DEVICE FOR MEASURING THE MEDIAN RADIUS OF BUBBLES IN A FOAMED PLASTER BLEND

Abstract

A method for determining a median radius R.sub.0 of a collection of bubbles in a foamed medium, which liquid is suitable for being cured and to form, after curing, a solid construction material or a solid polymer foam, the method including conveying the foamed medium into a cavity, transmitting an ultrasound pulse into the cavity, detecting the pulse, measuring a component chosen from an amplitude of the detected pulse and a phase of the pulse, and subsequently determining the median radius Ro of the bubbles in the foamed medium in the cavity on the basis of the determined component.

Claims

1. A method for determining a median radius R.sub.0 of a collection of bubbles comprised in a liquid foamed medium adapted to be cured and to form, after curing, a solid construction material or a solid polymer foam, the foamed medium having a liquid phase and a gaseous phase formed by the collection of bubbles, and having a predetermined gaseous volume fraction of between 0.05 and 0.8 inclusive, the method comprising: a) conveying the foamed medium into a cavity, b) transmitting an ultrasound pulse to the cavity by an ultrasound pulse transmitter, c) detecting the ultrasound pulse by an ultrasound pulse detector, d) determining, on the basis of the ultrasound pulse detected in step c) and a reference pulse, at least one feature selected from transmission T of the ultrasound pulse through the cavity and reflection R of the ultrasound pulse on a surface delimiting the cavity, e) determining the median radius R.sub.0 of the collection of bubbles from the at least one feature determined in step d) and the predetermined gas volume fraction .

2. The method according to claim 1, wherein the cavity has a width l, and wherein the ultrasound pulse transmitter and ultrasound pulse detector are arranged on either side of the width l of the cavity so that the ultrasound pulse propagates in the foamed medium along the width l of the cavity, and wherein, in step d) the transmission T of the ultrasound pulse through the cavity is determined, the method being adapted to determine a predetermined maximum median radius R.sub.0max of the collection of bubbles, wherein, in step b), the ultrasound pulse is transmitted at a transmission frequency f.sub.t strictly greater than a permitted propagation frequency f.sub.pp equal to ({square root over (3)}.Math.c.sub.0)/(2.Math.R.sub.0max), c.sub.0 being the ultrasound pulse velocity in the liquid phase of the foamed medium.

3. The method according to claim 2, wherein the cavity has a width l, and wherein the ultrasound pulse transmitter and ultrasound pulse detector are arranged on either side of the width l of the cavity so that the ultrasound pulse propagates in the foamed medium along the width l of the cavity, and wherein, in step d) the transmission T of the ultrasound pulse through the cavity is determined, the method is adapted to determine a predetermined maximum median radius R.sub.0max of the collection of bubbles, wherein, in step b), the ultrasound pulse is transmitted at a transmission frequency f.sub.t strictly less than a sensitivity limit frequency f.sub.ls of between 4.Math.({square root over (3)}.Math.c.sub.0)/(2.Math.R.sub.0max) and 10.Math.({square root over (3)}.Math.c.sub.0)/(2.Math.R.sub.0max), and preferably between 4.Math.({square root over (3)}.Math.c.sub.0)/(2.Math.R.sub.0max) and 6.Math.({square root over (3)}.Math.c.sub.0)/(2.Math.R.sub.0max).

4. The method according to claim 2, devoid of a step wherein an ultrasound pulse with a frequency lower than the permitted propagation frequency f.sub.pp is transmitted.

5. The method according to claim 2, wherein the transmission frequency f.sub.t is between 0.4 MHz and 56 MHz.

6. The method according to claim 1, wherein the cavity has a width l, and wherein the ultrasound pulse transmitter and ultrasound pulse detector are arranged on either side of the width l of the cavity so that the ultrasound pulse propagates in the foamed medium along the width l of the cavity, and wherein in step d), the transmission T of the ultrasound pulse through the cavity is determined, the width l being less than 5 mm.

7. The method according to claim 6, wherein, in step e), the median radius R.sub.0 is determined from the gas volume fraction , from the at least one feature, and from the width l.

