relevant theories describing ultrasonic propagation through liquid mixtures were revised and compared to the experimental data. The possibility of theoretically correlating density and ultrasonic velocity to the concentrations of the main components is reported.
2. Theory 2.1. Theoretical models The speed, c, of an elastic wave propagating through a pure liquid is given by the equation sffiffiffiffiffiffi 1 c¼ ; ð1Þ qj where q is the density and j is the adiabatic compressibility. Nevertheless, in the case of a mixture of liquids, a general equation to get the density and the compressibility as a function of the properties of the pure components does not exist. The same occurs when a solid substance is dissolved in a liquid. Probably, one of the most widespread models for the study of liquid suspensions is that developed by Urick (1947). He applied Eq. (1), considering a linear dependence of the density, q, and the adiabatic compressibility, j, with the volume concentration, / X q¼ /i qi ; ð2Þ
An empirical relation between sound velocity and molecular volume, valid for unassociated liquids, was established by Rao pffiffiffi ð6Þ V 3 c ¼ R const:; where V is the molecular volume. Nomoto calculated this expression in a large number of mixtures of various kinds (Sette, 1961). He found that R has a linear form in many systems !3 X 1=3 c¼ / i ci : ð7Þ i
However, in the case of polar liquid mixtures, where bonds between the molecules of different components appear, the predictions of these theories become unbefitting. Research papers about ultrasonic propagation velocity in these kinds of liquids can be found in the literature (Burton, 1948; Giacomini, 1947; Parshad, 1949; Sette, 1961). Ethanol–water mixtures show these molecular associations, which make the models unsuccessful, as it is clearly shown in Figs. 1 and 2, where density and velocity are plotted as a function of the ethanol concentration. These experimental data agree with the values found in the literature for the density (Lide, 2002–2003) and earlier velocity measurements obtained by Giacomini (1947), Burton (1948) and Parshad (1949). Great discrepancies between theoretical models and experimental data exist even at the lowest ethanol concentrations. Therefore, none of these approaches can be applied to determine the ultrasonic propagation in a fermenting liquid, where both ethanol and water are present. Others theoretical models lead to similar results (Douheret, Davis, Reis, & Blandamer, 2001; NutschKuhnkies, 1965).
i
j¼
X
/i ji ;
ð3Þ
i
1 c ¼ qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi P P ffi : i /i ji i /i qi
ð4Þ
Moreover, Natta and Baccaredda assumed that the time needed for a mechanical pulse to pass through a mixture is the sum of the times which would be required to pass successively through two layers, each formed by one of the two components and having thickness proportional to the relative volume concentration (Sette, 1961). This gives the following equation: !1 X/ i : ð5Þ c¼ ci i
Fig. 1. Density of the water–ethanol mixture at T ¼ 30 °C. Squares are experimental values and dash line was obtained from Eq. (2).
P. Resa et al. / Food Research International 37 (2004) 587–594
589
which means that the sound speed in the fermenting liquid is considered as the sum of the initial velocity and the speed increments due to the concentration changes of hexoses and ethanol. The advantage of this approach is that these increments can be obtained from the experimental measurements of the ultrasonic velocity in the binary mixture water–hexose and in the binary mixture water– ethanol. A parallel procedure can be applied to obtain density qðXh ; Xe Þ q0 þ Dqh ðXh Þ þ Dqe ðXe Þ:
Fig. 2. Ultrasonic velocity in the water–ethanol mixture at T ¼ 30 °C. Squares are experimental values and lines were obtained from the theoretical approaches: Urick (dash line), Nomoto (dash dot line) and Natta–Baccaredda (dot line).
2.2. Semi-empirical model In this work, it is considered that the velocity variation during the alcoholic fermentation is mainly due to the carbohydrate reduction and to the formation of ethanol molecules. The presence of yeasts seems to play a minor role in the ultrasonic velocity propagation as it was pointed out by Becker et al. (2001). To avoid carbon dioxide bubble interferences, a high frequency was chosen and slow reactions were induced, allowing the gas to exit out of the fermenting liquid by means of molecular diffusion and small bubbles. The sensitivity of ultrasonic velocity to diluted carbon dioxide was measured in distilled water at 30 °C and it was estimated to be smaller than +0.3 m/s for a carbon dioxide partial pressure of 1 atm. Under the experimental conditions of this work, carbon dioxide interferences have been considered negligible. Therefore, using a two variable Taylor expansion, the sound speed in the fermenting liquid can be written as oc oc ðXh Xh0 Þ þ Xe oXh oXe 2 1 o2 c 2 o2 c Xh Xh0 þ X 2 2 oXe2 e oXh o2 c ðXh Xh0 ÞXe þ oXh oXe
cðXh ; Xe Þ c0 þ þ
1 2
þ
1 2
ð8Þ
where c0 is the velocity at the beginning of the fermentation, X stands for the molar concentration and subscripts h and e refer to hexoses (glucose or fructose) and ethanol, respectively. For low ethanol concentrations, the interaction between carbohydrates and ethanol molecules can be discarded and crossed terms are eliminated in Eq. (8). With this assumption, the velocity can be calculated by cðXh ; Xe Þ c0 þ Dch ðXh Þ þ Dce ðXe Þ;
ð9Þ
ð10Þ
Relations between molar fractions (or mass concentrations) of the different components can be deduced from the fermentation reaction Zymase
C6 H12 O6 ! 2C2 H6 O þ 2CO"2 :
ð11Þ
Thereby, the relations between molar concentrations are Xe ¼ 2ðXh0 Xh Þ;
ð12Þ
Xs ¼ 1 Xe X h ;
ð13Þ
where superscript 0 refers to the beginning of the fermentation and subscript s refers to the solvent. The mass concentration, wi , of the ‘‘i’’ component is given by wi ¼
M i Xi ; M s Xs þ M h Xh þ M e Xe
ð14Þ
where M represents the molecular mass.
