- Email: [email protected]
Ultrasonic monitoring of yoghurt formation by using AT-cut quartz: Lighting of casein micelles interactions process during the acidification
Ultrasonics 44 (2006) e875–e879 www.elsevier.com/locate/ultras
Ultrasonic monitoring of yoghurt formation by using AT-cut quartz: Lighting of casein micelles interactions process during the acidification C. Ould-Ehssein, S. Serfaty *, P. Griesmar, J.-Y. Le Hue´rou, E. Caplain, L. Martinez, N. Wilkie-Chancellier, M. Gindre Equipe Circuits Instrumentation et Mode´lisation en Electronique (E.C.I.M.E.), Universite´ de Cergy, Rue d’Eragny, Neuville sur Oise, 95031 Cergy Pontoise Cedex, France Available online 5 June 2006
Abstract The behavior of weak gels during their formation singularly attracts attention of dairy products factories. In our study we investigate acidified pre-heated milk gels formation that are fairly often used to product yoghurts. The gel formation requires a tight control of the first step of micelles modification process and the kinetics reaction parameters. The most current rheological parameters used to achieve the monitoring are the storage G 0 and the loss G00 shear moduli and the gelation time. The study of these parameters is commonly performed at very low frequencies (1 Hz). Our technique uses a 6 MHz AT-cut quartz crystal immersed in an acidified milk solution kept at a constant temperature. This method is singularly effective to ensure a complete and a reliable follow-up of the viscoelastic parameters of casein gels. A suitable new model enables a complete follow-up of the micelles evolution from the viscoelastic properties. The experimental results of the G 0 and G00 moduli versus temperature and versus glucono-d-lactone (GDL) added to milk are analyzed. In order to understand the micelles modifications, an analysis of the viscoelastic evolution try to explain the validity of the various models of micelles modification. In addition a new accurate kinetics characteristic time is proposed. This time corresponds to the moment for which the elastic effect of material becomes significant. From the kinetics study of casein gels at various temperatures, the Arrhenius relationship and a modified Flory–Stockmayer relationship give us access to the activation energy. By using the proposed technique and the suitable models developed, the structure thus quality of dairy products may be better controlled. Ó 2006 Elsevier B.V. All rights reserved. Keywords: Micro-rheology; Quartz; Ultrasound; Shear wave; Milk; Casein micelle
1. Introduction Dairy products like soft cheeses and yoghurts depend on a crucial first step of milk proteins gelation process. Several kinds of proteins are able to form different types of network structures depending on the gelation conditions such as pH, temperature or salinity. Acidification of milk by addition of acid precursors or through a microbial production of lactic acid is fairly often used to also understand the
*
Corresponding author. Tel.: +33 1 34 25 70 91; fax: +33 1 34 25 69 01. E-mail address: [email protected] (S. Serfaty).
0041-624X/$ - see front matter Ó 2006 Elsevier B.V. All rights reserved. doi:10.1016/j.ultras.2006.05.034
structure evolution process. It appears that the Horne model for the structure of casein micelle can be used to help explain unusual rheological behaviors that are observed during the gelation of milk proteins [1]. In acid-induced milk gels made under high incubation temperatures or high levels of acidulant there is a peak in the complex shear modulus G profile at the beginning of gelation state. The occurrence of this peak is explained as the result of solubilization of colloidal calcium phosphate (CCP) within and between casein micelles, which causes a weakening of the network structure. In order to monitor milk gelation process, different techniques such as electrical conductivity, electron microscopy,
C. Ould-Ehssein et al. / Ultrasonics 44 (2006) e875–e879
dynamic light scattering, or rheological monitoring have been reported in several reviews [2–5]. A dynamic rheological technique which measures the strain response to an applied low frequency sinusoidal stress (typically 102 to 10 Hz) is commonly used to monitor the evolution of the storage G 0 and loss G00 shear moduli (relative to elasticity and viscosity). However, the acidified milk gels in which the structure of the network is characterized by weak inter-particle interactions can be easily affected or even destroyed by the applied stress. Moreover because of its sensitivity range, this method cannot afford a complete study with a unique experimental setup when the viscosity strongly increases before reaching a plateau. To allow a complete monitoring of the gel formation, an ultrasonic method using a thickness shear mode (TSM) quartz resonator is chosen. The AT-cut quartz generates a shear deformation wave propagating through the material by its vibrating surface in contact [6]. In particular cases, such as low load, an equivalent Butterworth–Van Dyke (BVD) circuit with lumped elements can be used. With a suitable modified BVD model, this technique gives access to the complex shear modulus G of the viscoelastic layer in contact [7]. In this paper, this TSM quartz crystal technique is used to monitor closely the rheological evolution in the first step of the gelation process of acidified milk gels. Different gels performed by adding glucono-d-lactone (GDL-Merck Eurolab), are studied at several incubation temperatures. The viscoelastic parameters of these gels are deduced using a model taking into account the mass effect [8]. This model is modified to include the electrical evolution of the acidified milk and its electrical effects on the quartz response. In order to study the reaction kinetics of these gels, the rheological evolution during the gelation process has been studied for temperatures in range of 25–40 °C. An analysis of the results is made singularly in correlation with the structural behavior observed by other techniques during the acidification of milk.
