Sensor and method for monitoring the change in the viscoelastic properties of a material

Abstract

The invention relates to a sensor for measuring the viscoelastic properties of a material, the sensor comprising a rigid support (10) and a membrane (11) attached to the support (10), wherein the material is intended to come into contact with an outer surface (111) of the membrane (11). The sensor further comprises an active assembly (12) comprising at least one piezoelectric element bonded to the inner face of the membrane (11), wherein the active assembly (12) is configured to cause the membrane (11) to oscillate in a resonant mode. The invention also relates to a method for measuring the viscoelastic properties of a material and to a method for monitoring the coagulation of milk using such a sensor.

Description

Sensor and method for monitoring the evolution of the viscoelastic properties of a material Technical field [1] The invention relates to a sensor dedicated to monitoring the evolution of the viscoelastic characteristics of a material. It also relates to a method for monitoring the evolution of the viscoelastic properties of a material, in particular milk in the coagulation phase. Prior art [2] Among the key stages of cheese making, milk coagulation is of particular interest to professionals. This stage consists of transforming the milk into a gel, the curdled milk, thanks to the action of a coagulating agent. This coagulation stage requires special attention. Indeed, the cheesemaker must make a multitude of observations at short and regular intervals to be able to detect the change in state of the milk and the evolution of the firmness of the gel thus formed. This transition will have an impact on all the stages that follow, such as cutting the gel, draining, acidification or even ripening and finally on the quality of the finished product. Consequently, during the milk coagulation stage, the cheesemaker must detect certain parameters that are essential such as: • measuring the setting time when transforming milk into gel, • the measurement of an optimal value of gel firmness corresponding to the moment of cutting this gel, this optimum being a function of the type of cheese technology. [3] The characterization of milk during its processing thus plays a key role. It is therefore necessary to propose instrumentation integrating a sensor adapted to the production conditions. [4] Different methods exist for simultaneously measuring the coagulation time and the gel properties. A technique commonly used in the field of dairy products is implemented by a device called "Formagraph". This device, designed in the early 1980s, sets a container containing the product being coagulated in motion and measures the transmission of this movement to a rod suspended in the liquid. The more viscous and gel-like the product becomes, the more movement is transmitted to the rod. Document FR 2 991 771 A1 uses this technique, perfecting the way of measuring the movement on the rod. [5] This method of measurement is unsatisfactory because it is necessary to take samples of the milk and the coagulation occurs in a separate volume from that in which the cheese is formed, with therefore potentially variations in ambient conditions. The coagulation conditions are therefore not identical, in particular the temperature may be different so that the coagulation of the sample does not necessarily represent the coagulation of the milk in the vat. [6] The same defects are found with the device described by document US 9,494,475 Bl. [7] The paper “PZN-PT based smart probe for high temperature fluid viscosity measurements” published by Chen Zhang et al in 2016 in Elsevier, Measurement 94 (2016) 753-758, shows a measurement technique with a plunger, which is set in oscillation. A piezoelectric cell is glued to the plunger with epoxy resin. The plunger allows access to the viscosity properties of the liquid in which the tip of the plunger is placed. The physical layout of the plunger does not allow the sensor to be placed in an interesting position for real-time monitoring of milk coagulation. Statement of the invention [8] The invention aims to provide a sensor and a method for monitoring the evolution of the viscoelastic properties of a material in situ. [9] With these objectives in view, the invention relates to a sensor for measuring the viscoelastic properties of a material comprising a rigid support and a membrane fixed to the support, the material being intended to come into contact on an external face of the membrane. The sensor further comprises an active assembly with at least one piezoelectric element bonded to the internal face of the membrane. The latter has on its external face a wettability characterized by a contact angle of a drop of distilled water of 1 pL less than 20°, preferably less than 10°. By providing a sensor having a membrane which can be in contact with the material to be measured, the sensor can be placed directly in contact with the material. It is therefore possible to directly monitor the evolution of the material in its container without having to take a sample.By choosing a good wettability of the membrane, the reproducibility of the measurements is guaranteed, including depending on variations in the quality of the material.