3. Materials and methods Two different types of experimental analysis were carried out: the measurement of the density and ultrasonic velocity as a function of mass concentration in the water–ethanol and water–carbohydrate binary mixtures, and the measurement of the density and ultrasonic velocity as a function of time during the carbohydrate solution fermentations. Distilled water, ethanol (purity >99.5%), glucose (purity >99.7%), fructose (purity >98.0%) and saccharose (purity >99.7%) were used to make the binary mixtures. Mass concentration, w, was measured using a digital Sartorius 1216 MP balance with a 0.1 g precision. Densities, q, were measured with an Anton Paar DMA 35 vibrating tube densimeter, whose resolution was 1 kg/m3 . The experimental set-up for the sound velocity measurements is shown in Fig. 3. The solutions were contained inside a glass bottle, with 64 mm inner diameter, and immersed in a circulating thermostated water bath to keep the temperature of the solution constant at 30 °C, with variations of the order of 0.01 °C. To ensure their homogeneity, the mixtures were constantly stirred with a magnetic agitator.
590
P. Resa et al. / Food Research International 37 (2004) 587–594
The ultrasonic velocity, c, in the medium can be calculated by dividing the distance by the time of flight
GPIB PC
c¼
PULSE GENERATOR
OSCILLOSCOPE
TRIGG
TEMPERATURE CONTROLLER CO2 DENSITY WATER BATH 30˚C
EXPERIMENTAL CELL
TRANSDUCER
MAGNETIC STIRRER
Fig. 3. Experimental set-up for the on-line measurement of the ultrasonic velocity and the off-line measurement of density.
The ultrasonic velocities were measured (on-line) using a tone-burst pulse through-transmission technique. Transducers were attached face to face at the sides of the glass bottle and coupled to it with a silicone layer. The emitting and receiving transducers were identically made of a PZT 5A piezoelectric ceramic, 20 mm diameter, bonded to a Plexiglas plate. Araldite D was used as backing. The emitting transducer was excited at its resonant frequency, f0 ¼ 2 MHz, using an Agilent 33250A pulse generator. Received signals were acquired using a Tektronix TDS 220 digital oscilloscope and, via GPIB, treated in a computer using a Fast Fourier Transform (FFT) algorithm to obtain the time of flight, s, which is the time taken by the tone-burst pulse to travel through the sample. Considering the first output signal, s0 ðtÞ, as a reference, the following output signals, sðtÞ, which undergo small shape alterations, can be expressed as sðtÞ ¼ As0 ðt þ DsÞ: ð15Þ Taking into account the Fourier transform time-delay theorem Sðf Þ ¼ Aei2pf Ds S0 ðf Þ;
ð16Þ
the time of flight variations, Ds, are obtained as a proportional function of the FFT signal phase variations, Du: Ds ¼
uðf0 Þ u0 ðf0 Þ : 2pf0
ð17Þ
d c0 ¼ ; s 1 þ c0dDs
ð18Þ
where c0 is the initial velocity and d is the distance travelled by the wave through the liquid, corresponding to the inner diameter of the bottle. The measurement of the sound velocity in the binary mixtures started with the bottle filled with distilled water, whose sound velocity value is well known. Discrete amounts of solute were gradually added to acquire the sound speed variations as a function of the solute mass concentration. The time of flight variation uncertainty was estimated to be smaller than 1 ns and the distance uncertainty, smaller than 0.5 mm. The speed of sound accuracy, calculated using error propagation, was 0.08 m/s. Small samples (2 cm3 ) of the solution were taken out, through a tube at the bottle plug, to measure density. The sound speed of the fermenting liquid was measured on-line using the same experimental arrangement. In this case, each fermentation test started with a 20% mass concentration of a given carbohydrate (glucose, fructose or saccharose) in 160 g of distilled water. When the ultrasonic velocity remained steady, 2 cm3 of a 33% wt dissolution of baker’s compressed yeast (S. cerevisiae yeasts, minerals, vitamins, nitrogen compounds, etc.) in distilled water were added to induce the fermentation process and to provide the essential nutrients for the yeast growth. The quantity of nutrients was small enough to not disturb the ultrasonic velocity; but, in return, this nutrient concentration was low enough that it caused a severe slowdown in the fermentation process. Carbon dioxide, produced during this reaction, goes out of the liquid by molecular diffusion or bubble formation through the liquid surface. Another tube at the bottle plug allowed the gas migration, maintaining the liquid at atmospheric pressure. Ultrasonic transmitted waves were captured and analysed automatically every minute over several days. Small samples of the fermenting liquid were taken (one or two per day) to measure density.
4. Results and discussion Figs. 4 and 5 show the experimental measurements of the density and the ultrasonic velocity in the water– glucose, water–fructose and water–saccharose binary mixtures. The lines were obtained as a cubic interpolation of the experimental data. It can be seen that both density and ultrasonic velocity grow with the solute mass concentration. The behaviour of the sound velocity measurements agrees with that shown by McClements (1997) for the same solutions. Discrepancies in the absolute velocity values are due to the experimental temperature, which was stated at 20 °C in the cited paper.
P. Resa et al. / Food Research International 37 (2004) 587–594 1,25
Density (g/cm3)
1,20
1,15
1,10
1,05
1,00 0
10
20
30
40
50
Mass concentration (%)
Fig. 4. Density of the water–glucose (circles/dot line), water–fructose (triangles/dash line) and water–saccharose (squares/solid line) binary mixtures at T ¼ 30 °C.
Ultrasonic velocity (m/s)
1750
1700
1650
1600
1550
1500 0
10
20
30
40
50
Mass concentration (%)
Fig. 5. Ultrasonic velocity in the water–glucose (circles), water–fructose (triangles) and water–saccharose (squares) binary mixtures at T ¼ 30 °C and f ¼ 2 MHz.