2. Materials and methods 2.1. Milk and acidified gels Milk was reconstituted at 11% solid content (casein 33.3 g/kg ) with the same batch of a low-heat skim milk powder (WPNI = 8.0) (Ingredia, Arras, France) in MilliQ water. The milk is heat-treated in a spiral stainless at 90 °C for 10 min. Immediately after heating, the milk is cooled by immersion of the sample in water at the desired temperature. The yoghurt sets are performed by adding glucono-d-lactone (GDL). To reach pH values in the interval of 6.7–3.6, the GDL is adjusted for each sample at 13, 19.5 or 26 g/L. The kinetics of the pH decrease depends on the incubation temperature range (25–40 °C) as shown in Fig. 1.
6.5 6 5.5 25 ° C pH
e876
5 30 °C 4.5 40 ° C
4
37 °C
3.5 2000
4000
6000
8000
1 × 10
4
Time after GDL addition (s) Fig. 1. pH kinetics at 25, 30, 37, 40 °C.
2.2. TSM quartz crystal device The experimental setup is presented in Fig. 2. An ATcut quartz crystal sensor resonating at 6 MHz is loaded on one side by the acidified milk. The other side is in contact with air. The acidified milk and the quartz are held during the gelation at the desired temperature. The admittance of the quartz is measured within a 7 kHz bandwidth near the resonance frequency using a HP4195A network analyzer. In order to observe the gelation process, the total admittance of the quartz is saved every 30 s. The viscoelastic parameters are then computed on line using an appropriate model developed in our laboratory. Because of the high negative charges of casein micelles and the electrical properties evolution of the acidified gel, the quartz response is significantly modified. Fig. 3 shows some typical plots in the complex plane of the quartz admittance near the resonance frequency during the formation of the acidified milk gel. The evolution of the center position of the admittance circle shows that the modified Butterworth–Van Dyke (BVD) equivalent circuit model [9] cannot be directly used to characterize the shear modulus G. A more complete lumped element model of the loaded quartz, shown in Fig. 4 and including electrical layer effects should be used. The motional branch of the unperturbed quartz (i.e. in air) consists of a serial capacitance C1, inductance L1 and resistance R1 circuit. Two motional impedances are added when the acidified milk is in contact with the quartz. The first one, given by ZL, represents the viscoelastic effect of the milk gel. The second, Ze, includes the effects of the electrical characteristic evolution of the gel. The electrodes on both sides of the crystal plate induce an additional parallel static lossy capacitor C0 given by its impedance Z0. Starting with the three ports Mason model, the expression link-
C. Ould-Ehssein et al. / Ultrasonics 44 (2006) e875–e879
e877
ing the mechanical impedance Zs on the quartz surface and ZL remains then unchanged
Gel phase
-3
3 ×10
ZL ¼ Gelation process
Imaginary part of admittance (S)
Fig. 2. Experimental setup.