[0010] According to a constructive arrangement, the active assembly is configured to generate the oscillation of the membrane according to a resonance mode greater than or equal to the second resonance mode of the membrane. The first resonance mode of a membrane, or fundamental mode, is a mode in which, when looking at a section from one side of the membrane to the other, the formation of a single maximum displacement between the two anchor points of the membrane on the support. The second resonance mode is characterized by the simultaneous presence of two displacement maxima on the membrane. The use of a resonance mode greater than or equal to the second resonance mode of the membrane allows interaction of the membrane and the material with movements of lesser amplitude than with the first resonance mode. The inventors found that with such a resonance mode, the damping of the movement was less, whereas with the first resonance mode, the damping was such that measurements became difficult, or even insignificant. The inventors also found that the characteristics of the resonance mode evolved according to the properties of the material. Knowledge of the characteristics of the resonance mode thus makes it possible to access the properties of the material.

[0011] According to a constructive arrangement, the membrane has the shape of a disc embedded by its periphery on the support. This shape is simple to produce and has shown good results. It also makes it possible to obtain a waterproof and resistant sensor.

[0012] According to a constructive arrangement, the active assembly only partially covers the inner face of the membrane. The addition of piezoelectric elements to the membrane surface stiffens it. By minimizing the surface occupied by the piezoelectric elements, the increase in membrane rigidity is also minimized, which allows for greater agreement with the frequencies that can be used to characterize the material.

[0013] According to one embodiment, the membrane has a center and the active assembly is off-center on said internal face. By having an active assembly off-center relative to the center of the membrane, the appearance of an operating mode superior to the fundamental resonance mode is favored. This increases the sensitivity of the sensor.

[0014] According to one embodiment, the active element is arranged to generate differential oscillations of the membrane. By generating differential oscillations is meant the act of moving the membrane in one direction at one location and in an opposite direction at another location. The generation of differential oscillations directly forces the membrane into a particular resonance mode.

[0015] It was found that when the outer surface had low wettability, measurements could be unreliable under certain conditions. The inventors believe this may be due to poor coupling between the fluid and the membrane. By working the surface to improve wettability, they found that these effects no longer occurred.

[0016] According to a constructive arrangement, the external face of the membrane has a coating to improve wettability. The addition of a coating makes it possible to maintain the elasticity of the membrane, while controlling the wettability properties.

[0017] According to one embodiment, the coating is chosen from a polymer coating, a silicon oxide deposit or an epoxy resin incorporating or not titanium oxide nanoparticles. A coating with silicon oxide is for example obtained from a precursor, tetraethyl orthosilicate.

[0018] According to an improvement, the coating is a deposit of nanoparticles comprising between 25 and 60%, preferably between 25 and 35%, in molar ratio of titanium oxide and the remainder in silicon oxide. The best results have been obtained with these characteristics.

[0019] According to one embodiment, the sensor is intended for use in monitoring milk coagulation. The sensor may be of dimensions adapted to this measurement and to environmental constraints, particularly hygiene. It may be used in the manufacture of any type of dairy product.

[0020] According to one embodiment, the sensor is intended for use in monitoring cheese production. The sensor can in fact be involved in monitoring production and in decision-making, particularly regarding the time of implementation of certain operations.

[0021] The invention also relates to a method for measuring the viscoelastic properties of a material, characterized in that a sensor as described above is used, the material is placed in contact with the external face of the membrane and the electrical characteristics of the piezoelectric element are measured when it is supplied at a frequency capable of inducing a resonance mode for the membrane. The measurements on the piezoelectric element are affected by the behavior of the membrane which is itself affected by the presence and the properties of the material in contact with the membrane. It is therefore possible to trace the properties of the material based on the electrical measurements at the terminals of the piezoelectric element.

[0022] According to an improvement of the measuring method, the piezoelectric element is supplied with a natural frequency to induce in the membrane a resonance mode greater than or equal to the second mode.