8. The method according to claim 7, wherein, in step e), the median radius R.sub.0 is determined from an attenuation factor representative of the attenuation of the ultrasound pulse amplitude in the foamed medium along the width l.

9. The method according to claim 1, wherein in step a), a flow of foamed medium is driven into a channel comprising the cavity.

10. The method according to claim 1, wherein the foamed medium comprises at least one member selected from a foam and a blend.

11. The method according to claim 1, wherein in step b) the ultrasound pulse has a duration of between 0.03 s and 10 s.

12. The method according to claim 1, wherein, in step d), the at least one feature is determined from the start of the ultrasound pulse to a predetermined duration.

13. The method according to claim 1, wherein the cavity has a width l, and wherein the ultrasound pulse transmitter and the ultrasound pulse detector are arranged on either side of the width l of the cavity so that the ultrasound pulse propagates along the width l of the cavity and wherein the ultrasound pulse is a longitudinal ultrasound pulse.

14. The method according to claim 1, wherein the step e) of determining the median radius R.sub.0 of the collection of bubbles is carried out without using the resonant frequency of the collection of bubbles.

15. The method according to claim 14, wherein the ultrasound pulse is transmitted at a transmission frequency f.sub.t of between 0.4 MHz and 56 MHz.

16. The method according to claim 1, wherein the cavity has a width l, and the ultrasound pulse transmitter and ultrasound pulse detector are arranged on either side of the width l of the cavity, so that the ultrasound pulse propagates in the foamed medium along the width l of the cavity, and wherein in step d), the transmission T of the ultrasound pulse through the cavity is determined, and, in step e), a modulus of a complex transmission of the ultrasound pulse through the cavity is determined at least from the transmission T, and the median radius R.sub.0 is determined from the ratio defined by: $\frac{A}{B-g_1\left(l,,.Math.T.Math.\right)}$ A being a distance between 20 m and 500 m, B being a dimensionless number between 0.1 and 1, and g.sub.1 being a function having as variables the width l expressed in mm, the gas volume fraction and the modulus of the complex transmission, the function g.sub.1 is equal to $\frac{E}{l.Math.}\ln .Math.T.Math.$ E being a constant value.

17. A device for determining a median radius R.sub.0 of a collection of bubbles comprised in a liquid foamed medium adapted to be cured and to form, after curing, a solid construction material or a solid polymer foam, the foamed medium having a liquid phase and a gaseous phase formed by the collection of bubbles, and having a predetermined gaseous volume fraction of between 0.05 and 0.8 inclusive, the device comprising: a cavity adapted to receive the foamed medium, an ultrasound pulse transmitter arranged to transmit an ultrasonic wave towards the cavity, an ultrasound pulse detector arranged to detect an ultrasound pulse and, a control unit configured to: determine, on the basis of the ultrasound pulse detected by the ultrasound pulse detector and a reference pulse, at least one feature selected from transmission T of the ultrasound pulse through the cavity and reflection R of the ultrasound pulse on a surface delimiting the cavity, and to determine the median radius R.sub.0 of the collection of bubbles from the determined element and the predetermined gas volume fraction .

18. The device according to claim 17, wherein the cavity has a width l, the ultrasound pulse transmitter and ultrasound pulse receiver being arranged on either side of the width l of the cavity so that the ultrasound pulse propagates across the width l of the cavity.

19. The device according to claim 17, comprising a channel adapted for the flow of foamed medium, the channel comprising the cavity.

20. The device according to claim 17, configured to measure a predetermined maximum median radius R.sub.0max of the collection of bubbles, the ultrasound pulse transmitter comprising a first transducer extending along a length L in a direction perpendicular to a direction of ultrasound pulse transmission by the transmitter, the length L being greater than 30.Math.R.sub.0max.

21. The device according to claim 17, wherein the control unit is configured to determine the median radius R.sub.0 of the collection of bubbles from the determined at least one feature and the predetermined gas volume fraction without using the resonant frequency of the collection of bubbles, the ultrasound pulse being transmitted at a transmission frequency f.sub.t of between 0.4 MHz and 56 MHz.

