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Ultrasonic velocity in water–ethanol–sucrose mixtures during alcoholic fermentation
Ultrasonics 43 (2005) 247–252 www.elsevier.com/locate/ultras
Ultrasonic velocity in water–ethanol–sucrose mixtures during alcoholic fermentation q P. Resa *, L. Elvira, F. Montero de Espinosa, Y. G omez-Ullate Dpto. Se~ nales, Sistemas y Tecnologıas Ultrasonicos, Instituto de Acustica (CSIC), c/. Serrano 144, 28006 Madrid, Spain Available online 6 July 2004
Abstract During alcoholic fermentation, sucrose and water are transformed into ethanol and carbon dioxide by the action of yeast enzymes. The measurement of the velocity of an ultrasonic pulse travelling through a fermentation tank can be used to characterize the state of the process. In this work, an experimental study of the density and ultrasonic velocity in the ternary mixture (water–ethanol– saccharose) is presented. Experimental results were compared to ideal density and to commonly used expressions of the sound velocity in liquid mixtures (Urick, Natta-Baccaredda and Nomoto). A semiempirical approach was proposed to improve the efficiency of theoretical models when dealing with mixtures of associated liquids. 2004 Elsevier B.V. All rights reserved. Keywords: Fermentation; Density; Ultrasonic Velocity; Ethanol; Water; Sucrose
1. Introduction The alcoholic fermentation induced by the presence of yeasts is a fundamental step in several biotechnological processes such as the production of alcoholic drinks, bread or pharmaceutical products. The optimisation of the process implies a reduction of costs for the industry. Ultrasonic techniques have been already proposed as a new method to determine the density during the elaboration of beer [1], which is the most important parameter to characterize the state of the reaction. Ultrasonics provide an appropriate (non-invasive, nondestructive, accuracy and non-expensive) on-line system to monitor the fermentation process. While the fermentation takes place in a water–saccharose solution, water and carbohydrates are transformed into ethanol and carbon dioxide by the yeast metabolism. Therefore, the liquid can be considered basically as a mixture of water, ethanol and saccharose (without considering carbon dioxide interferences). Changes in the concentration of these chemical components are accompanied
by the change of propagation velocity. In this work, experimental values of densities and speeds of sound in the binary mixtures (water–ethanol and water–saccharose) and in the ternary mixture (water–ethanol–saccharose) are reported. These results are also compared to theoretical approaches (Urick, Natta-Baccaredda and Nomoto) often used to model liquid mixtures [2–4]. It is shown that experimental results of density and sound speed for the ethanol–water mixture are not well described by these theories. It is established [5–7] that the deviation between the real sound speed and the theories is related to the formation of different associations between the molecules of the two liquids, which are often referred as associated liquids. A semiempirical approach based on the experimental data of the water–ethanol system is proposed to analyse the ternary mixture (water–ethanol–saccharose). The experimental results show a good fit with this model for low ethanol concentrations. Therefore, the model proposed constitutes a good alternative to calculate ultrasonic velocities in fermentation processes.
q
This article is based on a presentation given at the Ultrasonics International 2003. * Corresponding author. Tel.: +34-915-618806x051; fax: +34-914117651. E-mail address: [email protected] (P. Resa). 0041-624X/$ - see front matter 2004 Elsevier B.V. All rights reserved. doi:10.1016/j.ultras.2004.06.005