[0023] The invention also relates to a method for monitoring milk coagulation, according to which the impedance of the active assembly is measured at different frequencies, at least one of the parameters among the maximum phase cp max(t) of the impedance or admittance, the maximum modulus Z max(t) of the impedance or admittance, an offset of the anti-resonance frequency AFa or resonance AFr and the pseudo-resonance frequency for the phase Fcpmax(t), and it is determined that the milk is sufficiently curdled when the monitored parameter(s) have changed by a predetermined value or in a predetermined ratio. When a voltage at a predetermined frequency is applied to the terminals of the active assembly, an electric current is observed having an intensity and a phase related to the voltage supplied. This ratio is called the impedance which is broken down into a phase cp and a modulus Z. We can also work with the admittance which is the inverse ratio of the impedance. By changing the frequency close to the frequency corresponding to a resonance mode, we see that the phase and the modulus also change. We can thus determine a maximum for the phase as well as for the modulus.The frequency at which the maximum is observed for the phase or for the modulus also changes according to the properties of the milk in the coagulation phase. The resonance frequency Fr is the frequency at which the minimum of the modulus is reached. The anti-resonance frequency Fa is the frequency at which the maximum of the modulus is reached. The shift of the anti-resonance frequency AFa is the difference between the anti-resonance frequency between the initial moment and the moment when the measurement is made. Similarly, the shift of the resonance frequency AFr is the difference between the resonance frequency between the initial moment and the moment when the measurement is made. The pseudo-resonance frequency for the phase Fcpmax(t) is the frequency at which the maximum is observed for the phase at a given instant.Different criteria can be determined to consider that the milk is sufficiently curdled, for example on the pseudo-resonance frequency for the phase in an absolute manner, or in offset from the start of the curdling phase, or even in relative value always in relation to the start of the curdling phase. The criteria can also be a relative or absolute variation on the maximum modulus, or on the relative or absolute variation of phase for this maximum. The criteria must be adapted to the type of cheese that is being made. Brief description of the figures

[0024] The invention will be better understood and other features and advantages will appear on reading the description which follows, the description making reference to the appended drawings among which: • Figure 1 is a view of a cheese-making vat in which a sensor according to the invention is mounted; Figure 2 is a sectional view of the sensor of Figure 1; Figure 3 is a top view of a membrane of the sensor of Figure 2 according to different versions; • Figure 4 is a view of the membrane representing different vibration modes; • Figure 5 is a curve representing the evolution of the sensor impedance modulus as a function of frequency; • Figure 6 is a curve representing the evolution of the phase of the sensor impedance as a function of frequency; • Figure 7 is a graph showing the evolution of a parameter measured by the sensor as a function of time during milk coagulation; • Figure 8 is a graph similar to the graph in Figure 7 for two different milk preparations and the same sensor, with a membrane without surface treatment; • Figure 9 is a graph similar to the graph in Figure 8 for two different milk preparations and the same sensor with a sensor membrane surface treatment; • Figure 10 is a graph similar to the graph in Figure 8 for two different milk preparations and the same sensor as in Figure 9. Detailed description

[0025] A viscoelastic property measuring sensor according to the invention can be implemented during cheese production, in particular during the milk coagulation step and during the evolution of the rheology of the gel, and in particular its firmness. Figure 1 shows an example of a tank 2 into which the milk is poured at a controlled temperature, and coagulant is added to trigger the coagulation step. Tank 2 is equipped with a sensor 1 according to the invention by being arranged in tank 2.

[0026] As shown in detail in Figure 2, the sensor 1 for measuring viscoelastic properties comprises a rigid support 10 of annular shape and a disc-shaped membrane 11 fixed on the support 10. The support 10 and the membrane 11 are made of stainless steel. The support 10 comprises a groove 100 at the connection between an end face 101 and an internal bore 102. The membrane 11 is housed in this groove 100 in such a way that it comprises an external face 111 substantially aligned with the end face 101. For the manufacture of the sensor 1, a continuous weld is carried out between the periphery of the membrane 11 and the support 10 in such a way that the membrane 11 is embedded in a sealed manner on the support 10. external face 111 of the membrane 11 receives a surface treatment, as described below, so as to improve its wettability.

[0027] An active assembly 12 is also fixed on the internal face of the membrane 11 opposite the external face 111. In the example which is shown the active assembly only comprises a piezoelectric element 12 in the form of a pellet with a diameter smaller than the radius of the membrane 11. This pellet 12 has substantially the same thickness as the membrane 11 and is fixed on the membrane 11 by means of an epoxy type glue in an off-center manner.

[0028] The cavity behind the membrane 11 can receive electronic elements 13 necessary for the connection and power supply of the piezoelectric element. A cable, not shown, with electrical conductors passes radially through the support 10, the electrical conductors being connected to the electronic elements. The cavity is closed by a bottom wall 14 opposite the membrane 11 and also sealed by its periphery. The active assembly 12 is thus configured to generate the oscillation of the membrane 11 according to a resonance mode greater than or equal to the second resonance mode of the membrane 11.