-3
2.6 ×10
-3
2.2 ×10
Liquid phase -3
1.8 ×10 -3 3.6 ×10
-3
4 ×10
-3
4.4 ×10
-3
4.8 ×10
Real part of admittance (S) Fig. 3. Real and imaginary part of the total admittance of quartz.
1 ZS 8K f0 C 0 Z q 2
ð1Þ
where Zq is the mechanical impedance of unperturbed quartz, f0 is the fundamental motional resonance frequency, and K2 is the complex electromechanical coupling factor for quartz. For a semi-infinite layer without mass loading effect and without electrical effects, Zs can be related to the complex shear modulus G [7]. Assuming that for our setup the evaporation during the milk gel process is negligible, we can consider that both density and mass effect of the gel remains constant. Consequently, without the mass effect, the ZL expression becomes: "rffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi rffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi!# qðj G j þG0 Þ qðjGj G0 Þ ZL / þj ð2Þ 2 2 where q is the density of the layer and G its complex shear modulus (G = G 0 + jG00 ). 3. Results and discussion 3.1. General results and reaction kinetics
Fig. 4. Lumped element circuit including electrical variation of layer.
The damping effect due to the milk gel loading is shown on Fig. 3. The decrease of the admittance circle radius proves the increase of the additional impedance ZL in the motional branch. This shows that the device detects the evolution of the layer’s viscoelastic parameters. Note that the resonance frequency is also modified by the gel evolution at the same time. From this typical evolution and using the model shown in Fig. 4 the real and imaginary part of ZL (respectively R and X) can be extracted. The evolution of R and X during the gelation process gives access to the storage and loss moduli from Eq. (2). The
C. Ould-Ehssein et al. / Ultrasonics 44 (2006) e875–e879
Real and imaginary parts of shear modulus (Pa)
e878
Table 1 Apparent activation energy of gelation processes for three GDL concentrations
3 ×10 5
G"
2.5 ×105
[GDL]
13 g/L
19.5 g/L
26 g/L
Ea(kJ/mol)
101.6
87.8
80.7
2 ×10 5 5
1.5 × 10
1× 10 5
G'
5 × 10 4
0
0
100
200
300
400
500
Time (min.)
GDL concentration increases. A control of the viscoelastic time tvs during the gelation processes confirms these observations (Fig. 6). If the aggregation is kinetically controlled the reaction velocity can be linked to the apparent activation energy Ea according to the Arrhenius relationship. In addition with the Flory–Stockmayer theory a simple kinetic equation using the viscoelastic time can be derived [11]. The apparent activation energy found for GDL concentrations of 13, 19.5 and 26 g/L is given in Table 1. The values are in good agreement with the known activation energy of milk gelation.
Fig. 5. Typical evolution of G 0 and G00 .
3.2. Unusual detection of initial rheological behavior However, for a GDL content of 26 g/L other stages at the beginning of the gel’s formation are clearly detected. These stages are singularly characterized by a local G 0 maximum before reaching to a plateau. In order to highlight this phenomena, the loss tangent defined by tan(d) = G00 / G 0 is used. Indeed, tan(d) is sensitive to any slopes shift of dynamic (storage and loss) moduli. Fig. 7 shows that, at the beginning of the gelation, a clear minimum of tan(d) is observed. Note that tvs corresponds to the moment when tan(d) strongly decreases. This unusual rheological behavior was already observed in reviews [1,12,13]. This G 0 peak was interpreted as a partial loosening of bonds within and between casein micelles due to the solubilization of colloidal calcium phosphate (CCP) occurring for pH < 5.8. Assuming that the gel stability depends on milk acidification, tan(d) is plotted as a function of pH (Fig. 8). One can
40
Loss tangent G"/G' (tan δ)
typical evolution of G 0 and G00 observed for the yoghurt processes is presented in Fig. 5. These typical shapes show that two stages can be clearly distinguished. At the first one G 0 = 0 (R X) and no changes are observed. The acidified milk is in the sol phase. The acidification effect to casein micelles is not significant. At the second stage (R > X), after a viscoelastic time tvs (from which R and X becomes different) both G 0 and G00 start rising significantly. This stage corresponding to the gel phase indicates that acidification induces the formation of a three-dimensional casein micelles network. These results are in good agreement with general knowledge on the formation of acidified casein gels [10]. In order to study the gelation process, the temperature and the GDL concentration are modified. These two parameters strongly influence the reaction and the behavior of interaction of colloid particles. As a general shape, we note an acceleration of the gelation process when the temperature increases. The same effect is observed when the
30
40 °C
20
37 °C 10
30 °C
25 °C
0 0 Fig. 6. Evolution of tvs as a function of temperature and GDL concentration.
