DEVICE FOR MEASURING PHYSICOCHEMICAL PROPERTIES OF A DEFORMABLE MATRIX, IMPLEMENTATION METHOD AND USES

Abstract

Disclosed herein is a device for measuring physicochemical properties with regard to gases in contact with a material, especially material transport properties with regard to gases in contact with a material and mechanical properties, comprising: an upper end, in which a pressure sensor connected to an apparatus for recording and optionally processing a signal is hermetically inserted; a lower end in communication with the pressure sensor and which is open in order to allow (i) insertion of the measuring device into the material and (ii) formation of a gaseous chamber between the pressure sensor and the material when the measuring device is inserted therein; a system for scavenging a gas; at least one means for introducing the gas into the device, and advantageously at least one means for removing the gas from the device; the device made from a material which does not absorb the gas.

Claims

1. A device for measuring physicochemical properties with regard to gas in contact with a material, comprising: an upper end, into which a pressure sensor connected to a apparatus for recording and optionally processing a signal is hermetically inserted; a lower end, which is in communication with said pressure sensor and which is open to allow (i) the measuring device to be inserted into said material and to allow (ii) a gaseous chamber to be formed between said pressure sensor and said material when said measuring device is inserted therein; a system for scavenging a gas; at least one means for introducing said gas into the device, and advantageously at least one means for removing said gas from the device; said device being made from a material that does not absorb said gas.

2. The device according to claim 1, wherein said material that does not absorb said gas is selected from among metal, glass and polymer materials previously saturated with said gas or treated so as not to absorb said gas.

3. The device according to claim 1, said device being a hollow tube, optionally cylindrical.

4. The device according to claim 1, wherein the height of said device is greater than or equal to 5 mm, and the height between the lower end of the device and the pressure sensor is greater than 1 mm.

5. The device according to claim 1, further comprising at least one means for holding the device in position relative to said material.

6. The device according to claim 1 , further comprising an extension sealably connected with the lower end of said device.

7. The device according to claim 1, wherein said material is a food matrix, especially selected from among a cheese product, a bakery product, a meat, a fish, a meat or fish-based product, a fruit, a vegetable, a fruit or vegetable-based product, a food paste, and mixtures thereof, or a non-food matrix, especially selected from among concrete, cement, asphalt, plaster, polymers, gels, earth, wood, silicone, coal, rocks, and mixtures thereof.

8. A method for measuring the pressure of a gas in contact with a material, using a measuring device as defined in claim 1, comprising the following steps: (a) inserting said measuring device into the material; (b) optionally scavenging a gas from the gaseous chamber by means of the gas scavenging system at a constant pressure; (c) increasing or decreasing the pressure of the gaseous chamber by means of the gas scavenging system to a desired pressure; and (d) measuring the pressure and optionally the temperature of the gaseous chamber.

9. The method according to claim 8, wherein said gas is selected from among carbon dioxide, nitrogen, oxygen, rare gases, volatile organic compounds, ammonia, and a mixture thereof.

10. The method according to claim 8, wherein the pressure increase of step (c) is carried out progressively until said material is fractured.

11. A use of a measuring device as defined in claim 1, for measuring, in a material, at least one physicochemical property selected from among material transport properties with regard to gas, in particular the diffusion coefficient, the gaseous gas/dissolved gas equilibrium constant, the dissolved gas concentration and/or the production rate, and mechanical properties, in particular the elasticity, the viscosity, the visco-elasticity and the fracture point.

12. The use of a measuring device as defined in claim 1 , in the preparation or monitoring of the features of materials in which a gas is likely to solubilize and diffuse.

Description

BRIEF DESCRIPTION OF THE FIGURES

[0058] FIG. 1 shows the longitudinal cross-section of a schematic diagram of a measuring device according to the invention, also called “probe” hereafter.

[0059] A pressure sensor (2) (Kulite Semiconductor Products Inc., model XCQ-093-1.7.BARA) is inserted into a hollow cylindrical tube (15) of diameter (26) and of height (8), and that is preferably metal or glass, so as not to absorb CO.sub.2. The pressure sensor (2) is connected to an apparatus (3) for processing and recording the signal.

[0060] The seal is ensured at the upper end (1) of the device by a weld produced between the pressure sensor (2) and the metal tube. The lower end (4) of the device is open since the tube (15) is hollow, and is in contact with the food matrix to be analyzed.

[0061] A CO.sub.2 scavenging system (6), which is required to ensure that the environment is only made up of this gas, is also present. It is formed by a means (10) for introducing gas via the upper end (1) of the device, connected to a gas cylinder (16), and an outlet means (11) for discharging the gas.

[0062] A valve (17) allowing said gas to enter the device, and a valve (18) allowing said gas to exit from the device, allow the introduction/discharge of gas to be managed. The gas intake means (10) also allows the initial pressure to be adjusted that is to be imposed in order to carry out the measurements.

[0063] Finally, the device is provided with a means (9) for holding a food matrix in position in order to hold it in position during measurements, which means is made up of clamps in this embodiment.

[0064] In this embodiment, the device has the following dimensions: Height (7) = 40 mm, height (8) = 7 mm, Diameter (26) = 3 mm.

[0065] In another embodiment, not shown in the figures, in order to take the measurements, CO.sub.2 scavenging was carried out by conveying gas through the lower end (4) of the probe (only available opening) for at least 1 minute before it is planted into the cheese.

[0066] FIG. 2 shows the longitudinal cross-section of a schematic diagram of the measuring device of the type shown in FIG. 1, used with an extension (12). The extension (12) shown is made up of a hollow metal tube, the top (20) of which is open. This tube is optionally perforated on its sides (13) in order to let through the gas and/or is perforated at its lower end (14) in order to let through the gas. The extension (12) is also provided with a system (19) that provides the seal with the matrix to be analyzed (seal, screwing system, etc.). The extension (12) can be screwed, hooked to the rest of the probe.

[0067] FIG. 3 shows the longitudinal cross-section of a schematic diagram of the measuring device used with an extension (12) of the type shown in FIG. 2, inserted into a cylindrical hole (25) made in the matrix (26) to be analyzed. It is inserted so that the sealing system (19) of the extension (12) is positioned in order to prevent gas leaks. A free gaseous chamber (5) is present between the surface of the matrix to be analyzed and the extension (12) of the probe. A gaseous space is formed in the hole (25) between the extension and the matrix.

[0068] FIGS. 4 to 7 show the results of the 4 pressure measurements (in kPa) (respectively FIG. 4, FIG. 5, FIG. 6 and FIG. 7) conducted as a function of time (hours). In each of these figures, straight lines have been drawn as dashed lines (respectively “Measurement 1a” and “Measurement 1b” in FIG. 4, “Measurement 2” in FIG. 5, “Measurement 3a” and “Measurement 3b” in FIG. 6 and “Measurement 4a” and “Measurement 4b” in FIG. 7) to symbolize the durations used to compute the CO.sub.2 production rates.

[0069] FIG. 8 shows the CO.sub.2 production rate (r.sub.CO2, by mol.m.sup.-3.s.sup.-1) by the cheese as a function of the ripening duration (in days), for the obtained experimental data (stars), the data mentioned in Huc et al. ([1]) (dotted line curve) and the data mentioned in Acerbi et al. ([2]) (dashed line curve).

[0070] FIG. 9 shows the CO.sub.2 pressure measurement (kPa) as a function of time (seconds) with a hermetic (dashes) or non-hermetic (squares) probe. It can be clearly seen that with a non-hermetic probe, the pressure reduction is much faster and that the pressure returns to its initial value after a few minutes.