22. The device according to claim 17, wherein the cavity has a width l, and the ultrasound pulse transmitter and ultrasound pulse detector are arranged on either side of the width l of the cavity, so that the ultrasound pulse propagates in the foamed medium along the width l of the cavity, and wherein the control unit is configured to determine the transmission T of the ultrasound pulse through the cavity, determine a modulus of a complex transmission of the ultrasound pulse through the cavity at least from the transmission T, and determine the median radius R.sub.0 from the ratio defined by: $\frac{A}{B-g_1\left(l,,.Math.T.Math.\right)}$ A being a distance between 20 m and 500 m, B being a dimensionless number between 0.1 and 1, and g.sub.1 being a function having as variables the width l expressed in mm, the gas volume fraction and the modulus of the complex transmission, the function g.sub.1 is equal to $\frac{E}{l.Math.}\ln .Math.T.Math.$ E being a constant value.

Description

DESCRIPTION OF THE FIGURES

[0042] Other features, purposes and advantages of the invention will emerge from the following description, which is purely illustrative and non-limiting, and which must be read in conjunction with the appended drawings in which:

[0043] FIG. 1 schematically shows a method according to one embodiment of the invention,

[0044] FIG. 2 schematically shows a device according to one embodiment of the invention,

[0045] FIG. 3 shows a variation in the attenuation of an ultrasound pulse transmitted through a device cavity, as a function of pulse frequency,

[0046] FIG. 4 shows a variation of the real part of the Napierian logarithm of the transmission of a pulse through a cavity filled with a foamed medium comprising bubbles, as a function of the median radius of the bubbles,

[0047] FIG. 5 shows a device according to one embodiment of the invention adapted to allow the liquid medium to flow into the cavity,

[0048] FIG. 6 shows calibration of a device according to one embodiment of the invention.

[0049] In all the figures, similar elements are marked with identical references.

Definitions

[0050] Non-transparent means a foamed medium, arranged in a cavity of predetermined geometry, with a haze factor greater than 1%, in particular greater than 5% and preferably greater than 10%.

[0051] The haze factor is the ratio between the intensity of a light beam diffused by a passing through the medium (diffuse fraction) at an angle greater than 2.5 and the intensity of a light beam transmitted through the medium. The haze factor may be measured by spectroscopy techniques. The integration of the intensity over the whole of the visible range (from 380 nm to 780 nm) makes it possible to determine the normal transmission T.sub.L and diffuse transmission T.sub.d. Such a measurement may also be obtained using a Hazemeter.

[0052] The median radius R.sub.0 of a collection of bubbles is the median radius R.sub.0 determined from a distribution of radii, the distribution being formed by the radii of each bubble in the collection of bubbles.

[0053] Pulse transmission T means a quantity determined from a pulse detected after propagation of the pulse through a predetermined quantity of a foamed medium in a cavity and from a reference pulse. A pulse reflection R is a quantity determined from a pulse detected after the pulse is reflected on a surface delimiting the cavity and from a reference pulse.

[0054] Preferably, complex transmission T of a pulse transmitted through a predetermined quantity of foamed medium in a cavity is defined as the ratio between the complex Fourier transform, at transmission frequency f.sub.t, of the pulse transmitted through a cavity, for a cavity filled with foamed medium, and between the Fourier transform at frequency f.sub.t, for a cavity filled with water. The transmission T and/or reflection R of a pulse can be determined at 25 C.

[0055] In a system formed by a cavity of width l, formed by a first material, and comprising the medium to be measured, the complex transmission T of a pulse can be the quantity defined by the formula described in the following equation (1):

[00003]$\begin{array}{cc}T=\frac{z}{z_0}\frac{{\left(z_p+z_0\right)}^2}{{\left(z_p+z\right)}^2}.Math.e^{i.l.\left(k-k_0\right)}& \left(1\right)\end{array}$

where Z is the acoustic impedance of the medium being measured, Z.sub.p is the acoustic impedance of the first material, Z.sub.0 is the impedance of the water in the cavity, k is the wavenumber for pulse propagation in the medium being measured and k.sub.0 is the wavenumber for pulse propagation in the liquid phase of the medium being measured.