591
As discussed above, the behaviour of the ethanol– water mixture is quite different due to the strong molecular associations between the two liquids. As the ethanol concentration augments, the density decreases, whilst the sound velocity rises (reaching a maximum near 25% wt). During the alcoholic fermentation, carbohydrates are transformed into ethanol by the yeast enzymes. From Figs. 1 and 4, the density of the fermenting liquids is expected to decrease, because of the ethanol formation and the carbohydrate disappearance. On the other hand, the ultrasonic velocity behaviour is more difficult to predict because it increases with the formation of ethanol and decreases with the degradation of carbohydrates. Figs. 6–8 illustrate the on-line ultrasonic velocity and the off-line density measurements during the fermentation of water–glucose, water–fructose and water–saccharose culture media by S. cerevisiae yeasts. Density and ultrasonic velocity, during the glucose and fructose fermentation (Figs. 6 and 7), show a similar tendency. Nevertheless, there are not linearly proportional, as it can be deduced from Eq. (1), where the compressibility and the square root of the density influence the functional behaviour of the sound speed. It is observed that not only density but also ultrasonic velocity decreases in the course of time. If the binary mixture results are carefully analysed, it can be seen that the slope of the sound velocity in the water–glucose (or water–fructose) mixture is larger than the water–ethanol sound velocity slope for low ethanol concentration. Therefore, the sound velocity decrease, corresponding to the carbohydrates degradation, dominates at these concentrations. The sound speed obtained in the case of the saccharose fermentation (Figs. 8 and 9) shows a different behaviour. Two different stages, marked with numbers (1)
1590 1,075
1,070
1588
1587
1,065
1586
1,060
1585
Density (g/cm3)
Ultrasonic velocity (m/s)
1589
1,055
1584 1,050
1583 0
2
4
6
8
10
12
Time (days)
Fig. 6. Density (squares) and ultrasonic velocity (solid line) during the alcoholic fermentation of a water–glucose solution (w0g ¼ 20%), at T ¼ 30 °C and f ¼ 2 MHz.
592
P. Resa et al. / Food Research International 37 (2004) 587–594
1588
1587 1,070 1586 1,065
Density (g/cm3)
Ultrasonic velocity (m/s)
1,075
1585
1,060 1584 0
2
4
6
8
10
Time (days)
Fig. 7. Density (squares) and ultrasonic velocity (solid line) during the alcoholic fermentation of a water–fructose solution (w0f ¼ 20%), at T ¼ 30 °C and f ¼ 2 MHz.
1,08 1595 1,07
1,06 1585 1,05
1 1580
Density (g/cm3)
Ultrasonic velocity (m/s)
2 1590
1,04 1575 1,03 1570 0
1
2
3
4
5
6
7
Time (days)
Fig. 8. Density (squares) and ultrasonic velocity (solid line) during the alcoholic fermentation of a water–saccharose solution (w0s ¼ 20%), at T ¼ 30 °C and f ¼ 2 MHz.
and (2) in Fig. 8, can be clearly distinguished. During the first stage, lasting about 4 h, the density of the fermenting liquid remains constant while the ultrasonic velocity increases. This stage is detailed in Fig. 9. During the second stage, a situation similar to that of the glucose and fructose fermentation is reached: density and ultrasonic velocity decline in the course of time. These results can be explained by the fact that the saccharose fermentation follows a reaction different from glucose and fructose fermentation. In the presence of S. cerevisiae, saccharose molecules are firstly transformed into glucose and fructose by the action of the saccharase enzyme C12 H22 O11 þ H2 O
Saccharase
!
2C6 H12 O6
ð19Þ
after that, the zymase enzymes transform glucose and fructose as described by Eq. (11). The ultrasonic measurement nicely shows these two reactions. The first stage of Fig. 8 would be dominated by the hydrolysis of saccharose into glucose and fructose, making the velocity increase. This is coherent with the results shown in Fig. 5 where the ultrasonic velocity in a glucose–water (and a fructose–water) mixture is larger than in a saccharose–water mixture, at the same solute concentration. The second stage would predominantly correspond to the glycolysis of glucose and fructose, and the behaviour of curves in Figs. 7 and 8 is reproduced again. In the case of the glucose and fructose fermentation, it is possible to quantify the concentration of the liquid
P. Resa et al. / Food Research International 37 (2004) 587–594
593
20
1590
Mass concentration (%)
Ultrasonic velocity (m/s)
1595
1585
1 1580
18
Fructose
1,6
Ethanol
1,2 0,8
1575
0,4 1570 0
1
2
3
4
5
0,0 0
Time (hours)
components either from the measurement of the ultrasonic velocity or the density, following the approach proposed in the theoretical section. As it was explained, the incremental terms of Eqs. (9) and (10), Dch , Dce , Dqh , Dqe , were obtained from the experimental data of the binary mixtures (Figs. 1, 2, 4 and 5). The propagation velocity, c, and the density, q, of the fermenting liquid were also measured. From those experimental results, ethanol and carbohydrate concentrations, which are implicit variables in Eq. (9) and in Eq. (10), are numerically obtained as a function of time. The calculated concentrations during the glucose and fructose fermentations are presented in Figs. 10 and 11, respectively. A fairly good agreement was found between these results, with discrepancies less than 1% wt for carbohydrate concentrations and less than 0.5% wt for etha-
20
Mass concentration (%)
18
Glucose 16
2,5 2,0
Ethanol
1,5 1,0 0,5 0,0 2
4
6
4
6
8
10
Time (days)
Fig. 9. Ultrasonic velocity during the first stage of the water–saccharose solution fermentation (first hours of Fig. 8).