[0071] FIG. 10 shows the CO.sub.2 pressure measurement (kPa) as a function of time (seconds) with the device of the invention with a piece of cheese (dashes) and without cheese with a plastic plug to close the lower end of the device (squares). It can be seen that with a plastic device, the CO.sub.2 pressure quickly reduces due to the transfer of CO.sub.2 into the plastic.

[0072] FIG. 11 shows the CO.sub.2 pressure measurement (kPa) as a function of time (seconds), conducted 3 times, after an overpressure in the gaseous chamber in contact with the material. The measurements were carried out over a duration of approximately 10 min (600 s) with a pressure measurement every 10 seconds. Before taking the measurements, CO.sub.2 had been scavenged from the gaseous chamber for approximately 1 minute.

[0073] FIG. 12 shows the CO.sub.2 pressure measurement (kPa) as a function of time (seconds), for the experimental data (Measurement 3, diamond line curve) compared with the model adjusted with Equation 2 (D.sub.CO2= 2.6 x 10.sup.-10 m.sup.2.s.sup.-1). 0.5% error bars were used for the experimental values.

[0074] FIG. 13 shows the longitudinal cross-section of a schematic diagram of the measuring device of the type shown in FIG. 1, with the scavenging system (6) operating, that is with the gas intake valve (17) and the gas outlet valve (18) open. The device is planted in the matrix (26) to be analyzed at a height (22) > 3 mm.

[0075] FIG. 14 shows an N.sub.2 pressure measurement (kPa) as a function of time (seconds) for determining the viscosity of a cheese.

[0076] FIG. 15 shows the viscosity (Pa.s) computed with Equation 8 every minute when monitoring the pressure. It can be clearly seen that after a few minutes, the computed viscosity stabilizes because the material transfer becomes negligible.

[0077] FIG. 16 shows a diagram of a measurement probe for determining the Henry constant (temperature sensor (27) - pressure sensor (2)).

[0078] FIG. 17 shows the principle of the pressure variation for the measurement of the Henry constant.

[0079] FIG. 18 shows a diagram of the measurement probe used to determine the viscosity (temperature sensor (27) - pressure sensor (2)).

[0080] FIG. 19 shows the viscosity (.Math. in Pa.s) of the 70/100 Azalt bitumen determined with the probe (vertical bars, 9 measurements) and the value from the literature (dashed horizontal line).

[0081] FIG. 20 shows: a) the typical shape of the pressure (kPa) over time (s) for characterizing a bread dough obtained with an alveograph; - b) the typical shape of the pressure over time for characterizing a bread dough obtained with the probe.

[0082] FIG. 21 shows a diagram of the measurement probe used to determine the features of the bread dough (temperature sensor (27) - pressure sensor (2)).

[0083] FIG. 22 shows the pressure variation (kPa) over time (s) for characterizing the bread dough with the probe.

[0084] FIG. 23 shows a diagram of the measurement probe used to determine the CO.sub.2 diffusion coefficient in water (temperature sensor (27) - pressure sensor (2)).

[0085] FIG. 24 shows the experimental pressure (kPa) and the pressure (kPa) determined with Equation (5) of Example 11 relating to the diffusion of CO.sub.2 in water, as a function of time (s).

EXAMPLES

Example 1: Determining the CO.SUB.2 Production Rate of a Deformable Matrix

[0086] The CO.sub.2 production rate of a cheese was determined during the first 11 days of ripening using a pressure measurement only. The measuring device used is cylindrical with a height (8) = 7.0 mm and a diameter (26) = 2.7 mm, of the type described in FIG. 1.

[0087] Equations useful for determining the CO.sub.2 production rate of a deformable matrix.

[0088] Equation (1) is the CO.sub.2 materials balance in a semi-hard cheese of the Emmental type. The material transport by diffusion and the CO.sub.2 production (by propionic fermentation) are taken into account.

[00001]$\frac{\partial C}{\partial t}-{\text{D}}_{\text{CO2}}\times \nabla \text{C}\text{=}{\text{r}}_{\text{CO2}}$

[0089] With C being the CO.sub.2 concentration (mol.m.sup.-3), D.sub.CO2 being the CO.sub.2 diffusion coefficient in the cheese (m.sup.2.s.sup.-1) and r.sub.CO2 being the CO.sub.2 production rate (mol.m.sup.-3.s.sup.-1)

[0090] Equation 2 represents the thermodynamic equilibrium of the CO.sub.2 at the interface between a gas phase and a liquid phase (water + cheese fat). The equilibrium is based on the Henry equation.

[00002]$\text{C}\text{=}{\text{k}}_{\text{H}}^{\text{ch}}\times {\text{P}}_{\text{CO2}}$

[0091] With

[00003]${\text{k}}_{\text{H}}^{\text{ch}}$

being the Henry constant (mol.m.sup.-3.Pa.sup.-1) and P.sub.CO2 being the CO.sub.2 pressure in the gas phase (Pa).

[0092] In order to determine the CO.sub.2 production rate, the diffusion (very small D.sub.CO2) is considered to be very slow compared with CO.sub.2 production. In this case, Equation 1 becomes:

[00004]$\frac{\partial \text{C}}{\partial \text{t}}={\text{r}}_{\text{CO2}}$

By combining Equation 3 with Equation 2 (Henry’s law) and by integrating over time, Equation 4 is obtained, which linearly describes the pressure increase as a function of time. The pitch of the pressure increase due to CO.sub.2 production as a function of time allows the CO.sub.2 production rate to be obtained by knowing the Henry constant only.

[00005]$\text{P}\text{=}{\text{P}}_{\text{0}}\text{+}\frac{{\text{r}}_{\text{co2}}}{{\text{k}}_{\text{h}}}\times \text{t}$

Principle of the Measurements

[0093] The principle of the measurements involves planting the device into the cheese and monitoring the evolution of the pressure over time. By planting the device into the cheese, the volume of the gas phase decreases, which increases the pressure to a value P0 that is greater than atmospheric pressure. A pressure drop is initially observed due to the transfer of the CO.sub.2 from the gas phase to the cheese until an equilibrium (according to Equation 2) is reached. Once the equilibrium is reached, the pressure will then increase due to the CO.sub.2 production by the cheese and its transfer to the gas phase. The CO.sub.2 production rate is determined according to Equation 4 based on this pressure increase.

Operating Conditions

[0094] An Emmental-type semi-hard cheese is used to determine the CO.sub.2 production rate. For each measurement, a hole (25) is made in the cheese in order to take a core measurement (at a depth of 2 cm). In order to ensure a CO.sub.2 atmosphere, the probe is scavenged with CO.sub.2 for 1 minute before being planted into the cheese.

[0095] The measurements last between 1 and 2 days (10 seconds or 1 minute of pressure acquisition frequency) according to the pressure increase (that is according to the production rate). The average temperature in the piece was 20 ± 1.5° C. Four measurements were conducted, which covered the first 11 days of ripening.

Experimental Results of Pressure Measurements

[0096] FIGS. 4 to 7 show the results of the completed pressure measurements. Each curve has the same shape: as explained above, the pressure reduces over a first time period after the pressurization due to the material transfer of CO.sub.2 from the gas phase to the cheese; a ceiling is then reached, then the pressure re-increases, this time as a result of the production and the transfer of the CO.sub.2 to the gas phase.

[0097] In FIGS. 4 to 7, straight lines have also been drawn during periods when the pressure re-increases. It symbolizes the data with which the CO.sub.2 production rates were determined (the pitch of these straight lines allows the production rate to be computed with Equation 4).