[0029] The material whose viscoelastic properties are to be evaluated is brought into contact in particular with the end face 101 and on the external face 111 of the membrane 11.

[0030] We will now describe a surface treatment which makes it possible to improve the wettability of the external face 111 of the sensor 1.

[0031] A coating is applied to the outer face 111 of the membrane 11 by a sol-gel process. Sol-gel is a chemical reaction in solution which, after gelling, gives a solid matrix. This process, here based on titanium dioxide (TiO?) and silicon dioxide (SiO?), comprises four stages.

[0032] First, the preparation of a SiO2 solution, by mixing acidified water to pH 3 and tetraethyl orthosilicate (TEOS), in a molar ratio of 1:20. It is stirred for a minimum of 18 hours. The hydrolysis of the precursor (TEOS), by reaction between silica and water, takes place according to the reaction:

[0033] Si(OEt)4 + 4 H2O Si(OH)4 + 4 EtOH where Et is an ethyl group C2EU

[0034] This reaction is followed by a condensation reaction, allowing the formation of SiO2.:

[0035] 2 Si(OH) 4 (OH) 3 -Si-O-Si(OH)3 + H 2 O

[0036] This condensation step results in the formation of gels in which the Si-O-Si complexes are linked together.

[0037] (OH) 3 -Si-O-Si(OH) 3 ^ 2 SiO 2 + 3 H 2 O

[0038] The second step is the preparation of the TiO solution 2 . This is prepared from a mixture of distilled water / hydrochloric acid / glacial acetic acid / titanium tetraisopropoxide (TTIP), at 60°C for 2 hours, in a molar ratio of 88.6:1.4:5:5. The solution is then stirred for a minimum of 16 hours at room temperature before use. The reaction between TTIP, of formula Ti[OCH(CH 3 ) 2 ] 4 , and acidified water allows the formation of TiO 2 according to the following reactions:

[0039] Ti[OCH(CH 3 ) 2 ] 4 + H 2 O Ti(OH) 4 + 4 (CH 3 ) 2 CHOH

[0040] 2 Ti(OH) 4 (OH) 3 -Ti-O-Ti(OH) 3 + H 2 O 2 TiO 2 + 3 H 2 O

[0041] Then, a TiO mixture 2 / SiO 2 is then prepared and stirred for at least 1 hour according to molar ratios 30:70 50:50.

[0042] The mixture of TiO 2 / SiO 2 is deposited on the external face 111 of the membrane 11 of the sensor 1 by spin-coating. During spin-coating, the disc is positioned on a rotating support and a drop of solution is deposited in the center of the surface. The centrifugal force then distributes the solution evenly over the entire surface.

[0043] The stainless steel membrane is pre-activated by O plasma 2 before deposition. During spin coating, this is accelerated to a speed of 6000 rpm; a drop of at least 200 μl of TiO mixture 2 / SiO 2is deposited once the speed of 6000 rpm is reached. The disc is rotated for a total time of 1 minute.

[0044] The final step is annealing. The solvents are evaporated by drying, and a heat treatment will allow the film to densify. After deposition, the disc is placed in an oven at 80°C for 15 minutes to evaporate the solvent, then a heat treatment at 120°C for 25 minutes is carried out. The result is a super-hydrophilic coating with a thickness of a few tens of nanometers.

[0045] Different characterizations of the TiO coating 2 / SiO 2 on the disc are carried out to measure the wettability of the surface and its roughness.

[0046] The contact angle of a 1 pL drop of demineralized water deposited on the surface is measured with a goniometer. The roughness of the TiO film 2 / SiO 2 is determined by profilometry.

[0047] A polymer-based coating was also made by mixing TEOS with 2-(dodecyloxy)ethan-l-ol, supplied under the name Brij-30 (registered trademark).

[0048] Approximately 60 samples of a coated stainless steel plate were produced for each of the coatings, with for TiO2 / SiO2, on the one hand a molar proportion of 30 / 70 and on the other hand a proportion of 50 / 50, and a series of polished bare steel plates with a residual roughness of the order of 1 nm in average value.

[0049] .

[0050] The drop angle is less than 20°, on average 5° for TiO2 / SiO2 at 30 / 70, 11° for TiCh / SiCh at 50 / 50, but of the order of 50° for polished bare steel.