[0056] The attenuation d of a pulse propagating through a cavity of width l is the linear attenuation defined by =ln|T|/l. Preferably, the attenuation is measured for a pulse propagating through the cavity filled with a bubble-free liquid medium identical to the medium of the liquid phase of the foamed medium.

[0057] A solid construction material is any solid material suitable for use in a construction project. A solid construction material can be plaster, mortar, lime, cement, concrete and/or a coating.

DETAILED DESCRIPTION OF THE INVENTION

General Principle for Determining the Median Radius R.SUB.0 .of a Collection of Bubbles 1

[0058] With reference to FIG. 1 and FIG. 2, one aspect of the invention is a method 100 for determining a median radius R.sub.0 of a collection of bubbles 1 comprised in a liquid foamed medium 2 adapted to be cured and to form, after curing, a solid construction material or solid polymer foam. The foamed medium 2 can be a non-transparent medium, in particular an opaque medium.

[0059] The foamed medium 2 has a liquid phase and a gaseous phase formed by the collection of bubbles. The foamed medium 2 has a predetermined gas volume fraction of between 0.05 and 0.8 inclusive. The gas volume fraction can be predetermined by mixing a predetermined volume of bubble-free liquid with a predetermined volume of gas. The predetermined gas volume fraction can be confirmed or determined by weighing the foamed medium after the gas has been introduced into the liquid.

[0060] The method 100 comprises a step of conveying 101 the foamed medium 2 into a cavity 3. The cavity 3 is filled with foamed medium 2. A sample of the foamed medium 2 can be taken and poured into a cavity 3 to fill the cavity 3.

[0061] The method 100 comprises a step of transmitting 102 an ultrasound pulse to cavity 3 by an ultrasound pulse transmitter 4. The ultrasound pulse can then be transmitted through the cavity 3 or reflected by the cavity 3.

[0062] The method 100 comprises a pulse detection step 103 by an ultrasound pulse detector 5.

[0063] The method 100 comprises a step of determining 104, on the basis of the pulse detected in step 103 and a reference pulse, at least one feature selected from transmission T of the pulse through the cavity 3 and reflection R of the pulse on a surface delimiting the cavity 3.

[0064] Following the step 104 of determining at least one element, the method 100 comprises a step 105 of determining the median radius R.sub.0 of the collection of bubbles 1 from the element(s) determined in step 104 and from the predetermined gas volume fraction .

[0065] In this way, the transmission of the pulse through the cavity 3 or reflection of the pulse on the cavity 3 stresses the bubbles in the foamed medium 2, each of the bubbles acting as a local acoustic diffuser. The detected pulse comprises the contributions of each of the local diffusers formed by the bubbles, and the detection of the transmitted or reflected pulse makes it possible to determine the median radius R.sub.0 in the volume fraction range between 0.05 and 0.8.

[0066] Measuring the median radius of the bubbles is therefore simpler than using X-ray tomography.

Pulse Transmission Frequency f.SUB.T

[0067] The method 100 can be adapted to determine a predetermined maximum median radius R.sub.0max of the collection of bubbles. In other words, the method 100 can be adapted to determine a median radius R.sub.0 of the collection of bubbles that is smaller than a maximum median radius R.sub.0max of the predetermined collection of bubbles. The cavity 3 can have a width l. The transmitter 4 and detector 5 can be arranged on either side of the width l of the cavity 3 so that the pulse propagates in the foamed medium 2 along the width l of the cavity 3. This configuration enables pulse detection by pulse transmission. Referring to FIG. 3, in the transmission step 102, the pulse can be transmitted at a transmission frequency f.sub.t strictly higher than a permitted propagation frequency f.sub.PP. The frequency f.sub.PP is equal to ({square root over (3)}.Math.c.sub.0)/(2.Math.R.sub.0max), c.sub.0 being the pulse velocity in the liquid phase of the foamed medium 2, in particular one that is bubble-free. In this way, the pulse can be transmitted by propagation through the cavity. At frequencies f.sub.t below the permitted propagation frequency f.sub.PP, pulse transmission is due to an evanescent field in the cavity 3. In an evanescent field, the attenuation is very high compared to the attenuation in the propagation field, making it impossible to detect the pulse. For this reason, the frequency f.sub.t may be higher than the frequency f.sub.pp.