Determining CO.SUB.2 Production Rates

[0098] Based on the experimental data presented in the previous paragraph, the CO.sub.2 production rates were computed with Equation 4 using 3.5 x 10.sup.-4 mol.m.sup.-3.Pa.sup.-1 (Chaix et al. [7]; Chaix E. [6]) as the value of the Henry constant. The results are consolidated in Table 1 and are also shown in FIG. 8.

[0099] The production rate is lowest at the start of ripening (day 2). It then gradually increases up to day 10 or it reaches a maximum and then drops again on day 11.

[0100] Table 1 shows the experimental pressure increase rates and the corresponding CO.sub.2 production rates determined with Equation 4 (Henry constant equal to 3.5 x 10.sup.-4 mol.m.sup.-3.Pa.sup.-1).

TABLE-US-00001 Measurement reference Ripening day Pitch of the straight line representing the pressure increase (Pa.s.sup.-1) CO.sub.2 production rate computed with Equation 4 (mol.m.sup.-3.s.sup.-1) Measurement 1-a 2 1.63 × 10.sup.-2 5.70 × 10.sup.-6 Measurement 1-b 3 3.74 × 10.sup.-2 1.31 × 10.sup.-5 Measurement 2 6 4.84 × 10.sup.-2 1.70 × 10.sup.-5 Measurement 3-a 8 6.91 × 10.sup.-2 2.42 × 10.sup.-5 Measurement 3-b 9 7.62 × 10.sup.-2 2.67 × 10.sup.-5 Measurement 4-a 10 12.20 × 10.sup.-2 4.26 × 10.sup.-5 Measurement 4-b 11 7.09 × 10.sup.-2 2.48 × 10.sup.-5

Comparison With the Data From the Literature

[0101] FIG. 8 shows the CO.sub.2 production rate by the cheese as a function of the ripening duration (data from Table 1), as well as some values from the literature for comparison.

[0102] In general, the production rates determined in this study are consistent with the values from the literature (Huc et al. : “Influence of salt content on eye growth in semi-hard cheese studied using magnetic resonance imaging and CO.sub.2 production measurements”, International Dairy Journal (2014) ([1]); Acerbi et al. ([2])). Maximum production is obtained after 10 days of ripening by Huc et al. ([1]) for cheeses of the same type as that tested. By contrast, Acerbi et al. ([2]) determined maximum CO.sub.2 production after 3 days of ripening.

Conclusion

[0103] The CO.sub.2 production rates determined by means of the device of the invention are consistent with the values from the literature (of the order of 10.sup.-6 - 10.sup.-5 mol.m.sup.-3.s.sup.- .sup.1). The rate increases in the first 10 days of ripening (up to a maximum of 4.26 x 10.sup.-5 mol.m.sup.-3.s.sup.-1) and then decreases.

Example 2: Determining the CO.SUB.2 Diffusion Coefficient of a Deformable Matrix

[0104] In this example, in order to determine the properties of the cheese, a device of the type defined in FIG. 1 is used, having a pressure sensor (2) for a gaseous phase with CO.sub.2 only, the volume of which is small compared to that of the cheese (semi-infinite cheese, gas phase length e (corresponding to the height of the gas phase after the probe has been pushed in) << the insertion depth of the device into the cheese L. Moreover, CO.sub.2 production by fermentation is overlooked and it is considered that there is no compression of the cheese due to the pressure.

[0105] This device is a cylindrical tube with a height (8) = 7.0 mm and a diameter (26) = 2.7 mm made of tin. The seal is ensured by welding the pressure sensor (2) to the tin tube.

[0106] Equations useful for determining the CO.sub.2 diffusion coefficient of a deformable matrix.

[0107] Under these conditions, and assuming that the transfer occurs only in one direction, the material transport equation is (Equation 1):

[00006]$\frac{\partial \text{C}}{\partial \text{t}}-{\text{D}}_{\text{CO2}}\times \frac{{\partial }^2\text{C}}{\partial {\text{x}}^2}=0$

[0108] In order to solve this equation, it is assumed that the initial concentration of CO.sub.2 in the cheese is homogeneous in the cheese and is equal to C.sub.0. A pressure P.sub.0 greater than atmospheric pressure is imposed at the time t = 0. The limit and initial conditions are therefore: [0109] For x = 0 and t = 0: (Henry’s law for determining the equilibrium at the gas/liquid interface); [0110] For x > 0 and t = 0: C = C.sub.0 [0111] For

[0112] This equation has an analytical solution for a semi-infinite plate (Tveteraas O.: “A study of pressure decay in a closed C02-water system”, Master Thesis, 2011 ([3]), Ghaderi et al.: “Estimation of concentration-dependent diffusion coefficient in pressure-decay experiment of heavy oils and bitumen”, Fluid phase equilibria, 2011 ([4])):

[00009]$\begin{array}{l}\text{P}\left(\text{t}\right)\text{=}\frac{{\text{C}}_{\text{0}}}{{\text{k}}_{\text{h}}}+\left({\text{P}}_{\text{0}}\text{-}\frac{{\text{C}}_{\text{0}}}{{\text{k}}_{\text{h}}}\right)\times \exp \left[\frac{\text{t}}{{\text{D}}_{\text{CO2}}}\times {\left(\frac{{\text{R×T×D}}_{\text{CO2}}{\text{×k}}_{\text{h}}}{\text{e}}\right)}^2\right]\\ \times \text{erfc}\left[\sqrt{\frac{\text{t}}{{\text{D}}_{\text{CO2}}}}\times \left(\frac{{\text{R×T×D}}_{\text{CO2}}{\text{×k}}_{\text{h}}}{\text{e}}\right)\right]\end{array}$

[0113] Based on Equation 2, it is therefore possible to describe the evolution of the CO.sub.2 pressure as a function of the initial CO.sub.2 concentration, of the Henry constant and of the CO.sub.2 diffusion coefficient. By adjusting with experimental data of pressure measurements, it also would be possible to determine these parameters.

[0114] Please note: the function erfc ranges between 2 and 0, with values that tend towards 2 when the argument tends towards -∞ and it tends towards 0 when the argument tends towards +∞.

[0115] Based on Equation 2, two characteristic behaviors can be identified:

[0116] The behavior over a very long time:

[00010]$\underset{\text{t}.fwdarw.+\infty }{\lim }\text{P}\left(\text{t}\right)=\frac{{\text{C}}_0}{{\text{k}}_{\text{h}}}$

The behavior over a short time:

[00011]$\begin{array}{l}\underset{\text{t}.fwdarw.0}{\lim }\text{P}\left(\text{t}\right)=\frac{{\text{C}}_0}{{\text{k}}_{\text{h}}}+\left({\text{P}}_{\text{0}}-\frac{{\text{C}}_{\text{0}}}{{\text{k}}_{\text{h}}}\right)\times \\ \left[1-\frac{2}{\sqrt{\pi }}\times \frac{\sqrt{\text{t}}}{\sqrt{{\text{D}}_{\text{CO2}}}}\times \frac{{\text{R×T×D}}_{\text{CO2}}{\text{×k}}_{\text{h}}}{\text{e}}\right]\end{array}$

[0117] Equation 4 is derived from the product of the limits of the functions exp and erfc:

[00012]$\left(\underset{\text{x}.fwdarw.0}{\lim }\text{exp}\left(\text{x}\right)=\text{1}\text{and}\underset{\text{x}.fwdarw.0}{\lim }\text{erfc}\left(\text{x}\right)=1-\frac{2}{\sqrt{\pi }}\times \text{x}\right).$

[0118] Equation 3 provides information concerning the oversaturation of the cheese when the pressure has stabilized over a very long time. Nevertheless, the behavior over a very long time is difficult to use in practice since the CO.sub.2 production is no longer negligible (depending on the ripening duration and the features of the cheese).