2. Theoretical Different approaches have been proposed for expressing ultrasonic velocity in binary mixtures.
248
P. Resa et al. / Ultrasonics 43 (2005) 247–252
Among the most commonly used are the relations of Urick [2], Natta-Baccaredda [3] and Nomoto [4]. The model developed by Urick for the study of liquid suspensions is based on a linear dependence of the density and the adiabatic compressibility with the volume concentration: X q¼ /i qi ð1Þ i
j¼
X
ð2Þ
/i ji
i
1 c ¼ qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi P P ffi / j / q i i i i i i
ð3Þ
Table 1 Literature data of pure substances at T ¼ 30 C q (kg/m3 ) M (g/mol) c (m/s)
Water
Ethanol
Saccharos
995.64a 18.02a 1509.144b
780.97a 46.07a 1145c
1546.79a 342.30a –
a
Data taken from [12]. Data taken from [13]. c Data estimated from [5]. b
where c is the sound velocity, j is the adiabatic compressibility, q is the density and / is the volume fraction. Natta and Baccaredda proposed 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: !1 X /i ð4Þ c¼ ci i On the other hand, Rao [8] found an empirical relation between sound velocity and molecular volume, valid for unassociated liquids: pffiffiffi ð5Þ V 3 c ¼ R const: where V is the molecular volume. Nomoto calculated this expression in a large number of mixtures, including those formed by associated components. He found that R have a linear form in many systems, !3 X 1=3 c¼ / i ci ð6Þ i
Table 2 Experimental values of density q of binary and ternary mixtures (water, saccharose, ethanol) at T ¼ 30 C Water–saccharose 0.00 w2 (%) q (kg/m3 ) 995
6.07 1018
10.31 1034
15.25 1054
20.93 1079
30.07 1121
39.76 1169
50.12 1222
100.00 1547a
Water–ethanol 5%–saccharose w2 (%) 0.00 4.95 985 1004 q (kg/m3 )
10.07 1025
15.11 1048
20.51 1070
30.55 1118
40.00 1159
50.10 1217
100.00 1547a
Water–ethanol 10%–saccharose 0.00 5.66 w2 (%) q (kg/m3 ) 978 1001
10.00 1016
16.32 1045
20.63 1064
30.55 1111
40.12 1158
50.00 1211
100.00 1547a
Water–ethanol 15%–saccharose w2 (%) 0.00 5.66 q (kg/m3 ) 970 994
9.91 1011
15.25 1037
20.32 1056
29.82 1101
39.76 1150
50.00 1204
100.00 1547a
Water–ethanol 20%–saccharose w2 (%) 0.00 5.66 963 984 q (kg/m3 )
9.91 1006
15.25 1026
20.32 1047
29.82 1096
39.76 1147
50.00 1202
100.00 1547a
Water–ethanol 30%–saccharose w2 (%) 0.00 5.00 q (kg/m3 ) 947 968
10.00 989
15.00 1009
20.00 1029
30.00 1080
40.00 1135
50.00 1191
100.00 1547a
Water–ethanol 40%–saccharose w2 (%) 0.00 5.21 q (kg/m3 ) 929 949
10.00 969
15.00 990
20.00 1013
30.00 1063
40.30 1115
– –
100.00 1547a
Water–ethanol 50%–saccharose 0.00 5.00 w2 (%) q (kg/m3 ) 906 924
10.00 949
15.00 971
20.00 993
30.00 1048
40.00 1103
– –
100.00 1547a
Water–ethanol w3 (%) 0.00 q (kg/m3 ) 995
10.00 978
15.00 970
20.00 963
30.00 947
40.00 929
50.00 907
100.00 781
a
Value from literature.
5.00 985
P. Resa et al. / Ultrasonics 43 (2005) 247–252
Nevertheless none of these approaches or other existing theories [9] have shown a general validity, and binary systems such as water–ethanol are badly described by them. Reviews of various proposals of ultrasonic speed can be found in references [10,11]. Water and ethanol are both associated liquids. When ethanol is added to water, different associations are established and practically destruction of water associations takes place. In this kind of mixtures, not only interaction forces between molecules of different liquids appears, but also interaction forces between molecules of the pure liquids are modified.
It is proposed in this work that the water–ethanol system can be assumed as a solvent in which saccharose is solved. Taking water–ethanol mixture values of density q13 and velocity c13 (which are dependant of their respective concentrations) from experimental measurements, the above models were applied considering the ternary mixture (water–ethanol–saccharose) like a binary mixture of saccharose in the water–ethanol solvent. Hence, the expression for density gives q ¼ /2 q2 þ ð1 /2 Þq13
Experimental From Eq. (7)
Experimental From Eq. (1) 1400
ρ (Kg/m3)
1400
1200
1200
1000
1000
0
20
40
60
80
0
100
20
40
60
80
100
60
80
100
60
80
100
w2 (%)
w2 (%) 1600
1600
Experimental From Eq. (7)
Experimental From Eq. (7)
1400
1400
ρ (Kg/m3)
ρ (Kg/m3)
ð7Þ
1600
1600
ρ (Kg/m3)
249
1200
1000
1200
1000
0
20
40
60
80
100
0
20
40
w2 (%)
w2 (%)
1600
Experimental From Eq. (1)
1000
Experimental From Eq. (1)
ρ (Kg/m3)
ρ (Kg/m3)
1400
900
1200
1000
800
0
20
40
60
w2 (%)
80
100
0
20
40
w2 (%)
Fig. 1. Density, q, of the binary and ternary mixtures at T ¼ 30 C: (a) solvent: water, solute: saccharose; (b) solvent: water–ethanol 10%, solute: saccharose; (c) solvent: water–ethanol 20%, solute: saccharose; (d) solvent: water–ethanol 30%, solute: saccharose; (e) solvent: water, solute: ethanol; (f) solvent: water–ethanol 20%, solute: saccharose.