[0051] Measurements after air aging after several months and chemical cleaning give contact angle values ​​of less than 20° for all coated surfaces, except for bare steel.

[0052] The same is true after immersion in milk followed by immersion in a cleaning solution, in a cycle of one and a half hours. The results are confirmed when cleaning includes brushing.

[0053] Figure 4 shows different resonance modes of the membrane 11. Figure 4a shows the fundamental resonance mode, or first mode, in which the maximum amplitude of vibration appears at the center of the membrane 11. Figure 4b shows the second resonance mode, in which a bump 113 appears on one side of the membrane 11 while a symmetrical trough 114 appears on the other side. Figure 4c shows the third resonance mode in which two bumps 113' appear symmetrically about the center while two troughs 114' appear simultaneously, also symmetrical about the center but offset by a quarter turn from the bumps 113'. These resonance modes appear at different frequencies to which the membrane 11 is subjected by the active assembly 12.When a piezoelectric element is placed in a zone with high amplitudes in a specific resonance mode, this resonance mode is favored, i.e. the impedance obtained is particularly variable depending on the frequency.

[0054] To implement the method according to the invention, the material is placed in contact with the external face 111 of the membrane 11 and the electrical characteristics are measured at the terminals of the piezoelectric element. For this, an impedance measuring device is used which supplies the sensor 1 with an alternating voltage of adjustable frequency. The active assembly 12 is supplied at a frequency specific to inducing for the membrane 11 a resonance mode greater than or equal to the second mode. The nearby frequencies are explored by measuring for example the modulus and the phase shift of the impedance. Figures 5 and 6 show the evolution of the modulus and the phase respectively as a function of the frequency near the resonance. It can be seen that at the resonance frequency, Fr(t), the modulus is minimal Zmin(t) then increases to the maximum value Zmax(t) for the antiresonance frequency Fa(t) before decreasing. The diagram shows a second curve having roughly the same shape but more flattened and shifted towards higher frequencies. This second curve corresponds to a measurement with the presence of a more viscous material than during the measurement obtained on the first curve. In Figure 6, we see that the phase shift reaches a maximum Omax(t) for a frequency FOmax(t), then decreases with the increase in frequency. Figure 6 also shows a first and a second curve corresponding to measurements with the same sensor 1 but a more viscous material in contact with the membrane 11.

[0055] These measurements are applied to a milk coagulation monitoring process. Tank 2 is filled with milk at a controlled temperature, and measurements are started when the coagulant is added. Figure 7 shows the measurement of the evolution of the maximum phase Omax(t) as a function of the coagulation time, as well as a curve of variation of this value (derivative with respect to time).

[0056] We note that the value is initially stable, then begins to change rapidly, which corresponds to the setting time, then a little more slowly. We determine that the milk is sufficiently curdled when the maximum phase Omax(t) has changed to reach a predetermined value, for example 1.5°. This predetermined value is a setpoint defined by the cheesemaker.

[0057] In different variants of implementation of the assembly, as shown in Figure 3, the active assembly 12 is arranged to generate differential oscillations of the membrane 11. Example (c) is the one that was used previously with a piezoelectric element in the form of a pellet with a diameter smaller than the radius of the membrane 11. In example (a), the surface of the membrane 11 is covered by an active assembly 12' comprising eight piezoelectric elements 120 in the form of sectors. The adjacent sectors are powered so that their action is in phase opposition. Example (b) comprises a piezoelectric element 12” in the form of a circular pellet centered on the membrane 11. In example (d), the active assembly 12'” comprises 4 piezoelectric pellets 121 of circular shape arranged at the top of a square and inscribed in the diameter of the membrane 11.

[0058] Figure 8 shows a graph similar to that of Figure 7, with arbitrary units (AU) on the ordinate for the firmness index, and these arbitrary units per minute for an aggregation rate, i.e. the derivative with respect to time. The measurements were carried out with a sensor whose membrane is made of polished bare stainless steel. Curves A8, B8 and C8 represent the measurements from the sensor as a function of the coagulation time for the same milk with different dosages of coagulant. Curves DA8, DB8 and DC8 represent the derivatives with respect to time of curves A8, B8 and C8 respectively. It can be seen that the derivatives have a very variable amplitude and quite distinct shapes. This is attributed to poor coupling between the membrane and the milk in the coagulation phase.