[0119] Equation 4 describes the behavior over a short measurement time. In reality, this equation can be provided in the form of a straight line (Equation 5).

[00013]$\begin{array}{c}\begin{array}{l}\underset{\text{t}.fwdarw.0}{\lim }\text{P}\left(\text{t}\right)=\\ \frac{{\text{C}}_{\text{0}}}{{\text{k}}_{\text{h}}}+\left({\text{P}}_{\text{0}}-\frac{{\text{C}}_{\text{0}}}{{\text{k}}_{\text{h}}}\right)\times \left[1-\frac{2}{\sqrt{\pi }}\times \frac{\sqrt{\text{t}}}{\sqrt{{\text{D}}_{\text{CO2}}}}\times \frac{\text{R}\text{×}\text{T}\text{×}{\text{D}}_{\text{CO2}}{\text{×k}}_{\text{h}}}{\text{e}}\right]=\\ {\text{P}}_{\text{0}}-\left({\text{P}}_{\text{0}}-\frac{{\text{C}}_{\text{0}}}{{\text{k}}_{\text{h}}}\right)\times \frac{2}{\sqrt{\pi }}\times \frac{\sqrt{\text{t}}}{\sqrt{{\text{D}}_{\text{CO2}}}}\times \end{array}\\ \frac{\text{R}\text{×}\text{T}\text{×}{\text{D}}_{\text{CO2}}{\text{×k}}_{\text{h}}}{\text{e}}\end{array}$

[00014]$\underset{\text{t}.fwdarw.0}{\lim }\text{P}\left(\text{t}\right)\text{=}\text{b}-\text{a}\text{×}\sqrt{\text{t}}$

[00015]$\text{With}\text{b}\text{=}{\text{P}}_{\text{0}}$

[00016]$\text{a=}-\left({\text{P}}_{\text{o}}-\frac{{\text{C}}_{\text{0}}}{{\text{k}}_{\text{h}}}\right)\times \frac{2}{\sqrt{\pi }}\times \frac{\text{R×T×}\sqrt{{\text{D}}_{\text{CO2}}}{\text{×k}}_{\text{h}}}{\text{e}}$

[0120] Equation 6 provides a second relation between C.sub.0, k.sub.H and D.sub.CO2.

Seal Measurement

[0121] Several welds were produced between the pressure sensor (2) and the upper end (1) of the device. 2 sealing tests are carried out each time: (i) the shape of the CO.sub.2 pressure reduction curve and (ii) by immersing the probe into water and by injecting air using a syringe.

[0122] FIG. 9 compares the shape of the CO.sub.2 pressure reduction curves with a hermetic or a non-hermetic probe. It can be clearly seen that with a non-hermetic probe, the pressure reduction is much faster and that the pressure returns to its initial value after a few minutes.

[0123] Identifying the materials for constructing the probe

[0124] CO.sub.2 pressure measurements were carried out with the device of the invention, and with a piece of cheese and without cheese but with a plastic plug (not previously saturated with CO.sub.2). FIG. 10 compares the results obtained in both cases (with the device of the invention with a piece of cheese shown as dashes, and without cheese with a plastic plug to close the lower end of the device shown as squares). It can be seen that with a plastic device, the CO.sub.2 pressure quickly reduces due to the transfer of CO.sub.2 into the plastic, which illustrates that it is imperative for materials to be used that do not absorb the gas of interest (the CO.sub.2 in this case).

Principle of the Pressure Measurements

[0125] The principle involves planting the device as shown in FIG. 1 in a food matrix. By planting the tube in the cheese, the volume of the gas phase decreases, which increases the pressure to a value P.sub.0 that is greater than atmospheric pressure. A pressure drop is then observed in accordance with Equation 2.

[0126] In order to provide a CO.sub.2 atmosphere, the device is scavenged with CO.sub.2 for 1 minute before being planted into the cheese.

[0127] CO.sub.2 pressure measurements were carried out with the probe with a semi-hard cheese of the Emmental type after 2 months of ripening. Given the production date of the cheese, it is considered that there is no longer any CO.sub.2 production. The average temperature in the piece was 19.7° C.

[0128] The probe is planted in the core of the cheese (at a depth of approximately 2 cm) and a bracket is used to wedge the probe. The measurements were carried out over a duration of approximately 10 min (600 s) with a pressure measurement every 10 seconds. Such an experiment duration is reasonable with a fermentable cheese without the CO.sub.2 production significantly modifying the pressure measurements.

Results and Discussion

Experimental Results of Pressure Measurements

[0129] FIG. 11 shows the experimental results of the obtained pressure measurements. In all cases, the pressure reduces over time in accordance with Equation 2, which confirms that CO.sub.2 transfers from the gas phase to the cheese. The shape of the curves is the same for all the measurements, irrespective of the location of the measurement and the imposed initial pressure.

[0130] The aim is to determine the CO.sub.2 diffusion coefficient in the cheese and the initial CO.sub.2 concentration. It is considered that the Henry constant k.sub.H is known and is equal to 3.5 x 10.sup.-4 mol.m.sup.3.s.sup.-1 (Chaix et al. [7]). The 2 parameters are obtained by adjusting Equations 2 and 6 with the experimental data. In order to use Equation 2, the height of the gas phase e needs to be known. This parameter is obtained with the initial height h (7.0 mm) and the imposed initial pressure P.sub.0 according to Equation 7.

[00017]$\text{e}\text{=}\frac{{\text{h×P}}_{\text{atm}}}{{\text{P}}_{\text{0}}}$

[0131] FIG. 9 compares the model with the experimental data (Measurement 3). 0.5% error bars were used for the experimental values. The model is in good agreement with the experimental values with a CO.sub.2 diffusion coefficient of 2.6 x 10.sup.-9 m.sup.2.s.sup.-1 and a dissolved CO.sub.2 concentration of 26 mol.m.sup.-3. Given the value of the Henry constant, such a concentration indicates that the cheese is under-saturated with CO.sub.2, which is consistent after more than 2 months of ripening and with a cheese in contact with the ambient air during certain periods.

[0132] Table 2 summarizes the results obtained and compares them with the data from the literature. The diffusion coefficients obtained range between 2.6 x 10.sup.-10 and 5.7 x 10.sup.-10 m.sup.2.s.sup.-1. These values are consistent with those from the literature (Acerbi et al. [5]). Table 2 shows the values of the adjusted diffusion coefficients (k.sub.H = 3.5 x 10.sup.-4 mol.m.sup.-3.Pa.sup.-1) and the value from the literature.

TABLE-US-00002 Reference C.sub.0 (mol.m.sup.-3) Table Measurement 1 26 3.0 × 10.sup.-10 Measurement 2 25 5.7 × 10.sup.-10 Measurement 3 26 2.6 × 10.sup.-10 Average 26 3.8 × 10.sup.-10 Acerbi et al [5] - 6.8 × 10.sup.-10

Conclusion

[0133] Based on measurements of CO.sub.2 pressure variation in a gas phase in contact with a food matrix (cheese), it was possible to determine certain features of the food matrix (initial CO.sub.2 concentration and CO.sub.2 diffusion coefficient) by adjusting a model with the experimental data.

[0134] The measurements are carried out for 10 minutes. Several experimental precautions have been set forth:

[0135] The cheese must not be left in contact with the open air in order to avoid desolubilization of the CO.sub.2, which alters the quality of the adjusted parameters.

[0136] Plastic materials must not be used for the design of the probe since these materials absorb CO.sub.2.