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Urick relation, 1 c ¼ pffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi ½/2 j2 þ ð1 /2 Þj13 ½/2 q2 þ ð1 /2 Þq13 Natta-Baccaredda relation,
1 /2 1 /2 þ c¼ c2 c13
ð8Þ
ð9Þ
and Nomoto relation, 1=3
1=3 3
c ¼ ð/2 c2 þ ð1 /2 Þc13 Þ
ð10Þ
where subscript 1, 2 and 3 correspond to water, saccharose and ethanol, respectively. 3. Experimental procedure Distilled water, ethanol (purities > 99.5%) and saccharose (purities > 99.7%) in different concentration were used to make the mixtures. Densities, q, were measured with an Anton Paar DMA 35 vibrating tube densimeter, with a ±0.5 · 103 g/cm3 resolution. Mass concentrations, w, were measured using a digital Sartorius 1216 MP balance with a ±0.05 g precision. The ultrasonic velocities, c, were measured using a transmission-through technique. The emitting and receiving transducers were made of a PZT 5A, 20 mm diameter, piezoelectric ceramic bonded to a Plexiglas plate. Araldite D was used as backing. The emitting transducer was excited with tone bursts at its resonant frequency, 2 MHz, which makes the ceramic vibrate in a thickness mode.
The solutions, mixed with a magnetic stirrer until complete dissolution, were put inside a 250 ml glass bottle, with a 64 mm inner diameter, and placed in a thermostatization water bath to keep the temperature of the sample constant at 30 C, with variations of the order of 0.01 C. Transducers were attached face to face at the sides of the glass bottle, also submerged in the bath. Received signals were digitalized and treated using a FFT algorithm to obtain the time of flight Ds, which is related to the propagation velocity by c0 c¼ ð11Þ c0 Ds 1þ d where c0 is the velocity in the pure solvent and d is the distance travelled by the ultrasonic pulses through the mixture corresponding to the inner diameter of the bottle. The uncertainty of speed of sound is estimated to be smaller than ±2 m/s. The required data of pure components, at T ¼ 30 C, were taken from the literature (see Table 1). 4. Results and discussion The experimental data of densities of binary (water– saccharose and water–ethanol) and ternary (water–ethanol–saccharose) mixtures are given in Table 2. From Fig. 1a it can be seen that water–saccharose density agrees well with calculated ideal density. Nevertheless, important differences up to 10% appears in the water– ethanol system (Fig. 1e), which accord with the literature [14], showing the influence of the association
Table 3 Experimental values of ultrasonic velocity c of binary and ternary mixtures (water, saccharose, ethanol) at T ¼ 30 C, f ¼ 2 MHz Water–saccharose w2 (%) 0.00 c (m/s) 1509.1a
5.06 1522.5
10.05 1536.4
w2 (%) c (m/s)
45.04 1695.7
50.12 1728.5
Water–ethanol 10%–saccharose 0.00 5.38 w2 (%) c (m/s) 1569.2 1579.2
14.76 1551.5
19.57 1568.3
24.54 1589.0
30.07 1613.4
34.91 1638.6
34.91 1638.6
10.09 1589.4
13.99 1600.8
20.75 1620.7
24.98 1634.0
30.13 1655.3
35.03 1675.3
40.66 1699.9
Water–ethanol 20%–saccharose 0.00 5.32 w2 (%) c (m/s) 1609.8 1616.8
9.48 1624.4
14.76 1634.1
19.38 1644.9
24.70 1658.6
29.40 1674.5
35.11 1693.0
38.55 1709.0
Water–ethanol 30%–saccharose w2 (%) 0.00 5.08 c (m/s) 1595.4 1601.3
9.56 1607.9
14.80 1616.8
20.08 1627.4
24.69 1638.1
29.96 1652.3
35.04 1668.0
39.75 1685.9
Water–ethanol 0.00 w3 (%) c (m/s) 1509.1a
4.55 1537.3
8.50 1565.7
14.35 1594.6
18.70 1609.1
25.12 1607.4
29.38 1595.3
34.32 1571.7
34.32 1571.7
w3 (%) c (m/s)
44.76 1499.9
49.62 1466.1
a
39.96 1665.4
39.52 1538.6
Value from literature.