0
2
8
10
12
Time (days)
Fig. 10. Ethanol and glucose mass concentration obtained from density measurements (squares) and from ultrasonic velocity measurements (solid line), during the alcoholic fermentation of the water– glucose solution illustrated in Fig. 6.
Fig. 11. Ethanol and fructose mass concentration obtained from density measurements (squares) and from ultrasonic velocity measurements (solid line), during the alcoholic fermentation of the water– fructose solution illustrated in Fig. 7.
nol concentrations. This supports the hypothesis that the sound speed variations in a fermenting water–carbohydrate solution are mainly determined by both carbohydrate degradation and ethanol production. Unfortunately, this quantification could not be done for the water–saccharose fermentation because an analysis of the complex mixture (saccharose–glucose–fructose– water) is needed, which falls out of the scope of the present study. 5. Conclusions An analysis of the density and the ultrasonic velocity changes during the alcoholic fermentation of several aqueous mixtures was presented. Density and sound speed measurements, as a function of the mass concentration, in the binary solutions glucose–water, fructose– water, saccharose–water and ethanol–water, were carried out. It has been shown in this paper that these measurements can be used to relate both the sound velocity and the density to the concentration of the main components, during the course of the glucose (or fructose) fermentation. In addition, the suitability of the ultrasonic techniques to study fermentations in which important intermediate reactions take place has been shown, as happens in the saccharose fermentation. This is especially interesting when these intermediate reactions do not give rise to density changes. Consequently, this research establishes that ultrasonic techniques are well suited to monitor fermentation processes; being an accurate, readily automated, on-line and non-invasive method. Further studies are desirable to investigate the influence of carbon dioxide in faster fermentation reactions as well as the influence of other substances, over the concentration determination.
594
P. Resa et al. / Food Research International 37 (2004) 587–594
References Becker, T., Mitzscherling, M., & Delgado, A. (2001). Ultrasonic velocity – a non-invasive method for the determination of density during beer fermentation. Engineering Life Science, 1(2), 61–67. Becker, T., Mitzscherling, M., & Delgado, A. (2002). Hybrid data model for the improvement of an ultrasonic-based gravity measurement system. Food Control, 13, 223–233. Burton, C. J. (1948). A study of ultrasonic velocity and absorption in liquid mixtures. Journal of the Acoustical Society of America, 20(2), 186–199. Douheret, G., Davis, M. I., Reis, J. C. R., & Blandamer, M. J. (2001). Isentropic compressibilities – experimental origin and the quest for their rigorous estimation in thermodynamically ideal liquid mixtures. Chemphyschem, 2, 148–161. Giacomini, A. (1947). Ultrasonic velocity in ethanol–water mixtures. Journal of the Acoustical Society of America, 19(4), 701–702. Lide, D. R. (2002–2003). CRC handbook of chemistry and physics (83rd ed.). Boca Raton, FL: CRC Press LLCs.
McClements, D. J. (1997). Ultrasonic characterization of foods and drinks: Principles, methods and applications. Critical Reviews in Food Science and Nutrition, 37(1), 1–46. Nutsch-Kuhnkies, R. (1965). Uber schallkennlinien einiger bin€arer mischungen und l€ osungen. Acustica, 15, 383–386. Parshad, R. (1949). Supersonic waves in water–alcohol–sodium chloride mixture and analysis of its intermolecular action. Journal of the Acoustical Society of America, 21(3), 175–176. Povey, M. J. W., & Mason, T. J. (1998). Ultrasound in food processing. London: Blackie Academic & Professional. Sette, D. (1961). Dispersion and absorption of sound waves in liquids and mixtures of liquids. In S. Fl€ ugge (Ed.), Handbuch der Physik, BD. XI/1 (pp. 275–360). Berlin: Springer. Urick, J. R. (1947). A sound velocity method for determining the compressibility of finely divided substances. Journal of Applied Physics, 18, 983–987. Winder, W. C., Aulik, D. J., & Rice, A. C. (1970). An ultrasonic method for direct and simultaneous determination of alcohol and extract content of wines. American Journal of Enology and Viticulture, 21(1), 1–11.
Concentration control in alcoholic fermentation processes from ultrasonic velocity measurements Pablo Resa *, Luis Elvira, Francisco Montero de Espinosa Instituto de Acustica (CSIC), Serrano 144, 28006 Madrid, Spain Received 25 August 2003; accepted 3 December 2003
Abstract A study of the alcoholic fermentation of several carbohydrate aqueous solutions, using an ultrasonic velocity measurement technique, is presented in this paper. It is shown that the changes occurring during the course of an alcoholic fermentation can be monitored on-line by measuring the velocity of an elastic wave propagating through the fermenting medium. During the alcoholic fermentation, carbohydrates are transformed into ethanol and carbon dioxide by the action of the yeast’s metabolism. In this work, measurements of the ultrasonic velocities and densities of the binary mixtures glucose–water, fructose–water, saccharose–water and ethanol–water were carried out. These experimental results – due to the inaccuracy of the theoretical approaches – have been satisfactorily utilised to determine the concentrations of the main components during the glucose and fructose fermentation, induced by Saccharomyces cerevisiae yeasts, and to analyse the saccharose fermentation. Ó 2004 Elsevier Ltd. All rights reserved. Keywords: Alcoholic fermentation; Density; Ultrasonic velocity; Concentration; On-line control
1. Introduction Ultrasonic based devices have being applied to control many industrial processes for a number of decades. Nowadays, these technologies are emerging as wellsuited methods to monitor food processes, fulfilling important quality requirements of non-invasiveness, non-destructiveness and easy automation (McClements, 1997; Povey & Mason, 1998). Therefore, a good knowledge of the ultrasonic wave propagation through foods is required. From the acoustical point of view, food materials are often complex media and relations between elastic and quality properties remain unknown in many cases. An ultrasonic study of the alcoholic fermentation in liquid media is presented in this paper. This process is of great importance in the elaboration of alcoholic drinks like wine or beer, but also for drug synthesis. The evolution of the fermentation reaction is usually supervised *