[0137] A fully metal probe was manufactured in the laboratory. Assuming the known Henry constant (3.5 x 10.sup.-4 mol.m.sup.-3.Pa.sup.-1), it has been determined that the average value of the diffusion coefficient is 3.8 x 10.sup.-10 m.sup.2.s.sup.-1. This value is in good agreement with the results from the literature.

Example 3: Determining the Material Transport Properties of a Deformable Matrix by Means of the Device of the Invention

[0138] In this example, in order to determine the properties of the cheese, a device of the type defined in FIG. 1 is used.

[0139] Irrespective of the transport property to be determined, the measurement principle remains the same as for the previous examples, and it is described below:

[0140] The device, in the open air, is scavenged by the gas of interest, in this case CO.sub.2. The valve (18) allowing said gas to exit the device is open, the valve (17) allowing said gas to enter the device is also open.

[0141] 2) A hole (25) is made in the matrix to be analyzed, as in the present example, whether it is a food matrix or another material, in order to be able to take the core measurement if required. This hole can be made with a drill bit, for example.

[0142] 3) The device, with the scavenging system (6) operating, that is, with the gas intake valve (17) and the gas outlet valve (18) open, is planted into the matrix to be analyzed. It is planted at a height (22), which is at least 1 mm in the matrix (in order to comply with certain computation hypotheses for data processing) and preferentially at a height (22) > 3 mm, as shown in FIG. 14.

[0143] The open face of the probe must be that by which the probe is planted into the matrix.

[0144] The probe is quickly inserted into the matrix.

[0145] 4) The scavenging system (6) is maintained for a few tens of seconds with the probe planted in the cheese to ensure that the matrix is only in contact with the gas of interest.

[0146] This time must be close to the time that separates the production of the hole (25) and the production of the probe.

[0147] 5) Once the scavenging is complete, the valve (18) allowing said gas to exit the device is closed.

[0148] 6) The gas intake valve (17) then feeds the gaseous chamber (5) in contact with the matrix until the desired pressure (pressure pulse) is quickly reached. The pressure to be reached is between - 1 kPa and +200 kPa, preferentially +10 - 15 kPa.

[0149] 7) Once the desired pressure is reached, the valve (17) is closed. The valve (18) remains closed. The pressure measurement then begins with the valves (17) and (18) closed for the entire duration of the analysis.

Example 4: Experimental Determination of the Viscosity of a Cheese

[0150] In this example, in order to determine the mechanical properties of the cheese, in particular its viscosity, a device of the type defined in FIG. 2 is used, having an extension that is formed by a cylindrical tube perforated on the sides and at its lower end.

Equations Useful for Determining Viscosity

[0151] The viscosity and the pressure are connected to the deformation of the radius of the cylinder (the latter is assumed to be infinite) according to Equation (1).

[00018]${\text{P}}_{\text{cylinder}}-{\text{P}}_{\text{atm}}\text{=}\text{2}\text{×}\mu \text{×}\frac{\text{dR}}{\text{R}}\text{×}\frac{\text{1}}{\text{dt}}$

[0152] With P.sub.cylinder being the pressure (Pa) in the gas filled cylinder, P.sub.atm being the atmospheric pressure (Pa), .Math. being the viscosity of the cheese (Pa.s), R being the radius of the cylinder (m) and dt being the measurement time interval (s).

Principle for Determining Viscosity

[0153] Experimentally, a cylindrical hole is hollowed out of the cheese and the evolution of the pressure over time following an overpressure is measured. In accordance with the ideal gas law and by neglecting the material transfer relative to the mechanics, a pressure reduction corresponds to an increase in the volume of the cylinder that can be related to an increase in the radius of the cylinder (that is, the variation in the radius of a circle is proportional to the surface variation to the power of ½, Equation (2)).

[00019]$\frac{\Delta \text{R}}{\text{R}}=\frac{{\text{P}}_{\text{1}}{}^{1/2}-{\text{P}}_{\text{2}}{}^{1/2}}{{\text{P}}_{\text{1}}{}^{1/2}}$

[0154] With P.sub.1 being the pressure in the cylinder at the instant t.sub.1 (Pa) and P.sub.2 being the pressure in the cylinder at the instant t2 > t1 (Pa).

[0155] The measurements are carried out with a semi-hard cheese of the Emmental type. The gas used to take these measurements is nitrogen, which has low solubility in matrices with a lot of water (this is the case of the studied cheese).

[0156] The probe extension is 20 mm high. In order to take the measurements, a 60 mm high cylindrical hole is hollowed out with a small drill bit and then the probe is pushed into the hole until it comes into abutment with the cap that will seal the system from the outside. Two metal weights (500 g each) are then installed in order to hold the probe in position.

[0157] Before the measurement is taken, the gaseous chamber is scavenged by nitrogen for approximately 1 min. An overpressure ranging between +15 and +35 kPa is then imposed and the pressure is measured for approximately 10 minutes for each measurement with a time interval of 1 second.

Results and Discussion

[0158] Throughout the entire duration of the analysis, the pressure has reduced due to the increase in volume of the previously hollowed out cylindrical hole and also in the initial instants of the analysis of the transfer of the gas from the gas phase to the cheese. FIG. 15 shows a typical shape of the pressure over time.

[0159] The viscosity was determined by considering the pressure values every minute, since during this time interval the pressure hardly changes (FIG. 15). At the beginning of the analysis, the computed viscosity is low for this type of cheese and it increases over time (FIG. 13). This behavior is derived from the pressure that reduces both due to the increase in volume according to the ideal gas law and also due to the transfer of the gas into the cheese. After a few minutes (approximately 5 min), the material transfer becomes very low (the surface of the cheese in contact with the gaseous chamber is saturated with nitrogen) and negligible relative to the mechanical behavior and the computed viscosity becomes constant at a value of approximately 2.5 x 10.sup.8 Pa.s, in good agreement with the literature (Garnet et al., 2016 [9]).

Example 5: Determining the Mechanical Properties of a Deformable Matrix by Means of the Device of the Invention

[0160] In order to determine the mechanical properties, the measuring device is used with an extension (12), as shown in FIG. 2.

[0161] The principle of the measurement of the mechanical properties is described below. It differs depending on whether the property to be determined is the viscosity or the fracture point.

Determining Viscosity

[0162] 1) The probe with its extension (12), in the open air, is scavenged by gas. Valve (17) is open, valve (18) is also open. The gas used for this measurement preferably is a gas that is poorly soluble in the matrix to be analyzed in order to measure mechanical properties and not transport properties. For example, nitrogen N.sub.2 is preferably used for matrices with a lot of water (this is the case of cheeses, for example), in order to limit its transfer into the matrix to be analyzed.

[0163] 2) A preferably cylindrical hole (25) is made in the matrix to be analyzed. It preferably has a minimum height (23) of 60 mm. This hole (25) can be produced with a drill bit, for example.

[0164] 3) The probe with its extension (12), with the scavenging system (6) operating, that is, with valves (17) and (18) open, is inserted into the hole (25) in the matrix to be analyzed, as shown in FIG. 3.

[0165] It is inserted so that the system (19) for sealing the extension (12) is positioned in order to prevent gas leaks.

[0166] Afree gaseous chamber (5) must be present between the surface of the matrix to be analyzed and the extension (12) of the probe.

[0167] 4) The scavenging system (6) is maintained for a few tens of seconds with the probe planted in the cheese to ensure that the matrix is only in contact with the gas of interest.

[0168] 5) Once the scavenging is complete, the outlet valve (18) is closed.

[0169] 6) Valve (17) feeds the gaseous chamber (5) in contact with the matrix until the desired pressure (pressure pulse) is quickly reached. The pressure to be reached ranges between +1 kPa and +150 kPa.