P. Resa et al. / Ultrasonics 43 (2005) 247–252
between water and ethanol molecules. Like water, ethanol has an -O-H group that is polarized so that the oxygen has a partial negative charge and the hydrogen has a partial positive charge. The hydrogen bonding network of water is disrupted by ethanol molecules, which are able to form hydrogen bonds with water molecules. Fig. 1b–d show experimental results of density corresponding to the ternary mixtures (water– ethanol–saccharose) at different initial ethanol concentration compared to those calculated from Eq. (7). A good agreement between the measured density and the semiempirical model proposed at any solute concentra-
Experimental From Eq. (8) From Eq. (9) From Eq. (10)
1800
1700
c (m/s)
c (m/s)
tion exists. In contrast, Fig. 1f shows experimental results of ternary mixtures (water–ethanol 20%–saccharose) compared to the conventional ideal density, from Eq. (1). The experimental data of ultrasonic velocity of binary (water–saccharose and water–ethanol) and ternary (water–ethanol–saccharose) mixtures are given in Table 3. Minimizing standard deviation, ultrasonic velocity in saccharose has been estimated from Fig. 2a for each model (7659 m/s for Urick’s model, 2196 m/s for NattaBaccaredda’s model and 2072 m/s for Nomoto’s model). The sound speed results evidence even more the
Experimental From Eq. (3) From Eq. (4) From Eq. (6)
1800
251
1700
1600
1600
1500
1500 0
20
40
0
60
20
Experimental From Eq. (8) From Eq. (9) From Eq. (10)
60
40
60
Experimental From Eq. (8) From Eq. (9) From Eq. (10)
1800
1700
c (m/s)
c (m/s)
1800
40
w2 (%)
w2 (%)
1600
1700
1600
1500
1500
0
20
40
60
0
20
w2 (%)
w2 (%)
1700
Experimental From Eq. (8) From Eq. (9) From Eq. (10)
1600
1700
c (m/s)
c (m/s)
1500
1400
Experimental From Eq. (3) From Eq. (4) From Eq. (6)
1800
1600
1300 1500
1200
1400
1100 0
20
40
60
w3 (%)
80
100
0
20
40
60
w2 (%)
Fig. 2. Ultrasonic velocity, c, in the binary and ternary mixtures: experimental and theoretical curves at T ¼ 30 C, f ¼ 2 MHz: (a) solvent: water, solute: saccharose; (b) solvent: water–ethanol 10%, solute: saccharose; (c) solvent: water–ethanol 20%, solute: saccharose; (d) solvent: water–ethanol 30%, solute: saccharose; (e) solvent: water, solute: ethanol; (f) solvent: water–ethanol 10%, solute: saccharose.
252
P. Resa et al. / Ultrasonics 43 (2005) 247–252
associated character of the water–ethanol system (Fig. 2e), and differences between these data and the theoretical prediction of different theoretical approaches are significant, specially for an ethanol mass concentration near 30%. Again these experimental results agree with other taken from the literature [5–7]. From this observation it is expected that theoretical models would not be valid for the ternary mixture either. This is clearly shown in Fig. 2f for an initial ethanol–water mass concentration of 10%. When velocities c13 and densities q13 of water–ethanol are taken from the experiments, and Eqs. (8)–(10) are applied, a different situation arises. Fig. 2b–d display these results, and a good fit between theory and experiments are obtained for low alcohol concentrations (up to 20%).
5. Conclusions Ultrasonic measurements are an accurate, non-invasive and on-line method to monitor the alcoholic fermentation process. Speed of sound can be used to deduce the concentration of the main components present during this reaction. Nevertheless, existing theories describing the density and sound velocity of liquid mixtures are not valid for associated liquids. This is the case in water– ethanol and water–saccharose–ethanol solutions. A semiempirical approach was proposed to avoid the deviation of the theories from the real values of density and sound velocity in the ternary mixture water–ethanol–saccharose. In this work, water–ethanol solution is considered as a solvent, whilst saccharose is considered
the solute. The experimental data of ultrasonic velocity and density of the ethanol–water system are used as the solvent input parameters for conventional theories describing the binary mixture behaviour. By this approximation, the theories considered predict densities and sound velocities of the ternary mixture fairly well for low alcohol concentrations (under 20%), which is in the range found in the alcoholic fermentation processes. Under these theoretical considerations, ultrasonic measurements can be related to the concentration of the main substances present in the fermentation.
References [1] T. Becker, M. Mitzscherling, A. Delgado, Eng. Life Sci. 1 (2) (2001) 61. [2] J.R. Urick, J. Appl. Phys. 18 (1947) 983. [3] G. Natta, M. Baccaredda, Atti Accad. Lincei Roma 4 (1948) 360. [4] O. Nomoto, J. Phys. Soc. Jpn. 13 (1958) 1528. [5] A. Giacomini, J. Acoust. Soc. Am. 19 (4) (1947) 701. [6] C.J. Burton, J. Acoust. Soc. Am. 20 (2) (1948) 186. [7] R. Parshad, J. Acoust. Soc. Am. 21 (3) (1949) 175. [8] M.R. Rao, J. Chem. Phys. 9 (1941) 682. [9] R. Nutsch-Kuhnkies, Acustica 15 (1965) 383. [10] D. Sette, Handbuck der Physik, Bol. XI/1, s. Fl€ ugge, SpringerVerlag, Berlin, 1961, p. 275. [11] G. Douheret, M.I. Davis, J.C.R. Reis, M.J. Blandamer, Chemphyschem 2 (2001) 148. [12] D.R. Lide, CRC Handbook of Chemistry and Physics, 83rd ed., 2002–2003. [13] N. Bilaniuk, G.S.K. Wong, J. Acoust. Soc. Am. 93 (3) (1993) 1609. [14] R.C. Weast, CRC Handbook of Chemistry and Physics, 67th ed., 1986–1987.