2000 4000 6000 Time after addition of GDL (s)
8000
Fig. 7. Beginning of gelation process: rheological behaviour.
C. Ould-Ehssein et al. / Ultrasonics 44 (2006) e875–e879
mer growth. Upon acidification, the net negative charge is lowered, resulting in the decrease in both electrostatic repulsion and steric stabilization, which are both largely responsible for micelle stability. For a pH less than 5, the stability cannot be ensured which implies a reorganization of the casein micelles to form the final milk gel (yoghurt). These results are confirmed by scanning electron microscopy [14].
40
Loss tangent G"/G' (tan δ)
35 30
40 °C
25 20
37 °C
15 10
e879
4. Conclusions
30 °C
observe that for any incubation temperature the minimum of tan(d) occurs when the pH reaches 5.3. In comparison with Fig. 7 the kinetics of acidified milk gelation mainly depends on the pH. That is why the reaction kinetics will be indirectly affected by the GDL concentration and the temperature.
The TSM quartz device allows the measurement of viscoelastic parameters in a large dynamical range. For acidified milk gels, a new model including electrical properties variation is required to extract the viscoelastic parameters. Compared with the classical rheological method, our quartz device allows the monitoring of the entire reaction with a unique device. From the temporal evolution of the storage G 0 and loss G00 moduli and using tan(d), this technique gives access to an unusual viscoelastic behavior at the beginning of the gelation process. This result has been compared, with a good agreement, to similar behavior observed with classical rheological measurement. The correlation with scanning electron microscopy results can help in explaining the structural changes of casein micelles and proves that our technique can monitor on line these changes.
3.3. Correlation with the microstructure
Acknowledgement
Correlation between microstructural and rheological changes during milk acidification can help to explain the different steps of the gel’s structure formation observed in Fig. 7 [14]. Due to the importance of casein micelles for the functional behavior the nature and structure of these micelles have been extensively studied and presented in a concise review [15]. However, the exact structure of casein micelles is still under debate. Up to date, the Horne model is the only one explaining the observed behavior [16]. It describes the internal structure and specifies the aggregation mode of the different caseins as a function of pH including two main features: the cementing role of colloidal calcium phosphate (CCP) and the surface location of hairy layer of j-casein. In the first step observed in Fig. 7 (pH 6– 5), the charged j-casein hairs on the micelle surface provide a stabilizing layer including both steric and electrostatic contributions. This model suggests that the proteins in a casein micelles are bound together by two types of forces and that there is a balance between the attractive hydrophobic interactions and electrostatic repulsion. Hydrophobic attraction is the driving force for the formation of casein micelles, while electrostatic repulsion limits the poly-
Special thanks to Denis Paquet of Danone Corporation for the GDL and skim milk products.
5 0 5.8
25 °C 5.6
5.4
5.2
5
4.8
4.6
4.4
pH Fig. 8. Loss tangent versus pH.