[0170] 7) Once the desired pressure has been reached, the intake valve (17) is closed. Valve (18) remains closed. The pressure measurement then begins with valves (17) and (18) closed for the entire duration of the analysis (a few minutes).

Determining the Fracture Point

[0171] The operating principle of the probe for determining the fracture point is as follows:

[0172] 1) The probe with its extension (12), in the open air, is scavenged by gas. Valve (17) is open, valve (18) is also open.

[0173] The gas used for this measurement preferably is a gas that is poorly soluble in the matrix to be analyzed in order to measure mechanical properties and not transport properties. For example, using nitrogen N2 is preferable for matrices with a lot of water, such as cheeses, for example, in order to limit its transfer into the matrix to be analyzed.

[0174] 2) A hole (25), optionally cylindrical, is made in the matrix to be analyzed. This hole (25) can be produced with a drill bit, for example.

[0175] 3) The device with its extension (12), with the scavenging system (6) operating, that is, with valves (17) and (18) open, is inserted into the hole (25) in the matrix to be analyzed.

[0176] It is inserted so that the means (19) for sealing the extension (12) is positioned in order to prevent gas leaks.

[0177] A free gaseous chamber (5) must be present between the surface of the matrix to be analyzed and the extension (12) of the probe, as shown in FIG. 3.

[0178] 4) The scavenging system (6) is maintained for a few tens of seconds with the probe planted in the cheese to ensure that the matrix is only in contact with the gas of interest.

[0179] 5) Once the scavenging is complete, the outlet valve (18) is closed.

[0180] 6) Valve (17) feeds the gaseous chamber (5) in contact with the matrix to be analyzed. The pressure progressively increases until the matrix is “fractured”, from which moment the pressure returns to atmospheric pressure.

Example 6: Determining the Henry Constant of CO.SUB.2 With Regard to a Cheese

1. Theory

[0181] In order to determine the Henry constant k.sub.H of a gas with regard to a matrix to be characterized, a piece of the matrix with a known volume V.sub.matrix is placed in a closed volume enclosure V.sub.enclosure containing only the gas of interest. The gas phase in the measurement enclosure has a volume V.sub.gas (V.sub.gas = V.sub.enclosure - V.sub.matrix) and it must be in equilibrium with the matrix to be analyzed at a pressure P.sub.ini.

[0182] An initial overpressure P.sub.0 is then imposed and the return to equilibrium is measured at a new pressure P.sub.eq (due to the transfer of some of the gas to the matrix to be analyzed). Under these conditions, assuming that the temperature is constant and that the thermodynamic equilibrium can be described by Henry’s law, the Henry constant is determined with Equation (1).

[00020]${\text{k}}_{\text{H}}=\frac{\raisebox{1ex}{$\left({\text{P}}_{\text{0}}-{\text{P}}_{\text{eq}}\right)\times {\text{V}}_{\text{gas}}$}\!\left/ \!\raisebox{-1ex}{$\text{R}\text{×T}$}\right.}{{\text{V}}_{\text{matrix}}}\times \frac{1}{{\text{P}}_{\text{eq}}-{\text{P}}_{\text{ini}}}$

[0183] Where P.sub.0 is the imposed overpressure (Pa), P.sub.eq is the equilibrium pressure (Pa), V.sub.gas is the volume of the gas phase (m.sup.3), V.sub.matrix is the volume of the matrix to be analyzed (m.sup.3), R is the ideal gas constant, T is the temperature (K) and P.sub.ini is the initial equilibrium pressure (Pa).

Material and Method

[0184] A block of cheese, stored for several months at 4° C., and then for several weeks at 19° C., was used to take the measurement. A piece of cheese weighing 0.33 g was taken for the analysis. Since the density of the cheese is 1,120 kg.m.sup.-3, the volume of the piece of cheese was 0.3 cm.sup.3. The CO.sub.2 originated from a gas cylinder (purity > 99.99%).

[0185] The measurement was carried out with the probe shown in FIG. 16. It is provided with a pressure sensor (2) and a sensor (27) for measuring the temperature of the gaseous phase inside the probe. Two valves (an intake valve (17) and an outlet valve (18)) allow the probe to be scavenged with the gas of interest. An internal tube (28) was added into the probe in order to ensure that the scavenging is properly carried out throughout the volume of the probe. The last part of the probe is made up of a cylindrical tube (29), into which the piece of matrix (30) to be analyzed was inserted and which was then hermetically sealed. The probe is entirely metallic and its void volume is 1.3 cm.sup.3.

[0186] Experimentally, the following procedure was applied: [0187] o the piece of matrix (30) to be analyzed (cheese in this case) is inserted into the probe; [0188] o the probe is closed; [0189] o the probe is scavenged with the gas of interest (CO.sub.2 in this case) for several seconds (ensuring that the temperature remains constant and equal to the ambient temperature); [0190] o by closing the gas outlet valve (18), an overpressure is imposed in the gaseous chamber (5); [0191] o the gas intake valve (17) is closed. This results in the gas transferring to the matrix (30) to be analyzed, the pressure reduces and then stabilizes at a value P.sub.ini; [0192] o in the same way, a second overpressure P.sub.0 is imposed and the stabilization of the pressure to a value P.sub.eq that is greater than the first stabilization pressure is awaited.

[0193] FIG. 17 shows the overall shape of the pressure variation during the experiment for determining the Henry constant.

3. Results

[0194] The following experimental pressures were measured at a temperature of 18.5° C.: [0195] P.sub.ini=99.1 kPa [0196] P.sub.0=126.4 kPa [0197] P.sub.eq=119.2 kPa

[0198] The Henry constant of CO.sub.2 with regard to cheese determined with Equation (1) in this case is equal to 5.0 x 10.sup.-4 mol.m.sup.-3.Pa.sup.-1. This value is of the same order of magnitude as the values from the literature (Acerbi ([2]); Jakobsen ([8])). The difference from the literature can originate from differences in the composition of the cheese or in the ripening duration, which was not the same.

Example 7: Determining the Henry Constant of CO.SUB.2 With Regard to Water

1. Theory

[0199] Equation (1) explained in Example 6 was also used to determine the Henry constant of CO.sub.2 in water.

2. Material and Method

[0200] Distilled water was used and the CO.sub.2 originated from a gas cylinder (purity > 99.99%). The experiments were carried out in a temperature regulated enclosure set to 18.5° C.

[0201] The measurement was carried out with the probe shown in FIG. 16 of Example 7. It is provided with a pressure sensor (2) and a sensor (27) for measuring the temperature of the gaseous phase inside the probe. Two valves ((17), (18)) allow the probe to be scavenged with the gas of interest. An internal tube (28) has been added into the probe in order to ensure that the scavenging is fully carried out throughout the volume of the probe. The last part of the probe is made up of a cylindrical tube (29), into which the water to be analyzed was inserted and which was then hermetically sealed. The probe is entirely metallic and its void volume is 1.3 cm.sup.3.

[0202] Experimentally, the following procedure was applied: [0203] 1.0 mL of water is injected into the probe; [0204] the probe is closed; [0205] the probe is scavenged with the gas of interest (CO.sub.2 in this case) for several seconds; [0206] by closing the gas outlet valve (18), an overpressure is imposed in the gaseous chamber (5); [0207] the gas intake valve (17) is closed. This results in the gas transferring to the water, the pressure reduces and then stabilizes at a value P.sub.ini [0208] in the same way, a second overpressure P.sub.0 is imposed and the stabilization of the pressure to a value P.sub.eq that is greater than the first stabilization pressure is awaited.