[0068] The method 100 can be adapted to determine a maximum median radius of less than 700 m, in particular 250 m. For a maximum median radius R.sub.0max equal to 250 m and a gas volume fraction equal to 0.05, the permitted propagation frequency f.sub.pp is equal to 0.4 MHz. The transmission frequency f.sub.t can be higher than 0.4 MHz, particularly when the foamed medium 2 is a blend, notably higher than 1 MHz and preferably higher than 4 MHz.

[0069] The method 100 can be adapted to determine a minimum median radius R.sub.0min greater than 20 m.

[0070] FIG. 3 shows the attenuation of a pulse transmitted through the cavity 3 comprising a foamed medium 2 with a gas volume fraction equal to 0.35 and bubbles with a median radius R.sub.0 equal to 75 m.

[0071] With reference to FIG. 4, the method 100 can be adapted to determine a predetermined maximum median radius R.sub.0max of the collection of bubbles 1. In the transmission step 102, the pulse can be transmitted at a transmission frequency f.sub.t strictly below a sensitivity limit frequency f.sub.ls between 4.Math.({square root over (3)}.Math.c.sub.0)/(2.Math.R.sub.0max) and 10.Math.({square root over (3)}.Math.c.sub.0)/(2.Math.R.sub.0max) and preferably between 4.Math.({square root over (3)}.Math.c.sub.0)/(2.Math.R.sub.0max) and 6.Math.({square root over (3)}.Math.c.sub.0)/(2.Math.R.sub.0max). In this way, it is possible to increase the sensitivity of the median radius R.sub.0 determination when the median radius R.sub.0 tends towards R.sub.0max. Indeed, the sensitivity of detecting the median radius R.sub.0 is significantly higher when f.sub.t is less than f.sub.ls compared to when f.sub.t is greater than fls.

[0072] The sensitivity limit frequency f.sub.ls can be between 2.5 MHz and 140 MHz, preferably between 3 MHz and 10 MHz.

[0073] The method 100 may be devoid of a frequency f.sub.t sweep. In fact, pulse detection at a single frequency f.sub.t can be used to determine the median radius R.sub.0. The transmitted pulse can have a frequency spectrum centered on the transmission frequency f.sub.t. The method 100 may be devoid of a step in which a pulse with a frequency lower than the permitted propagation frequency f.sub.pp is transmitted. In this way, the determination of the resonant frequency of the bubbles in a foamed medium can be eliminated in order to determine the median radius R.sub.0, thus speeding up and simplifying the determination of the median radius R.sub.0 relative to a method wherein the acquisition of a frequency spectrum covering the resonant frequency of the foamed medium would be necessary.

Determining the Median Radius R.sub.0 from the Element

[0074] The cavity 3 can have a width l, and the transmitter 4 and detector 5 can be arranged on either side of the width l of the cavity 3 so that the pulse propagates in the foamed medium 2 along the width l of the cavity. In step d), the transmission T of the pulse through the cavity 3 can be determined. In determination step 105, the median radius R.sub.0 can be determined from the gas volume fraction , from the component, and from the width l.

[0075] Preferably, the median radius R.sub.0 can be determined by evaluating a radius determination function g.sub.dr having as variables the gas volume fraction , the width l, and the complex transmission T The radius determination function g.sub.dr can have as a variable the modulus |T| of the complex transmission.

[0076] The well-known independent scattering approximation model (ISA, described in Sheng P., 2006, Introduction to wave scattering, localization and mesoscopic phenomena, Vol. 88, Springer Science & Business Media) does not allow the median radius R.sub.0 to be determined for a gas volume fraction greater than 2%.