References [1] D.S. Horne, in: E. Dickinson, R. Miller, (Eds.), Food Colloids Fundamentals of Formulation, Royal Society of Chemistry, Cambridge, pp. 345–351. [2] J. Thomasow, E. Voss, IDF Bulletin, Brussels 99 (1977). [3] M.L. Green et al., J. Dairy. Res. 45 (1978) 413–422. [4] P. Walstra et al., Biochim. Biophys. Acta. 669 (1981) 258–259. [5] S. Blair, J.C. Osthuizen, J. Dairy Res. 28 (1961) 165–173. [6] R.W. Cernosek et al., IEEE Trans. Ultrason. Ferroelectr. Freq. Control 45 (1998) 1399–1407. [7] H.L. Bandey et al., Anal. Chem. 71 (1999) 2205–2214. [8] S.J. Martin, Sens. Actuators A 44 (1994) 209. [9] S.J. Martin et al., Anal. Chem. 63 (1991) 2272–2281. [10] V.A. Buckin, E. Kudryashov, Adv. Colloid Interf. Sci. 89–90 (2001) 401–422. [11] C. Ould Ehssein et al., IEEE UFFC Ultrason. Symp. 319–322 (2004). [12] J.A. Lucey et al., J. Text. Stud. 29 (1998) 413–426. [13] A. Laligant, Lait 83 (2003) 181–192. [14] E. Gastaldi et al., J. Food Sci. 61 (1) (1996) 59–65. [15] C. Phandengath, J. Sci. Technol. 27 (1) (2005) 201–212. [16] D.S. Horne, Int. Dairy J. 8 (1998) 171–177.
Ultrasonic monitoring of yoghurt formation by using AT-cut quartz: Lighting of casein micelles interactions process during the acidification C. Ould-Ehssein, S. Serfaty *, P. Griesmar, J.-Y. Le Hue´rou, E. Caplain, L. Martinez, N. Wilkie-Chancellier, M. Gindre Equipe Circuits Instrumentation et Mode´lisation en Electronique (E.C.I.M.E.), Universite´ de Cergy, Rue d’Eragny, Neuville sur Oise, 95031 Cergy Pontoise Cedex, France Available online 5 June 2006
Abstract The behavior of weak gels during their formation singularly attracts attention of dairy products factories. In our study we investigate acidified pre-heated milk gels formation that are fairly often used to product yoghurts. The gel formation requires a tight control of the first step of micelles modification process and the kinetics reaction parameters. The most current rheological parameters used to achieve the monitoring are the storage G 0 and the loss G00 shear moduli and the gelation time. The study of these parameters is commonly performed at very low frequencies (1 Hz). Our technique uses a 6 MHz AT-cut quartz crystal immersed in an acidified milk solution kept at a constant temperature. This method is singularly effective to ensure a complete and a reliable follow-up of the viscoelastic parameters of casein gels. A suitable new model enables a complete follow-up of the micelles evolution from the viscoelastic properties. The experimental results of the G 0 and G00 moduli versus temperature and versus glucono-d-lactone (GDL) added to milk are analyzed. In order to understand the micelles modifications, an analysis of the viscoelastic evolution try to explain the validity of the various models of micelles modification. In addition a new accurate kinetics characteristic time is proposed. This time corresponds to the moment for which the elastic effect of material becomes significant. From the kinetics study of casein gels at various temperatures, the Arrhenius relationship and a modified Flory–Stockmayer relationship give us access to the activation energy. By using the proposed technique and the suitable models developed, the structure thus quality of dairy products may be better controlled. Ó 2006 Elsevier B.V. All rights reserved. Keywords: Micro-rheology; Quartz; Ultrasound; Shear wave; Milk; Casein micelle
1. Introduction Dairy products like soft cheeses and yoghurts depend on a crucial first step of milk proteins gelation process. Several kinds of proteins are able to form different types of network structures depending on the gelation conditions such as pH, temperature or salinity. Acidification of milk by addition of acid precursors or through a microbial production of lactic acid is fairly often used to also understand the
*
Corresponding author. Tel.: +33 1 34 25 70 91; fax: +33 1 34 25 69 01. E-mail address: [email protected] (S. Serfaty).