3. Results

[0209] The following experimental pressures were measured at a temperature of 18.5° C.: [0210] P.sub.ini = 99.6 kPa [0211] P.sub.0 = 103.0 kPa [0212] P.sub.eq = 101.0 kPa

[0213] The Henry constant of CO.sub.2 with regard to the water determined with Equation (1) is equal to 3.5 x 10.sup.-4 mol.m.sup.-3.Pa.sup.-1. This value is very close to that of the literature (Sander, 2015 ([13]); Versteeg ([14])) with an 8% deviation and appears to confirm the use of the probe for determining the Henry constant.

Example 8: Determining the Viscosity of a Bitumen and of a Bread Dough

1. Theory

[0214] The principle for determining the viscosity of a matrix involves applying an overpressure in a gaseous phase in contact with the matrix and measuring the pressure variation. Indeed, the pressure reduces over time due to the increase in volume of the gaseous phase. In this case, a gas needs to be selected that hardly reacts or solubilizes in the matrix or the elements used to provide the seal over the duration of the measurement, so that the entire pressure variation is attributable to the variation in volume of the matrix.

[0215] For a cylindrical geometry, and assuming that the variation in volume is only due to a variation in the radius of the gaseous cylinder, the pressure can be connected to the viscosity and to the radial deformation with Equation (1).

[00021]$\text{P}-{\text{P}}_{\text{atm}}=2\times \mu \times \frac{\text{dR}}{\text{R}}\times \frac{1}{\text{dt}}$

Where P is the pressure in the gas phase in contact with the matrix to be analyzed (Pa), P.sub.atm is the surrounding atmospheric pressure at the time of the test (approximately equal to 101.325 Pa at sea level), .Math. is the viscosity of the matrix to be analyzed (Pa.s), R is the radius of the gaseous cylinder created in the matrix to be analyzed (m) and t is the time (s). Ideally, the initial imposed pressure must be high compared to the pressure variation of the atmosphere in the matrix during the measurement.

[0216] The relative variation of the radius of the gaseous phase

[00022]$\frac{\text{dR}}{\text{R}}$

corresponds to a variation in volume at an exponent of ½ (since it is only radial deformation). In accordance with the ideal gas law (Equation (2)), the relative variation of the radius of the gaseous phase therefore can be determined with the pressure variation in the gas phase with Equation (3).

[00023]$\text{P}\text{×}\text{V}\text{=}\text{n}\text{×}\text{R}\text{×}\text{T}$

Where V is the volume of the gaseous cylinder in the matrix to be analyzed (m.sup.3), n is the amount of gas (mol), R is the constant of the ideal gases (J.mol.sup.-1.K.sup.-1) and T is the temperature (K).

[00024]$\frac{\Delta \text{R}}{\text{R}}=\frac{{\text{P}}_{\text{1}}{}^{1/2}-{\text{P}}_{\text{2}}{}^{1/2}}{{\text{P}}_{\text{1}}{}^{1/2}}$

Where P.sub.1 is the pressure at the time t.sub.1 (Pa) and P.sub.2 is the pressure at the time t.sub.2 > t.sub.1 (Pa).

2. Material and Methods

[0217] The viscosity measurements were carried out on the commercially available Azalt 70/100 (Total) bitumen and on a bread dough with a commercial composition. The measurements were carried out with nitrogen (purity > 99.99%).

[0218] The probe described in FIG. 18 was used to take the measurements. It is provided with a pressure sensor (2) and a temperature sensor (27). Two valves (an intake valve (17) and an outlet valve (18)) allow the probe to be scavenged with the gas of interest. An internal tube (28) was added into the probe in order to ensure that the scavenging is properly carried out throughout the volume of the probe. The fourth part of the probe is made up of a cylindrical tube (29) that is open at its end and is inserted into the matrix to be analyzed (30) in order to allow the gas to come into contact with the matrix. A plug (31) provides the seal with the matrix to be analyzed (30). The measurements were carried out in a temperature regulated chamber set to 22 ± 1° C. for the bitumen and 19 ± 1° C. for the bread dough.

[0219] Experimentally, the following protocol was applied: [0220] a 60 mm high and 7.5 mm diameter cylindrical cavity is hollowed out of the matrix to be analyzed (30) using a drill bit; [0221] the probe is inserted into the cylindrical cavity as illustrated in FIG. 18; [0222] an overpressure of approximately +2 kPa is imposed with nitrogen by conveying gas through the intake valve (17) and by closing the outlet valve (18); [0223] the gas intake valve (17) is closed and the pressure is measured for several minutes with an acquisition frequency of 1 second.

3. Results

[0224] With the bitumen, nine tests were carried out and the results are consolidated in FIG. 19. The measurements are reproducible and the average value of the viscosity is 5.6 ± 0.6 x 10.sup.5 Pa.s. This value is of the same order of magnitude as that from the literature (4.34 x 10.sup.5 Pa.s at 22° C. (Mouazen, 2011 ([11]))) and the difference can originate from the slight temperature deviation (measurements carried out with the probe at 21.4° C.).

[0225] In the same way with the bread dough, a viscosity of 1.0 x 10.sup.5 Pa.s was determined at 19.5° C. This value is also in good agreement with the literature (Bloksma, 1975 ([10])).

Example 9: Application of the Probe for Characterizing the Bread Dough Like an Alveograph

[0226] With the probe, it is possible to determine certain features of a bread dough like an alveograph. The principle, which is similar to that of an alveograph, involves continuously bringing gas into contact with the bread dough, which leads to an increase in the pressure and a deformation of the bread dough. The main difference with the alveograph originates from the fact that the measurements with the probe take place in a core in a block of dough (which allows the actual atmosphere of the bread dough to be preserved).

[0227] FIG. 20 shows the shape of a pressure curve obtained with the probe and the comparison with the alveograph. In FIG. 20-a, corresponding to the alveograph, several data items can be obtained for characterizing the bread dough: [0228] the maximum overpressure P characterizes the resistance to deformation (toughness of the dough); [0229] the area under the curve W allows the strength of the flour to be characterized, it is called baking strength; [0230] the elasticity index characterizes the elastic resistance; [0231] the abscissa at breakpoint L provides information concerning the extensibility of the bread dough.

[0232] With the probe (FIG. 20-b), similar information can be obtained (except the abscissa at breakpoint L, which is not observed since the measurement occurs on a large block of bread dough and not on a film): [0233] The maximum overpressure P.sub.max characterizes the resistance to deformation; [0234] The area under the curve (after a pre-defined measurement time) W allows the strength of the flour to be characterized; [0235] The elasticity index characterizes the elastic resistance.

Material and Method

[0236] The measurements were carried out with a bread dough with a commercial composition and with air. The probe used for the measurements is described in FIG. 21. It is provided with a pressure sensor and a temperature sensor. Two valves (an intake valve (17) and an outlet valve (18)) allow the gas to enter and to exit. The probe is also made up of a cylindrical tube (29), which is open at its end that is inserted into the matrix (30) to be analyzed in order to allow the gas to come into contact with the matrix (30). A syringe pump (32) and a syringe (33) allow the continuous arrival of the gas to be controlled at a controlled flow rate.

[0237] The following experimental procedure was adopted: [0238] The probe is planted into a block of bread dough [0239] The gas is continuously injected using the syringe pump at a flow rate of 0.8 mL.min.sup.- .sup.1 for 2 minutes [0240] The pressure is measured throughout the duration of the analysis with an acquisition frequency of 1 second. The temperature is also measured.

3. Results

[0241] FIG. 22 shows an example of a signal obtained with the probe for characterizing the bread dough. The pressure variation is very similar to that obtained with an alveograph, firstly with a pressure increase that characterizes the deformation resistance of the dough (P.sub.max = 0.7 kPa) and then with a gradual pressure reduction that reflects the extensibility of the bread dough.