[0059] Figure 9 represents a graph similar to that of Figure 8, obtained with the measurements of a sensor having received a coating with 30% titanium oxide, as previously described. Curve A9 concerns a milk with 5.6% protein by mass while curve B9 concerns a milk with 3.7% protein by mass, both preparations having received the same dose of coagulant, namely 20 mg / l. Curves DA9 and DB9 represent the derivatives with respect to time respectively of curves A9 and B9.

[0060] Figure 10 represents a graph similar to that of Figure 8, obtained with measurements from the same sensor as that used for the measurements in Figure 9. Curve A10 concerns milk with 5.6% protein by mass having received a coagulant dose of 10 mg / 1 while curve B 10 is the same curve as curve B9. Curves DA10 and DB10 represent the derivatives with respect to time of curves A10 and B10 respectively.

[0061] We therefore observe better reproducibility when the sensor has received a coating improving wettability. In fact, the measurements are reproducible in terms of expected curve shapes / patterns, especially when it comes to milks that differ in terms of composition.

[0062] Without a coating, the system is more sensitive to deviations in milk properties related to external conditions, such as milk being more or less fatty from one day to the next. Figure 8 shows, in particular, very different maximum values ​​for the derivative from one milk quality to another.

[0063] The coating allows for consistency in the interaction between the dairy matrix and the membrane surface, which is not necessarily the case when the membrane has not been coated with a material improving wettability.

[0064] The invention is not limited to the embodiment just described. The coating to improve wettability could be a polymer coating. One could monitor the evolution of the maximum of the modulus instead of that of the phase, or the evolution of the pseudoresonance frequency. One could also combine these parameters.

Claims

Claims 1. Sensor for measuring the viscoelastic properties of a material comprising a rigid support (10) and a membrane (11) fixed on the support (10), the material being intended to come into contact on an external face (111) of the membrane (11). The sensor further comprises an active assembly (12) with at least one piezoelectric element bonded to the internal face of the membrane (11). On the external face (111) the wettability characterized by a contact angle of a drop of distilled water of 1 pL is less than 20°, preferably less than 10°.

2. Sensor according to claim 1, in which the membrane (11) has the shape of a disc embedded by its periphery on the support (10).

3. Sensor according to claim 1 or 2, in which the active assembly (12) only partially covers the internal face of the membrane (11).

4. Sensor according to one of the preceding claims, in which the active assembly (12) is configured to generate the oscillation of the membrane (11) according to a resonance mode greater than or equal to the second resonance mode of the membrane (11).

5. Sensor according to claim 4, in which the membrane (11) has a center and the active assembly (12) is off-center on said internal face.

6. Sensor according to one of claims 4 or 5, in which the active assembly (12) is arranged to generate differential oscillations of the membrane (H).

7. Sensor according to one of the preceding claims, in which the external face (111) of the membrane (11) comprises a wettability-improving coating.

8. Sensor according to claim 7, in which the coating is chosen from a polymer coating and a deposit of nanoparticles of titanium oxide and silicon oxide.

9. Sensor according to claim 8, in which the coating is a deposit of nanoparticles comprising between 25 and 60%, preferably between 25 and 35%, in molar ratio of titanium oxide and the remainder in silicon oxide.

10. Sensor according to one of the preceding claims, intended for use in monitoring milk coagulation.

11. Sensor according to one of the preceding claims, intended for use in controlling cheese production.

12. Method for measuring the viscoelastic properties of a material, characterized in that a sensor according to one of the preceding claims is used, the material is placed in contact with the external face (111) of the membrane (11) and the electrical characteristics of the piezoelectric element are measured when it is supplied at a frequency capable of inducing a resonance mode for the membrane (11).

13. Measuring method according to claim 12, according to which the piezoelectric element is supplied at a frequency suitable for inducing in the membrane (11) a resonance mode greater than or equal to the second mode.

14. Method for monitoring milk coagulation, characterized in that a measuring method according to claim 12 or 13 is implemented and according to which the impedance of the active assembly (12) is measured at different frequencies, at least one of the parameters among the maximum phase (pmax(t) of the impedance or the admittance, the maximum modulus Zmax(t) of the impedance or the admittance, an offset of the antiresonance frequency AFa or resonance frequency AFr, the pseudoresonance frequency for the phase Fcpmax(t) is determined, and it is determined that the milk is sufficiently curdled when the monitored parameter(s) have changed by a predetermined value or in a predetermined ratio.

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