Ultrasonic velocity in water–ethanol–sucrose mixtures during alcoholic fermentation q P. Resa *, L. Elvira, F. Montero de Espinosa, Y. G omez-Ullate Dpto. Se~ nales, Sistemas y Tecnologıas Ultrasonicos, Instituto de Acustica (CSIC), c/. Serrano 144, 28006 Madrid, Spain Available online 6 July 2004
Abstract During alcoholic fermentation, sucrose and water are transformed into ethanol and carbon dioxide by the action of yeast enzymes. The measurement of the velocity of an ultrasonic pulse travelling through a fermentation tank can be used to characterize the state of the process. In this work, an experimental study of the density and ultrasonic velocity in the ternary mixture (water–ethanol– saccharose) is presented. Experimental results were compared to ideal density and to commonly used expressions of the sound velocity in liquid mixtures (Urick, Natta-Baccaredda and Nomoto). A semiempirical approach was proposed to improve the efficiency of theoretical models when dealing with mixtures of associated liquids. 2004 Elsevier B.V. All rights reserved. Keywords: Fermentation; Density; Ultrasonic Velocity; Ethanol; Water; Sucrose
1. Introduction The alcoholic fermentation induced by the presence of yeasts is a fundamental step in several biotechnological processes such as the production of alcoholic drinks, bread or pharmaceutical products. The optimisation of the process implies a reduction of costs for the industry. Ultrasonic techniques have been already proposed as a new method to determine the density during the elaboration of beer [1], which is the most important parameter to characterize the state of the reaction. Ultrasonics provide an appropriate (non-invasive, nondestructive, accuracy and non-expensive) on-line system to monitor the fermentation process. While the fermentation takes place in a water–saccharose solution, water and carbohydrates are transformed into ethanol and carbon dioxide by the yeast metabolism. Therefore, the liquid can be considered basically as a mixture of water, ethanol and saccharose (without considering carbon dioxide interferences). Changes in the concentration of these chemical components are accompanied
by the change of propagation velocity. In this work, experimental values of densities and speeds of sound in the binary mixtures (water–ethanol and water–saccharose) and in the ternary mixture (water–ethanol–saccharose) are reported. These results are also compared to theoretical approaches (Urick, Natta-Baccaredda and Nomoto) often used to model liquid mixtures [2–4]. It is shown that experimental results of density and sound speed for the ethanol–water mixture are not well described by these theories. It is established [5–7] that the deviation between the real sound speed and the theories is related to the formation of different associations between the molecules of the two liquids, which are often referred as associated liquids. A semiempirical approach based on the experimental data of the water–ethanol system is proposed to analyse the ternary mixture (water–ethanol–saccharose). The experimental results show a good fit with this model for low ethanol concentrations. Therefore, the model proposed constitutes a good alternative to calculate ultrasonic velocities in fermentation processes.
q
This article is based on a presentation given at the Ultrasonics International 2003. * Corresponding author. Tel.: +34-915-618806x051; fax: +34-914117651. E-mail address: [email protected] (P. Resa). 0041-624X/$ - see front matter 2004 Elsevier B.V. All rights reserved. doi:10.1016/j.ultras.2004.06.005
2. Theoretical Different approaches have been proposed for expressing ultrasonic velocity in binary mixtures.
248
P. Resa et al. / Ultrasonics 43 (2005) 247–252
Among the most commonly used are the relations of Urick [2], Natta-Baccaredda [3] and Nomoto [4]. The model developed by Urick for the study of liquid suspensions is based on a linear dependence of the density and the adiabatic compressibility with the volume concentration: X q¼ /i qi ð1Þ i
j¼
X
ð2Þ
/i ji
i
1 c ¼ qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi P P ffi / j / q i i i i i i
ð3Þ