0041-624X/$ - see front matter Ó 2006 Elsevier B.V. All rights reserved. doi:10.1016/j.ultras.2006.05.034
structure evolution process. It appears that the Horne model for the structure of casein micelle can be used to help explain unusual rheological behaviors that are observed during the gelation of milk proteins [1]. In acid-induced milk gels made under high incubation temperatures or high levels of acidulant there is a peak in the complex shear modulus G profile at the beginning of gelation state. The occurrence of this peak is explained as the result of solubilization of colloidal calcium phosphate (CCP) within and between casein micelles, which causes a weakening of the network structure. In order to monitor milk gelation process, different techniques such as electrical conductivity, electron microscopy,
C. Ould-Ehssein et al. / Ultrasonics 44 (2006) e875–e879
dynamic light scattering, or rheological monitoring have been reported in several reviews [2–5]. A dynamic rheological technique which measures the strain response to an applied low frequency sinusoidal stress (typically 102 to 10 Hz) is commonly used to monitor the evolution of the storage G 0 and loss G00 shear moduli (relative to elasticity and viscosity). However, the acidified milk gels in which the structure of the network is characterized by weak inter-particle interactions can be easily affected or even destroyed by the applied stress. Moreover because of its sensitivity range, this method cannot afford a complete study with a unique experimental setup when the viscosity strongly increases before reaching a plateau. To allow a complete monitoring of the gel formation, an ultrasonic method using a thickness shear mode (TSM) quartz resonator is chosen. The AT-cut quartz generates a shear deformation wave propagating through the material by its vibrating surface in contact [6]. In particular cases, such as low load, an equivalent Butterworth–Van Dyke (BVD) circuit with lumped elements can be used. With a suitable modified BVD model, this technique gives access to the complex shear modulus G of the viscoelastic layer in contact [7]. In this paper, this TSM quartz crystal technique is used to monitor closely the rheological evolution in the first step of the gelation process of acidified milk gels. Different gels performed by adding glucono-d-lactone (GDL-Merck Eurolab), are studied at several incubation temperatures. The viscoelastic parameters of these gels are deduced using a model taking into account the mass effect [8]. This model is modified to include the electrical evolution of the acidified milk and its electrical effects on the quartz response. In order to study the reaction kinetics of these gels, the rheological evolution during the gelation process has been studied for temperatures in range of 25–40 °C. An analysis of the results is made singularly in correlation with the structural behavior observed by other techniques during the acidification of milk.
2. Materials and methods 2.1. Milk and acidified gels Milk was reconstituted at 11% solid content (casein 33.3 g/kg ) with the same batch of a low-heat skim milk powder (WPNI = 8.0) (Ingredia, Arras, France) in MilliQ water. The milk is heat-treated in a spiral stainless at 90 °C for 10 min. Immediately after heating, the milk is cooled by immersion of the sample in water at the desired temperature. The yoghurt sets are performed by adding glucono-d-lactone (GDL). To reach pH values in the interval of 6.7–3.6, the GDL is adjusted for each sample at 13, 19.5 or 26 g/L. The kinetics of the pH decrease depends on the incubation temperature range (25–40 °C) as shown in Fig. 1.
6.5 6 5.5 25 ° C pH
e876
5 30 °C 4.5 40 ° C
4
37 °C
3.5 2000
4000
6000
8000
1 × 10
4
Time after GDL addition (s) Fig. 1. pH kinetics at 25, 30, 37, 40 °C.
2.2. TSM quartz crystal device The experimental setup is presented in Fig. 2. An ATcut quartz crystal sensor resonating at 6 MHz is loaded on one side by the acidified milk. The other side is in contact with air. The acidified milk and the quartz are held during the gelation at the desired temperature. The admittance of the quartz is measured within a 7 kHz bandwidth near the resonance frequency using a HP4195A network analyzer. In order to observe the gelation process, the total admittance of the quartz is saved every 30 s. The viscoelastic parameters are then computed on line using an appropriate model developed in our laboratory. Because of the high negative charges of casein micelles and the electrical properties evolution of the acidified gel, the quartz response is significantly modified. Fig. 3 shows some typical plots in the complex plane of the quartz admittance near the resonance frequency during the formation of the acidified milk gel. The evolution of the center position of the admittance circle shows that the modified Butterworth–Van Dyke (BVD) equivalent circuit model [9] cannot be directly used to characterize the shear modulus G. A more complete lumped element model of the loaded quartz, shown in Fig. 4 and including electrical layer effects should be used. The motional branch of the unperturbed quartz (i.e. in air) consists of a serial capacitance C1, inductance L1 and resistance R1 circuit. Two motional impedances are added when the acidified milk is in contact with the quartz. The first one, given by ZL, represents the viscoelastic effect of the milk gel. The second, Ze, includes the effects of the electrical characteristic evolution of the gel. The electrodes on both sides of the crystal plate induce an additional parallel static lossy capacitor C0 given by its impedance Z0. Starting with the three ports Mason model, the expression link-
C. Ould-Ehssein et al. / Ultrasonics 44 (2006) e875–e879
e877
ing the mechanical impedance Zs on the quartz surface and ZL remains then unchanged
Gel phase
-3
3 ×10
ZL ¼ Gelation process
Imaginary part of admittance (S)
Fig. 2. Experimental setup.