[0242] Depending on the maximum measured pressure and the gradual pressure reduction, the quality of the bread dough thus can be qualified.

Example 10: Determining the CO.SUB.2 Diffusion Coefficient in Water

1. Theory

[0243] The principle of the measurement for determining the diffusion coefficient of a gas dissolved in a food matrix involves applying an overpressure in a gas phase (with the gas of interest only) in contact with the matrix to be analyzed. Due to the transfer of the gas from the gaseous phase to the matrix (according to Henry’s law) and then its diffusion into the matrix (according to Fick’s law), the pressure reduces in the gas phase. The evolution of this pressure reduction can be connected to the properties of the matrix with regard to the gas of interest, in particular the diffusion coefficient with Equation (1).

[00025]$\begin{array}{l}\text{P}\left(\text{t}\right)=\frac{{\text{C}}_{\text{0}}}{{\text{k}}_{\text{h}}}+\left({\text{P}}_{\text{0}}-\frac{{\text{C}}_{\text{0}}}{{\text{k}}_{\text{h}}}\right)\times \\ \exp \left[\frac{\text{t}}{{\text{D}}_{\text{CO2}}}\times {\left(\frac{{\text{R×T×D}}_{\text{CO2}}{\text{×k}}_{\text{h}}}{\text{e}}\right)}^2\right]\times \\ \text{erfc}\left[\sqrt{\frac{\text{t}}{{\text{D}}_{\text{CO2}}}}\times \left(\frac{{\text{R×T×D}}_{\text{CO2}}{\text{×k}}_{\text{h}}}{\text{e}}\right)\right]\end{array}$

[0244] With P being the pressure (Pa) over time t (s), C.sub.0 being the initial concentration of dissolved gas in the matrix to be analyzed (mol.m.sup.-3), k.sub.h being the Henry constant (mol.m.sup.3.Pa.sup.-1), P.sub.0 being the initial imposed overpressure (Pa), D.sub.CO2 being the diffusion coefficient of the gas in the matrix to be analyzed (m.sup.2.s.sup.-1) and e being the height of the gas phase in contact with the matrix to be analyzed (m).

2. Material and Method

[0245] Distilled water was used and the CO.sub.2 originated from a gas cylinder (purity > 99.99%). The experiments were carried out at a temperature of 20.0° C.

[0246] The measurement was carried out with the probe shown in FIG. 23. It is provided with a pressure sensor (2) and a sensor (27) for measuring the temperature of the gaseous phase inside the probe. Two valves (an intake valve (17) and an outlet valve (18)) allow the probe to be scavenged with the gas of interest. An internal tube (28) has been added into the probe in order to ensure that the scavenging is fully carried out throughout the volume of the probe. The last part of the probe is made up of a cylindrical tube (29), in which the water to be analyzed (34) was inserted using a syringe (33) and which was then hermetically sealed. The probe is entirely metallic and its void volume is 1.3 cm.sup.3.

[0247] Experimentally, the following procedure was applied: [0248] Scavenging of the probe is started by opening the gas intake and outlet valves; [0249] 1.0 mL of water is injected into the probe with the syringe; [0250] The scavenging, with water in the probe, is maintained for 1 minute; [0251] The gas outlet valve is closed; [0252] By closing the gas outlet valve, an overpressure P.sub.0 is imposed in the gaseous chamber (5); [0253] the supply of gas is cut by closing the gas intake valve and the pressure measurement is started for 120 seconds.

[0254] The CO.sub.2 diffusion coefficient in water was assessed considering that the Henry constant of CO.sub.2 in water is equal to 3.4 x 10.sup.-4 mol.m.sup.-3.Pa.sup.-1 and by assuming that the surface of the water is initially saturated with CO.sub.2 due to the CO.sub.2 scavenging for 1 minute before the start of the measurement.

3. Results

[0255] FIG. 24 shows the agreement between the experimental pressure values and those determined with the model (Equation (5)) for a diffusion coefficient of 1.6 x 10.sup.-9 m.sup.2.s.sup.-1. It should be noted that the model is in good agreement with the experimental values, which confirms that Equation (5) clearly describes the transfer and the diffusion of the CO.sub.2 in water. This value of the CO.sub.2 diffusion coefficient in water is in good agreement with the values of the literature with 11% deviation (Moultos et al., 2014 ([12]); Versteeg, 1988 ([14])).

[0256] Lists of references [0257] 1. Huc et al.: “Influence of salt content on eye growth in semi-hard cheese studied using magnetic resonance imaging and CO2 production measurements”, International Dairy Journal (2014). [0258] 2. Acerbi et al.: “Impact of salt concentration, ripening temperature and ripening time on CO2 production of semi-hard cheese with propionic acid fermentation”, Journal of Food Engineering, 177, 72-79 (2016). [0259] 3. Tveteraas O.: “A study of pressure decay in a closed CO2-water system”, Master Thesis, 2011. [0260] 4. Ghaderi et al.: “Estimation of concentration-dependent diffusion coefficient in pressure-decay experiment of heavy oils and bitumen”, Fluid phase equilibria, 2011. [0261] 5. Acerbi et al.: “An appraisal of the impact of compositional and ripening parameters on CO2 diffusivity in semi-hard cheese”, Food Chemistry, 2016. [0262] 6. Chaix E.: “Caracterisation et modelisation des transferts de gaz (O2/CO2) dans le systeme emballage/aliment en lien avec les reactions de croissance microbienne (microbiologie previsionnelle) (Characterization and modeling of the gas transfers (O2/CO2) in the packaging/food system in relation to the microbial growth reactions (predictive Microbiology))”, Thesis of the University of Montpellier 2, 2014. [0263] 7. Chaix et al.: “Oxygen and carbon dioxide solubility and diffusivity in solid food matrix: a review of past and current knowledge”, Comprehensive reviews in food science and food safety, Chaix et al., 2014. [0264] 8. Jakobsen M., Nygaard Jensen P.: “Assessment of carbon dioxide solubility coefficients for semi-hard cheeses: the effect of temperature and fat content”, Eur. Food Res. Technol., 229, 287-294 (2009). [0265] 9. Grenier D., Laridon Y., Le Ray D., Challois S., Lucas T.: “Monitoring of single eye growth under known gas pressure: Magnetic resonance imaging measurements and insights into the mechanical behavior of a semi-hard cheese”, Journal of Food Engineering 171, 119-128, (2016). [0266] 10. Bloksma, A., Nieman, W., (1975), “The effect of temperature on some rheological properties of wheat flour doughs”, Journal of Texture studies 6(3), 343-361. [0267] 11. Mouazen, M., (2011), “Evolution des proprietes rheologiques des enrobes bitume, vers une loi vieillissement/viscosite. (Evolution of the rheological properties of coated bitumen, towards an aging/viscosity law)″, Ecole Nationale Superieure des Mines de Paris (Higher National School of Mines, Paris). [0268] 12. Moultos, O.A., Tsimpanogiannis, I.N., Panagiotopoulos, A.Z., Economou, I.G., (2014), “Atomistic molecular dynamics simulations of CO2 diffusivity in H2O for a wide range of temperatures and pressures”, The Journal of Physical Chemistry B 118(20), 5532-5541. [0269] 13. Sander, R., (2015), “Compilation of Henry’s law constants (version 4.0) for water as solvent”, Atmospheric Chemistry and Physics 15(8), 4399-4981. [0270] 14. Versteeg, G.F., Van Swaaij, W.P., (1988), “Solubility and diffusivity of acid gases (carbon dioxide, nitrous oxide) in aqueous alkanolamine solutions”, Journal of Chemical & Engineering Data 33(1), 29-34.