Table 1 Literature data of pure substances at T ¼ 30 C q (kg/m3 ) M (g/mol) c (m/s)
Water
Ethanol
Saccharos
995.64a 18.02a 1509.144b
780.97a 46.07a 1145c
1546.79a 342.30a –
a
Data taken from [12]. Data taken from [13]. c Data estimated from [5]. b
where c is the sound velocity, j is the adiabatic compressibility, q is the density and / is the volume fraction. Natta and Baccaredda proposed 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: !1 X /i ð4Þ c¼ ci i On the other hand, Rao [8] found an empirical relation between sound velocity and molecular volume, valid for unassociated liquids: pffiffiffi ð5Þ V 3 c ¼ R const: where V is the molecular volume. Nomoto calculated this expression in a large number of mixtures, including those formed by associated components. He found that R have a linear form in many systems, !3 X 1=3 c¼ / i ci ð6Þ i
Table 2 Experimental values of density q of binary and ternary mixtures (water, saccharose, ethanol) at T ¼ 30 C Water–saccharose 0.00 w2 (%) q (kg/m3 ) 995
6.07 1018
10.31 1034
15.25 1054
20.93 1079
30.07 1121
39.76 1169
50.12 1222
100.00 1547a
Water–ethanol 5%–saccharose w2 (%) 0.00 4.95 985 1004 q (kg/m3 )
10.07 1025
15.11 1048
20.51 1070
30.55 1118
40.00 1159
50.10 1217
100.00 1547a
Water–ethanol 10%–saccharose 0.00 5.66 w2 (%) q (kg/m3 ) 978 1001
10.00 1016
16.32 1045
20.63 1064
30.55 1111
40.12 1158
50.00 1211
100.00 1547a
Water–ethanol 15%–saccharose w2 (%) 0.00 5.66 q (kg/m3 ) 970 994
9.91 1011
15.25 1037
20.32 1056
29.82 1101
39.76 1150
50.00 1204
100.00 1547a
Water–ethanol 20%–saccharose w2 (%) 0.00 5.66 963 984 q (kg/m3 )
9.91 1006
15.25 1026
20.32 1047
29.82 1096
39.76 1147
50.00 1202
100.00 1547a
Water–ethanol 30%–saccharose w2 (%) 0.00 5.00 q (kg/m3 ) 947 968
10.00 989
15.00 1009
20.00 1029
30.00 1080
40.00 1135
50.00 1191
100.00 1547a
Water–ethanol 40%–saccharose w2 (%) 0.00 5.21 q (kg/m3 ) 929 949
10.00 969
15.00 990
20.00 1013
30.00 1063
40.30 1115
– –
100.00 1547a
Water–ethanol 50%–saccharose 0.00 5.00 w2 (%) q (kg/m3 ) 906 924
10.00 949
15.00 971
20.00 993
30.00 1048
40.00 1103
– –
100.00 1547a
Water–ethanol w3 (%) 0.00 q (kg/m3 ) 995
10.00 978
15.00 970
20.00 963
30.00 947
40.00 929
50.00 907
100.00 781
a
Value from literature.
5.00 985
P. Resa et al. / Ultrasonics 43 (2005) 247–252
Nevertheless none of these approaches or other existing theories [9] have shown a general validity, and binary systems such as water–ethanol are badly described by them. Reviews of various proposals of ultrasonic speed can be found in references [10,11]. Water and ethanol are both associated liquids. When ethanol is added to water, different associations are established and practically destruction of water associations takes place. In this kind of mixtures, not only interaction forces between molecules of different liquids appears, but also interaction forces between molecules of the pure liquids are modified.
It is proposed in this work that the water–ethanol system can be assumed as a solvent in which saccharose is solved. Taking water–ethanol mixture values of density q13 and velocity c13 (which are dependant of their respective concentrations) from experimental measurements, the above models were applied considering the ternary mixture (water–ethanol–saccharose) like a binary mixture of saccharose in the water–ethanol solvent. Hence, the expression for density gives q ¼ /2 q2 þ ð1 /2 Þq13
Experimental From Eq. (7)
Experimental From Eq. (1) 1400
ρ (Kg/m3)
1400
1200
1200
1000
1000
0
20
40
60
80
0
100
20
40
60
80
100
60
80
100
60
80
100
w2 (%)
w2 (%) 1600
1600
Experimental From Eq. (7)
Experimental From Eq. (7)
1400
1400
ρ (Kg/m3)
ρ (Kg/m3)
ð7Þ
1600
1600
ρ (Kg/m3)
249
1200
1000
1200
1000
0
20
40
60
80
100
0
20
40
w2 (%)
w2 (%)
1600
Experimental From Eq. (1)
1000
Experimental From Eq. (1)
ρ (Kg/m3)
ρ (Kg/m3)
1400
900
1200
1000
800
0
20
40
60
w2 (%)
80
100
0
20
40
w2 (%)
Fig. 1. Density, q, of the binary and ternary mixtures at T ¼ 30 C: (a) solvent: water, solute: saccharose; (b) solvent: water–ethanol 10%, solute: saccharose; (c) solvent: water–ethanol 20%, solute: saccharose; (d) solvent: water–ethanol 30%, solute: saccharose; (e) solvent: water, solute: ethanol; (f) solvent: water–ethanol 20%, solute: saccharose.