Corresponding author. Tel.: +34-91-561-88-06; fax: +34-91-411-76-
51. E-mail address: [email protected] (P. Resa). 0963-9969/$ - see front matter Ó 2004 Elsevier Ltd. All rights reserved. doi:10.1016/j.foodres.2003.12.012
by measuring the liquid density. Nevertheless, this kind of control is not easily achieved by a non-invasive and on-line technique. Winder, Aulik, and Rice (1970) proposed an ultrasonic method to determine alcohol and extract content in wines. They used a resonant cell to analyse these parameters. Although they did not study the fermentation process itself, an empirical relation between ultrasonic parameters and the concentrations of alcohol and soluble solids was proposed indicating that these concentrations mainly determine the speed of sound in fermenting media. Recently, Becker, Mitzscherling, and Delgado (2001, 2002) have used an ultrasonic technique to determine the density during beer fermentation. They discarded the possibility of obtaining a theoretical relation between density and ultrasonic propagation velocity, being aware of the lack of a representative model for liquid mixtures and solutions. This paper focuses on the relations between both the density and the ultrasonic velocity with the concentrations of the main components in fermenting liquids. Three different water–carbohydrate mixtures were tested (glucose, fructose and saccharose). Saccharomyces ce-
588
P. Resa et al. / Food Research International 37 (2004) 587–594
revisiae, contained in baker’s compressed yeast, was used to provoke the fermentations. Densities and ultrasonic velocities were measured in the binary mixtures of water–carbohydrate and water– ethanol, and in the fermenting media. These media are mostly constituted by a complex mixture of carbohydrates, ethanol, carbon dioxide, yeast and water. Some of the most relevant theories describing ultrasonic propagation through liquid mixtures were revised and compared to the experimental data. The possibility of theoretically correlating density and ultrasonic velocity to the concentrations of the main components is reported.
2. Theory 2.1. Theoretical models The speed, c, of an elastic wave propagating through a pure liquid is given by the equation sffiffiffiffiffiffi 1 c¼ ; ð1Þ qj where q is the density and j is the adiabatic compressibility. Nevertheless, in the case of a mixture of liquids, a general equation to get the density and the compressibility as a function of the properties of the pure components does not exist. The same occurs when a solid substance is dissolved in a liquid. Probably, one of the most widespread models for the study of liquid suspensions is that developed by Urick (1947). He applied Eq. (1), considering a linear dependence of the density, q, and the adiabatic compressibility, j, with the volume concentration, / X q¼ /i qi ; ð2Þ
An empirical relation between sound velocity and molecular volume, valid for unassociated liquids, was established by Rao pffiffiffi ð6Þ V 3 c ¼ R const:; where V is the molecular volume. Nomoto calculated this expression in a large number of mixtures of various kinds (Sette, 1961). He found that R has a linear form in many systems !3 X 1=3 c¼ / i ci : ð7Þ i
However, in the case of polar liquid mixtures, where bonds between the molecules of different components appear, the predictions of these theories become unbefitting. Research papers about ultrasonic propagation velocity in these kinds of liquids can be found in the literature (Burton, 1948; Giacomini, 1947; Parshad, 1949; Sette, 1961). Ethanol–water mixtures show these molecular associations, which make the models unsuccessful, as it is clearly shown in Figs. 1 and 2, where density and velocity are plotted as a function of the ethanol concentration. These experimental data agree with the values found in the literature for the density (Lide, 2002–2003) and earlier velocity measurements obtained by Giacomini (1947), Burton (1948) and Parshad (1949). Great discrepancies between theoretical models and experimental data exist even at the lowest ethanol concentrations. Therefore, none of these approaches can be applied to determine the ultrasonic propagation in a fermenting liquid, where both ethanol and water are present. Others theoretical models lead to similar results (Douheret, Davis, Reis, & Blandamer, 2001; NutschKuhnkies, 1965).
i
j¼
X
/i ji ;
ð3Þ
i
1 c ¼ qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi P P ffi : i /i ji i /i qi
ð4Þ
Moreover, Natta and Baccaredda assumed that the time needed for a mechanical pulse to pass through a mixture is the sum of the times which would be required to pass successively through two layers, each formed by one of the two components and having thickness proportional to the relative volume concentration (Sette, 1961). This gives the following equation: !1 X/ i : ð5Þ c¼ ci i
Fig. 1. Density of the water–ethanol mixture at T ¼ 30 °C. Squares are experimental values and dash line was obtained from Eq. (2).
P. Resa et al. / Food Research International 37 (2004) 587–594
589
which means that the sound speed in the fermenting liquid is considered as the sum of the initial velocity and the speed increments due to the concentration changes of hexoses and ethanol. The advantage of this approach is that these increments can be obtained from the experimental measurements of the ultrasonic velocity in the binary mixture water–hexose and in the binary mixture water– ethanol. A parallel procedure can be applied to obtain density qðXh ; Xe Þ q0 þ Dqh ðXh Þ þ Dqe ðXe Þ:
Fig. 2. Ultrasonic velocity in the water–ethanol mixture at T ¼ 30 °C. Squares are experimental values and lines were obtained from the theoretical approaches: Urick (dash line), Nomoto (dash dot line) and Natta–Baccaredda (dot line).