-3
2.6 ×10
-3
2.2 ×10
Liquid phase -3
1.8 ×10 -3 3.6 ×10
-3
4 ×10
-3
4.4 ×10
-3
4.8 ×10
Real part of admittance (S) Fig. 3. Real and imaginary part of the total admittance of quartz.
1 ZS 8K f0 C 0 Z q 2
ð1Þ
where Zq is the mechanical impedance of unperturbed quartz, f0 is the fundamental motional resonance frequency, and K2 is the complex electromechanical coupling factor for quartz. For a semi-infinite layer without mass loading effect and without electrical effects, Zs can be related to the complex shear modulus G [7]. Assuming that for our setup the evaporation during the milk gel process is negligible, we can consider that both density and mass effect of the gel remains constant. Consequently, without the mass effect, the ZL expression becomes: "rffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi rffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi!# qðj G j þG0 Þ qðjGj G0 Þ ZL / þj ð2Þ 2 2 where q is the density of the layer and G its complex shear modulus (G = G 0 + jG00 ). 3. Results and discussion 3.1. General results and reaction kinetics
Fig. 4. Lumped element circuit including electrical variation of layer.
The damping effect due to the milk gel loading is shown on Fig. 3. The decrease of the admittance circle radius proves the increase of the additional impedance ZL in the motional branch. This shows that the device detects the evolution of the layer’s viscoelastic parameters. Note that the resonance frequency is also modified by the gel evolution at the same time. From this typical evolution and using the model shown in Fig. 4 the real and imaginary part of ZL (respectively R and X) can be extracted. The evolution of R and X during the gelation process gives access to the storage and loss moduli from Eq. (2). The
C. Ould-Ehssein et al. / Ultrasonics 44 (2006) e875–e879
Real and imaginary parts of shear modulus (Pa)
e878
Table 1 Apparent activation energy of gelation processes for three GDL concentrations
3 ×10 5
G"
2.5 ×105
[GDL]
13 g/L
19.5 g/L
26 g/L
Ea(kJ/mol)
101.6
87.8
80.7
2 ×10 5 5
1.5 × 10
1× 10 5
G'
5 × 10 4
0
0
100
200
300
400
500
Time (min.)
GDL concentration increases. A control of the viscoelastic time tvs during the gelation processes confirms these observations (Fig. 6). If the aggregation is kinetically controlled the reaction velocity can be linked to the apparent activation energy Ea according to the Arrhenius relationship. In addition with the Flory–Stockmayer theory a simple kinetic equation using the viscoelastic time can be derived [11]. The apparent activation energy found for GDL concentrations of 13, 19.5 and 26 g/L is given in Table 1. The values are in good agreement with the known activation energy of milk gelation.
Fig. 5. Typical evolution of G 0 and G00 .