250
P. Resa et al. / Ultrasonics 43 (2005) 247–252
Urick relation, 1 c ¼ pffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi ½/2 j2 þ ð1 /2 Þj13 ½/2 q2 þ ð1 /2 Þq13 Natta-Baccaredda relation,
1 /2 1 /2 þ c¼ c2 c13
ð8Þ
ð9Þ
and Nomoto relation, 1=3
1=3 3
c ¼ ð/2 c2 þ ð1 /2 Þc13 Þ
ð10Þ
where subscript 1, 2 and 3 correspond to water, saccharose and ethanol, respectively. 3. Experimental procedure Distilled water, ethanol (purities > 99.5%) and saccharose (purities > 99.7%) in different concentration were used to make the mixtures. Densities, q, were measured with an Anton Paar DMA 35 vibrating tube densimeter, with a ±0.5 · 103 g/cm3 resolution. Mass concentrations, w, were measured using a digital Sartorius 1216 MP balance with a ±0.05 g precision. The ultrasonic velocities, c, were measured using a transmission-through technique. The emitting and receiving transducers were made of a PZT 5A, 20 mm diameter, piezoelectric ceramic bonded to a Plexiglas plate. Araldite D was used as backing. The emitting transducer was excited with tone bursts at its resonant frequency, 2 MHz, which makes the ceramic vibrate in a thickness mode.
The solutions, mixed with a magnetic stirrer until complete dissolution, were put inside a 250 ml glass bottle, with a 64 mm inner diameter, and placed in a thermostatization water bath to keep the temperature of the sample constant at 30 C, with variations of the order of 0.01 C. Transducers were attached face to face at the sides of the glass bottle, also submerged in the bath. Received signals were digitalized and treated using a FFT algorithm to obtain the time of flight Ds, which is related to the propagation velocity by c0 c¼ ð11Þ c0 Ds 1þ d where c0 is the velocity in the pure solvent and d is the distance travelled by the ultrasonic pulses through the mixture corresponding to the inner diameter of the bottle. The uncertainty of speed of sound is estimated to be smaller than ±2 m/s. The required data of pure components, at T ¼ 30 C, were taken from the literature (see Table 1). 4. Results and discussion The experimental data of densities of binary (water– saccharose and water–ethanol) and ternary (water–ethanol–saccharose) mixtures are given in Table 2. From Fig. 1a it can be seen that water–saccharose density agrees well with calculated ideal density. Nevertheless, important differences up to 10% appears in the water– ethanol system (Fig. 1e), which accord with the literature [14], showing the influence of the association
Table 3 Experimental values of ultrasonic velocity c of binary and ternary mixtures (water, saccharose, ethanol) at T ¼ 30 C, f ¼ 2 MHz Water–saccharose w2 (%) 0.00 c (m/s) 1509.1a
5.06 1522.5
10.05 1536.4
w2 (%) c (m/s)
45.04 1695.7
50.12 1728.5
Water–ethanol 10%–saccharose 0.00 5.38 w2 (%) c (m/s) 1569.2 1579.2
14.76 1551.5
19.57 1568.3
24.54 1589.0
30.07 1613.4
34.91 1638.6
34.91 1638.6
10.09 1589.4
13.99 1600.8
20.75 1620.7
24.98 1634.0
30.13 1655.3
35.03 1675.3
40.66 1699.9
Water–ethanol 20%–saccharose 0.00 5.32 w2 (%) c (m/s) 1609.8 1616.8
9.48 1624.4
14.76 1634.1
19.38 1644.9
24.70 1658.6
29.40 1674.5
35.11 1693.0
38.55 1709.0
Water–ethanol 30%–saccharose w2 (%) 0.00 5.08 c (m/s) 1595.4 1601.3
9.56 1607.9
14.80 1616.8
20.08 1627.4
24.69 1638.1
29.96 1652.3
35.04 1668.0
39.75 1685.9
Water–ethanol 0.00 w3 (%) c (m/s) 1509.1a
4.55 1537.3
8.50 1565.7
14.35 1594.6
18.70 1609.1
25.12 1607.4
29.38 1595.3
34.32 1571.7
34.32 1571.7
w3 (%) c (m/s)
44.76 1499.9
49.62 1466.1
a
39.96 1665.4
39.52 1538.6
Value from literature.