2.2. Semi-empirical model In this work, it is considered that the velocity variation during the alcoholic fermentation is mainly due to the carbohydrate reduction and to the formation of ethanol molecules. The presence of yeasts seems to play a minor role in the ultrasonic velocity propagation as it was pointed out by Becker et al. (2001). To avoid carbon dioxide bubble interferences, a high frequency was chosen and slow reactions were induced, allowing the gas to exit out of the fermenting liquid by means of molecular diffusion and small bubbles. The sensitivity of ultrasonic velocity to diluted carbon dioxide was measured in distilled water at 30 °C and it was estimated to be smaller than +0.3 m/s for a carbon dioxide partial pressure of 1 atm. Under the experimental conditions of this work, carbon dioxide interferences have been considered negligible. Therefore, using a two variable Taylor expansion, the sound speed in the fermenting liquid can be written as oc oc ðXh Xh0 Þ þ Xe oXh oXe 2 1 o2 c 2 o2 c Xh Xh0 þ X 2 2 oXe2 e oXh o2 c ðXh Xh0 ÞXe þ oXh oXe
cðXh ; Xe Þ c0 þ þ
1 2
þ
1 2
ð8Þ
where c0 is the velocity at the beginning of the fermentation, X stands for the molar concentration and subscripts h and e refer to hexoses (glucose or fructose) and ethanol, respectively. For low ethanol concentrations, the interaction between carbohydrates and ethanol molecules can be discarded and crossed terms are eliminated in Eq. (8). With this assumption, the velocity can be calculated by cðXh ; Xe Þ c0 þ Dch ðXh Þ þ Dce ðXe Þ;
ð9Þ
ð10Þ
Relations between molar fractions (or mass concentrations) of the different components can be deduced from the fermentation reaction Zymase
C6 H12 O6 ! 2C2 H6 O þ 2CO"2 :
ð11Þ
Thereby, the relations between molar concentrations are Xe ¼ 2ðXh0 Xh Þ;
ð12Þ
Xs ¼ 1 Xe X h ;
ð13Þ
where superscript 0 refers to the beginning of the fermentation and subscript s refers to the solvent. The mass concentration, wi , of the ‘‘i’’ component is given by wi ¼
M i Xi ; M s Xs þ M h Xh þ M e Xe
ð14Þ
where M represents the molecular mass.
3. Materials and methods Two different types of experimental analysis were carried out: the measurement of the density and ultrasonic velocity as a function of mass concentration in the water–ethanol and water–carbohydrate binary mixtures, and the measurement of the density and ultrasonic velocity as a function of time during the carbohydrate solution fermentations. Distilled water, ethanol (purity >99.5%), glucose (purity >99.7%), fructose (purity >98.0%) and saccharose (purity >99.7%) were used to make the binary mixtures. Mass concentration, w, was measured using a digital Sartorius 1216 MP balance with a 0.1 g precision. Densities, q, were measured with an Anton Paar DMA 35 vibrating tube densimeter, whose resolution was 1 kg/m3 . The experimental set-up for the sound velocity measurements is shown in Fig. 3. The solutions were contained inside a glass bottle, with 64 mm inner diameter, and immersed in a circulating thermostated water bath to keep the temperature of the solution constant at 30 °C, with variations of the order of 0.01 °C. To ensure their homogeneity, the mixtures were constantly stirred with a magnetic agitator.
590
P. Resa et al. / Food Research International 37 (2004) 587–594
The ultrasonic velocity, c, in the medium can be calculated by dividing the distance by the time of flight
GPIB PC
c¼
PULSE GENERATOR
OSCILLOSCOPE
TRIGG
TEMPERATURE CONTROLLER CO2 DENSITY WATER BATH 30˚C
EXPERIMENTAL CELL
TRANSDUCER
MAGNETIC STIRRER
Fig. 3. Experimental set-up for the on-line measurement of the ultrasonic velocity and the off-line measurement of density.
The ultrasonic velocities were measured (on-line) using a tone-burst pulse through-transmission technique. Transducers were attached face to face at the sides of the glass bottle and coupled to it with a silicone layer. The emitting and receiving transducers were identically made of a PZT 5A piezoelectric ceramic, 20 mm diameter, bonded to a Plexiglas plate. Araldite D was used as backing. The emitting transducer was excited at its resonant frequency, f0 ¼ 2 MHz, using an Agilent 33250A pulse generator. Received signals were acquired using a Tektronix TDS 220 digital oscilloscope and, via GPIB, treated in a computer using a Fast Fourier Transform (FFT) algorithm to obtain the time of flight, s, which is the time taken by the tone-burst pulse to travel through the sample. Considering the first output signal, s0 ðtÞ, as a reference, the following output signals, sðtÞ, which undergo small shape alterations, can be expressed as sðtÞ ¼ As0 ðt þ DsÞ: ð15Þ Taking into account the Fourier transform time-delay theorem Sðf Þ ¼ Aei2pf Ds S0 ðf Þ;
ð16Þ
the time of flight variations, Ds, are obtained as a proportional function of the FFT signal phase variations, Du: Ds ¼
uðf0 Þ u0 ðf0 Þ : 2pf0
ð17Þ
d c0 ¼ ; s 1 þ c0dDs
ð18Þ
where c0 is the initial velocity and d is the distance travelled by the wave through the liquid, corresponding to the inner diameter of the bottle. The measurement of the sound velocity in the binary mixtures started with the bottle filled with distilled water, whose sound velocity value is well known. Discrete amounts of solute were gradually added to acquire the sound speed variations as a function of the solute mass concentration. The time of flight variation uncertainty was estimated to be smaller than 1 ns and the distance uncertainty, smaller than 0.5 mm. The speed of sound accuracy, calculated using error propagation, was 0.08 m/s. Small samples (2 cm3 ) of the solution were taken out, through a tube at the bottle plug, to measure density. The sound speed of the fermenting liquid was measured on-line using the same experimental arrangement. In this case, each fermentation test started with a 20% mass concentration of a given carbohydrate (glucose, fructose or saccharose) in 160 g of distilled water. When the ultrasonic velocity remained steady, 2 cm3 of a 33% wt dissolution of baker’s compressed yeast (S. cerevisiae yeasts, minerals, vitamins, nitrogen compounds, etc.) in distilled water were added to induce the fermentation process and to provide the essential nutrients for the yeast growth. The quantity of nutrients was small enough to not disturb the ultrasonic velocity; but, in return, this nutrient concentration was low enough that it caused a severe slowdown in the fermentation process. Carbon dioxide, produced during this reaction, goes out of the liquid by molecular diffusion or bubble formation through the liquid surface. Another tube at the bottle plug allowed the gas migration, maintaining the liquid at atmospheric pressure. Ultrasonic transmitted waves were captured and analysed automatically every minute over several days. Small samples of the fermenting liquid were taken (one or two per day) to measure density.