3.2. Unusual detection of initial rheological behavior However, for a GDL content of 26 g/L other stages at the beginning of the gel’s formation are clearly detected. These stages are singularly characterized by a local G 0 maximum before reaching to a plateau. In order to highlight this phenomena, the loss tangent defined by tan(d) = G00 / G 0 is used. Indeed, tan(d) is sensitive to any slopes shift of dynamic (storage and loss) moduli. Fig. 7 shows that, at the beginning of the gelation, a clear minimum of tan(d) is observed. Note that tvs corresponds to the moment when tan(d) strongly decreases. This unusual rheological behavior was already observed in reviews [1,12,13]. This G 0 peak was interpreted as a partial loosening of bonds within and between casein micelles due to the solubilization of colloidal calcium phosphate (CCP) occurring for pH < 5.8. Assuming that the gel stability depends on milk acidification, tan(d) is plotted as a function of pH (Fig. 8). One can
40
Loss tangent G"/G' (tan δ)
typical evolution of G 0 and G00 observed for the yoghurt processes is presented in Fig. 5. These typical shapes show that two stages can be clearly distinguished. At the first one G 0 = 0 (R X) and no changes are observed. The acidified milk is in the sol phase. The acidification effect to casein micelles is not significant. At the second stage (R > X), after a viscoelastic time tvs (from which R and X becomes different) both G 0 and G00 start rising significantly. This stage corresponding to the gel phase indicates that acidification induces the formation of a three-dimensional casein micelles network. These results are in good agreement with general knowledge on the formation of acidified casein gels [10]. In order to study the gelation process, the temperature and the GDL concentration are modified. These two parameters strongly influence the reaction and the behavior of interaction of colloid particles. As a general shape, we note an acceleration of the gelation process when the temperature increases. The same effect is observed when the
30
40 °C
20
37 °C 10
30 °C
25 °C
0 0 Fig. 6. Evolution of tvs as a function of temperature and GDL concentration.
2000 4000 6000 Time after addition of GDL (s)
8000
Fig. 7. Beginning of gelation process: rheological behaviour.
C. Ould-Ehssein et al. / Ultrasonics 44 (2006) e875–e879
mer growth. Upon acidification, the net negative charge is lowered, resulting in the decrease in both electrostatic repulsion and steric stabilization, which are both largely responsible for micelle stability. For a pH less than 5, the stability cannot be ensured which implies a reorganization of the casein micelles to form the final milk gel (yoghurt). These results are confirmed by scanning electron microscopy [14].
40
Loss tangent G"/G' (tan δ)
35 30
40 °C
25 20
37 °C
15 10
e879
4. Conclusions
30 °C
observe that for any incubation temperature the minimum of tan(d) occurs when the pH reaches 5.3. In comparison with Fig. 7 the kinetics of acidified milk gelation mainly depends on the pH. That is why the reaction kinetics will be indirectly affected by the GDL concentration and the temperature.
The TSM quartz device allows the measurement of viscoelastic parameters in a large dynamical range. For acidified milk gels, a new model including electrical properties variation is required to extract the viscoelastic parameters. Compared with the classical rheological method, our quartz device allows the monitoring of the entire reaction with a unique device. From the temporal evolution of the storage G 0 and loss G00 moduli and using tan(d), this technique gives access to an unusual viscoelastic behavior at the beginning of the gelation process. This result has been compared, with a good agreement, to similar behavior observed with classical rheological measurement. The correlation with scanning electron microscopy results can help in explaining the structural changes of casein micelles and proves that our technique can monitor on line these changes.
3.3. Correlation with the microstructure
Acknowledgement
Correlation between microstructural and rheological changes during milk acidification can help to explain the different steps of the gel’s structure formation observed in Fig. 7 [14]. Due to the importance of casein micelles for the functional behavior the nature and structure of these micelles have been extensively studied and presented in a concise review [15]. However, the exact structure of casein micelles is still under debate. Up to date, the Horne model is the only one explaining the observed behavior [16]. It describes the internal structure and specifies the aggregation mode of the different caseins as a function of pH including two main features: the cementing role of colloidal calcium phosphate (CCP) and the surface location of hairy layer of j-casein. In the first step observed in Fig. 7 (pH 6– 5), the charged j-casein hairs on the micelle surface provide a stabilizing layer including both steric and electrostatic contributions. This model suggests that the proteins in a casein micelles are bound together by two types of forces and that there is a balance between the attractive hydrophobic interactions and electrostatic repulsion. Hydrophobic attraction is the driving force for the formation of casein micelles, while electrostatic repulsion limits the poly-
Special thanks to Denis Paquet of Danone Corporation for the GDL and skim milk products.
5 0 5.8
25 °C 5.6
5.4
5.2
5
4.8
4.6
4.4
pH Fig. 8. Loss tangent versus pH.
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