P. Resa et al. / Ultrasonics 43 (2005) 247–252
between water and ethanol molecules. Like water, ethanol has an -O-H group that is polarized so that the oxygen has a partial negative charge and the hydrogen has a partial positive charge. The hydrogen bonding network of water is disrupted by ethanol molecules, which are able to form hydrogen bonds with water molecules. Fig. 1b–d show experimental results of density corresponding to the ternary mixtures (water– ethanol–saccharose) at different initial ethanol concentration compared to those calculated from Eq. (7). A good agreement between the measured density and the semiempirical model proposed at any solute concentra-
Experimental From Eq. (8) From Eq. (9) From Eq. (10)
1800
1700
c (m/s)
c (m/s)
tion exists. In contrast, Fig. 1f shows experimental results of ternary mixtures (water–ethanol 20%–saccharose) compared to the conventional ideal density, from Eq. (1). The experimental data of ultrasonic velocity of binary (water–saccharose and water–ethanol) and ternary (water–ethanol–saccharose) mixtures are given in Table 3. Minimizing standard deviation, ultrasonic velocity in saccharose has been estimated from Fig. 2a for each model (7659 m/s for Urick’s model, 2196 m/s for NattaBaccaredda’s model and 2072 m/s for Nomoto’s model). The sound speed results evidence even more the
Experimental From Eq. (3) From Eq. (4) From Eq. (6)
1800
251
1700
1600
1600
1500
1500 0
20
40
0
60
20
Experimental From Eq. (8) From Eq. (9) From Eq. (10)
60
40
60
Experimental From Eq. (8) From Eq. (9) From Eq. (10)
1800
1700
c (m/s)
c (m/s)
1800
40
w2 (%)
w2 (%)
1600
1700
1600
1500
1500
0
20
40
60
0
20
w2 (%)
w2 (%)
1700
Experimental From Eq. (8) From Eq. (9) From Eq. (10)
1600
1700
c (m/s)
c (m/s)
1500
1400
Experimental From Eq. (3) From Eq. (4) From Eq. (6)
1800
1600
1300 1500
1200
1400
1100 0
20
40
60
w3 (%)
80
100
0
20
40
60
w2 (%)
Fig. 2. Ultrasonic velocity, c, in the binary and ternary mixtures: experimental and theoretical curves at T ¼ 30 C, f ¼ 2 MHz: (a) solvent: water, solute: saccharose; (b) solvent: water–ethanol 10%, solute: saccharose; (c) solvent: water–ethanol 20%, solute: saccharose; (d) solvent: water–ethanol 30%, solute: saccharose; (e) solvent: water, solute: ethanol; (f) solvent: water–ethanol 10%, solute: saccharose.
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P. Resa et al. / Ultrasonics 43 (2005) 247–252
associated character of the water–ethanol system (Fig. 2e), and differences between these data and the theoretical prediction of different theoretical approaches are significant, specially for an ethanol mass concentration near 30%. Again these experimental results agree with other taken from the literature [5–7]. From this observation it is expected that theoretical models would not be valid for the ternary mixture either. This is clearly shown in Fig. 2f for an initial ethanol–water mass concentration of 10%. When velocities c13 and densities q13 of water–ethanol are taken from the experiments, and Eqs. (8)–(10) are applied, a different situation arises. Fig. 2b–d display these results, and a good fit between theory and experiments are obtained for low alcohol concentrations (up to 20%).
5. Conclusions Ultrasonic measurements are an accurate, non-invasive and on-line method to monitor the alcoholic fermentation process. Speed of sound can be used to deduce the concentration of the main components present during this reaction. Nevertheless, existing theories describing the density and sound velocity of liquid mixtures are not valid for associated liquids. This is the case in water– ethanol and water–saccharose–ethanol solutions. A semiempirical approach was proposed to avoid the deviation of the theories from the real values of density and sound velocity in the ternary mixture water–ethanol–saccharose. In this work, water–ethanol solution is considered as a solvent, whilst saccharose is considered
the solute. The experimental data of ultrasonic velocity and density of the ethanol–water system are used as the solvent input parameters for conventional theories describing the binary mixture behaviour. By this approximation, the theories considered predict densities and sound velocities of the ternary mixture fairly well for low alcohol concentrations (under 20%), which is in the range found in the alcoholic fermentation processes. Under these theoretical considerations, ultrasonic measurements can be related to the concentration of the main substances present in the fermentation.
References [1] T. Becker, M. Mitzscherling, A. Delgado, Eng. Life Sci. 1 (2) (2001) 61. [2] J.R. Urick, J. Appl. Phys. 18 (1947) 983. [3] G. Natta, M. Baccaredda, Atti Accad. Lincei Roma 4 (1948) 360. [4] O. Nomoto, J. Phys. Soc. Jpn. 13 (1958) 1528. [5] A. Giacomini, J. Acoust. Soc. Am. 19 (4) (1947) 701. [6] C.J. Burton, J. Acoust. Soc. Am. 20 (2) (1948) 186. [7] R. Parshad, J. Acoust. Soc. Am. 21 (3) (1949) 175. [8] M.R. Rao, J. Chem. Phys. 9 (1941) 682. [9] R. Nutsch-Kuhnkies, Acustica 15 (1965) 383. [10] D. Sette, Handbuck der Physik, Bol. XI/1, s. Fl€ ugge, SpringerVerlag, Berlin, 1961, p. 275. [11] G. Douheret, M.I. Davis, J.C.R. Reis, M.J. Blandamer, Chemphyschem 2 (2001) 148. [12] D.R. Lide, CRC Handbook of Chemistry and Physics, 83rd ed., 2002–2003. [13] N. Bilaniuk, G.S.K. Wong, J. Acoust. Soc. Am. 93 (3) (1993) 1609. [14] R.C. Weast, CRC Handbook of Chemistry and Physics, 67th ed., 1986–1987.