4. Results and discussion Figs. 4 and 5 show the experimental measurements of the density and the ultrasonic velocity in the water– glucose, water–fructose and water–saccharose binary mixtures. The lines were obtained as a cubic interpolation of the experimental data. It can be seen that both density and ultrasonic velocity grow with the solute mass concentration. The behaviour of the sound velocity measurements agrees with that shown by McClements (1997) for the same solutions. Discrepancies in the absolute velocity values are due to the experimental temperature, which was stated at 20 °C in the cited paper.
P. Resa et al. / Food Research International 37 (2004) 587–594 1,25
Density (g/cm3)
1,20
1,15
1,10
1,05
1,00 0
10
20
30
40
50
Mass concentration (%)
Fig. 4. Density of the water–glucose (circles/dot line), water–fructose (triangles/dash line) and water–saccharose (squares/solid line) binary mixtures at T ¼ 30 °C.
Ultrasonic velocity (m/s)
1750
1700
1650
1600
1550
1500 0
10
20
30
40
50
Mass concentration (%)
Fig. 5. Ultrasonic velocity in the water–glucose (circles), water–fructose (triangles) and water–saccharose (squares) binary mixtures at T ¼ 30 °C and f ¼ 2 MHz.
591
As discussed above, the behaviour of the ethanol– water mixture is quite different due to the strong molecular associations between the two liquids. As the ethanol concentration augments, the density decreases, whilst the sound velocity rises (reaching a maximum near 25% wt). During the alcoholic fermentation, carbohydrates are transformed into ethanol by the yeast enzymes. From Figs. 1 and 4, the density of the fermenting liquids is expected to decrease, because of the ethanol formation and the carbohydrate disappearance. On the other hand, the ultrasonic velocity behaviour is more difficult to predict because it increases with the formation of ethanol and decreases with the degradation of carbohydrates. Figs. 6–8 illustrate the on-line ultrasonic velocity and the off-line density measurements during the fermentation of water–glucose, water–fructose and water–saccharose culture media by S. cerevisiae yeasts. Density and ultrasonic velocity, during the glucose and fructose fermentation (Figs. 6 and 7), show a similar tendency. Nevertheless, there are not linearly proportional, as it can be deduced from Eq. (1), where the compressibility and the square root of the density influence the functional behaviour of the sound speed. It is observed that not only density but also ultrasonic velocity decreases in the course of time. If the binary mixture results are carefully analysed, it can be seen that the slope of the sound velocity in the water–glucose (or water–fructose) mixture is larger than the water–ethanol sound velocity slope for low ethanol concentration. Therefore, the sound velocity decrease, corresponding to the carbohydrates degradation, dominates at these concentrations. The sound speed obtained in the case of the saccharose fermentation (Figs. 8 and 9) shows a different behaviour. Two different stages, marked with numbers (1)
1590 1,075
1,070
1588
1587
1,065
1586
1,060
1585
Density (g/cm3)
Ultrasonic velocity (m/s)
1589
1,055
1584 1,050
1583 0
2
4
6
8
10
12
Time (days)
Fig. 6. Density (squares) and ultrasonic velocity (solid line) during the alcoholic fermentation of a water–glucose solution (w0g ¼ 20%), at T ¼ 30 °C and f ¼ 2 MHz.
592
P. Resa et al. / Food Research International 37 (2004) 587–594
1588
1587 1,070 1586 1,065
Density (g/cm3)
Ultrasonic velocity (m/s)
1,075
1585
1,060 1584 0
2
4
6
8
10
Time (days)
Fig. 7. Density (squares) and ultrasonic velocity (solid line) during the alcoholic fermentation of a water–fructose solution (w0f ¼ 20%), at T ¼ 30 °C and f ¼ 2 MHz.
1,08 1595 1,07
1,06 1585 1,05
1 1580
Density (g/cm3)
Ultrasonic velocity (m/s)
2 1590
1,04 1575 1,03 1570 0
1
2
3
4
5
6
7
Time (days)
Fig. 8. Density (squares) and ultrasonic velocity (solid line) during the alcoholic fermentation of a water–saccharose solution (w0s ¼ 20%), at T ¼ 30 °C and f ¼ 2 MHz.
and (2) in Fig. 8, can be clearly distinguished. During the first stage, lasting about 4 h, the density of the fermenting liquid remains constant while the ultrasonic velocity increases. This stage is detailed in Fig. 9. During the second stage, a situation similar to that of the glucose and fructose fermentation is reached: density and ultrasonic velocity decline in the course of time. These results can be explained by the fact that the saccharose fermentation follows a reaction different from glucose and fructose fermentation. In the presence of S. cerevisiae, saccharose molecules are firstly transformed into glucose and fructose by the action of the saccharase enzyme C12 H22 O11 þ H2 O
Saccharase
!
2C6 H12 O6
ð19Þ
after that, the zymase enzymes transform glucose and fructose as described by Eq. (11). The ultrasonic measurement nicely shows these two reactions. The first stage of Fig. 8 would be dominated by the hydrolysis of saccharose into glucose and fructose, making the velocity increase. This is coherent with the results shown in Fig. 5 where the ultrasonic velocity in a glucose–water (and a fructose–water) mixture is larger than in a saccharose–water mixture, at the same solute concentration. The second stage would predominantly correspond to the glycolysis of glucose and fructose, and the behaviour of curves in Figs. 7 and 8 is reproduced again. In the case of the glucose and fructose fermentation, it is possible to quantify the concentration of the liquid
P. Resa et al. / Food Research International 37 (2004) 587–594
593
20
1590
Mass concentration (%)
Ultrasonic velocity (m/s)
1595
1585
1 1580
18
Fructose
1,6
Ethanol
1,2 0,8
1575
0,4 1570 0
1
2
3
4
5
0,0 0
Time (hours)
components either from the measurement of the ultrasonic velocity or the density, following the approach proposed in the theoretical section. As it was explained, the incremental terms of Eqs. (9) and (10), Dch , Dce , Dqh , Dqe , were obtained from the experimental data of the binary mixtures (Figs. 1, 2, 4 and 5). The propagation velocity, c, and the density, q, of the fermenting liquid were also measured. From those experimental results, ethanol and carbohydrate concentrations, which are implicit variables in Eq. (9) and in Eq. (10), are numerically obtained as a function of time. The calculated concentrations during the glucose and fructose fermentations are presented in Figs. 10 and 11, respectively. A fairly good agreement was found between these results, with discrepancies less than 1% wt for carbohydrate concentrations and less than 0.5% wt for etha-
20
Mass concentration (%)
18
Glucose 16
2,5 2,0
Ethanol
1,5 1,0 0,5 0,0 2
4
6
4
6
8
10
Time (days)
Fig. 9. Ultrasonic velocity during the first stage of the water–saccharose solution fermentation (first hours of Fig. 8).
0
2
8
10
12
Time (days)
Fig. 10. Ethanol and glucose mass concentration obtained from density measurements (squares) and from ultrasonic velocity measurements (solid line), during the alcoholic fermentation of the water– glucose solution illustrated in Fig. 6.
Fig. 11. Ethanol and fructose mass concentration obtained from density measurements (squares) and from ultrasonic velocity measurements (solid line), during the alcoholic fermentation of the water– fructose solution illustrated in Fig. 7.
nol concentrations. This supports the hypothesis that the sound speed variations in a fermenting water–carbohydrate solution are mainly determined by both carbohydrate degradation and ethanol production. Unfortunately, this quantification could not be done for the water–saccharose fermentation because an analysis of the complex mixture (saccharose–glucose–fructose– water) is needed, which falls out of the scope of the present study. 5. Conclusions An analysis of the density and the ultrasonic velocity changes during the alcoholic fermentation of several aqueous mixtures was presented. Density and sound speed measurements, as a function of the mass concentration, in the binary solutions glucose–water, fructose– water, saccharose–water and ethanol–water, were carried out. It has been shown in this paper that these measurements can be used to relate both the sound velocity and the density to the concentration of the main components, during the course of the glucose (or fructose) fermentation. In addition, the suitability of the ultrasonic techniques to study fermentations in which important intermediate reactions take place has been shown, as happens in the saccharose fermentation. This is especially interesting when these intermediate reactions do not give rise to density changes. Consequently, this research establishes that ultrasonic techniques are well suited to monitor fermentation processes; being an accurate, readily automated, on-line and non-invasive method. Further studies are desirable to investigate the influence of carbon dioxide in faster fermentation reactions as well as the influence of other substances, over the concentration determination.
594
P. Resa et al. / Food Research International 37 (2004) 587–594
References Becker, T., Mitzscherling, M., & Delgado, A. (2001). Ultrasonic velocity – a non-invasive method for the determination of density during beer fermentation. Engineering Life Science, 1(2), 61–67. Becker, T., Mitzscherling, M., & Delgado, A. (2002). Hybrid data model for the improvement of an ultrasonic-based gravity measurement system. Food Control, 13, 223–233. Burton, C. J. (1948). A study of ultrasonic velocity and absorption in liquid mixtures. Journal of the Acoustical Society of America, 20(2), 186–199. Douheret, G., Davis, M. I., Reis, J. C. R., & Blandamer, M. J. (2001). Isentropic compressibilities – experimental origin and the quest for their rigorous estimation in thermodynamically ideal liquid mixtures. Chemphyschem, 2, 148–161. Giacomini, A. (1947). Ultrasonic velocity in ethanol–water mixtures. Journal of the Acoustical Society of America, 19(4), 701–702. Lide, D. R. (2002–2003). CRC handbook of chemistry and physics (83rd ed.). Boca Raton, FL: CRC Press LLCs.
McClements, D. J. (1997). Ultrasonic characterization of foods and drinks: Principles, methods and applications. Critical Reviews in Food Science and Nutrition, 37(1), 1–46. Nutsch-Kuhnkies, R. (1965). Uber schallkennlinien einiger bin€arer mischungen und l€ osungen. Acustica, 15, 383–386. Parshad, R. (1949). Supersonic waves in water–alcohol–sodium chloride mixture and analysis of its intermolecular action. Journal of the Acoustical Society of America, 21(3), 175–176. Povey, M. J. W., & Mason, T. J. (1998). Ultrasound in food processing. London: Blackie Academic & Professional. Sette, D. (1961). Dispersion and absorption of sound waves in liquids and mixtures of liquids. In S. Fl€ ugge (Ed.), Handbuch der Physik, BD. XI/1 (pp. 275–360). Berlin: Springer. Urick, J. R. (1947). A sound velocity method for determining the compressibility of finely divided substances. Journal of Applied Physics, 18, 983–987. Winder, W. C., Aulik, D. J., & Rice, A. C. (1970). An ultrasonic method for direct and simultaneous determination of alcohol and extract content of wines. American Journal of Enology and Viticulture, 21(1), 1–11.