[0077] To this end, the inventors have developed a phenomenological model based on data comprising pairs associating the complex transmission T with the median radius R.sub.0.

[0078] With reference to FIG. 4, the median radius R.sub.0 can be determined from a predetermined function by a fit defined from a set of element series, each element series comprising at least one predetermined median radius R.sub.0i and a complex transmission T associated with the median radius R.sub.0. Each series can also comprise a gas volume fraction associated with the median radius R.sub.0i, and/or a width l associated with the median radius R.sub.0i. The predetermined median radius R.sub.0i can be obtained by various types of known measurement, such as optical measurement or X-ray tomography measurement.

[0079] The median radius R.sub.0 can be determined from the formula defined in equation 2 below:

[00004]$\begin{array}{cc}{R}_0=\frac{A}{B-g_1\left(l,,.Math.T.Math.\right)}& \left(2\right)\end{array}$

wherein A is a distance between 20 m and 500 m and in particular between 100 m and 150 m, B is a dimensionless number between 0.1 and 1 and in particular between 0.2 and 0.6, and g.sub.1 is a function having as variables the width l expressed in mm, the gas volume fraction and the modulus of the complex transmission |T|.

[0080] The function g.sub.1 can be defined as described in equation 3 below:

[00005]$\begin{array}{cc}{g}_1=\frac{E}{l.Math.}\ln .Math.T.Math.& \left(3\right)\end{array}$

wherein E is a constant value homogeneous to a distance, preferably between 0.01 mm and 0.5 mm, and in particular between 0.070 mm and 0.090 mm.

[0081] The method 100 can be adapted to measure a median radius R.sub.0 between 20 m and 120 m, with A equal to 120 m, B equal to 0.5 and E equal to 0.072 mm. Curve (a) in FIG. 4 shows the variation in |T| for a model including these parameters.

[0082] The method 100 can be adapted to measure a median radius R.sub.0 between 50 m and 200 m, with A equal to 110 m, B equal to 0.25 and E equal to 0.072 mm. Curve (b) in FIG. 4 shoes the variation in ln|T| for a model including these parameters.

[0083] Determination of the median radius R.sub.0 can be implemented on the basis of an attenuation factor representative of the linear attenuation of the pulse amplitude in the foamed medium 2. The phenomenological model developed can take into account the attenuation of the pulse as it propagates through the cavity 3, which is filled with a bubble-free liquid medium identical to the liquid medium of the liquid phase of the foamed medium. Each series used to determine the predetermined function by a fit may comprise the attenuation . The median radius R.sub.0 can be determined from the formula defined in equation 4 below:

[00006]$\begin{array}{cc}{R}_0=\frac{A}{B-g_2\left(l,,.Math.T.Math.,\right)}& \left(4\right)\end{array}$

[0084] The function g.sub.2 can be defined by equation 5 below:

[00007]$\begin{array}{cc}{g}_2=\frac{E}{l.Math.}\ln .Math.T.Math.+l& \left(5\right)\end{array}$

Architecture of the Device 6 for Determining the Median Radius R.SUB.0

[0085] Referring to FIG. 2, another aspect of the invention is a device 6 for determining the median radius R.sub.0 of the collection of bubbles 1 comprised in the foamed medium 2. The device 6 is suitable for implementing method 100.

Foamed Medium 2

[0086] The foamed medium 2 is liquid and suitable for curing to form a solid construction material or solid polymer foam. The foamed medium 2 can be non-transparent, and preferably opaque. In fact, the method 100 makes it possible to determine the median radius R.sub.0 of collection of bubbles 1 without having to use the optical transmission properties of foamed medium 2.

[0087] The predetermined gas volume fraction of the foamed medium 2 is between 0.05 and 0.8 inclusive, in particular between 0.1 and 0.8 inclusive and preferentially between 0.3 and 0.8. In fact, the method 100 enables measurement of media with predetermined gas volume fractions that are very high compared with the prior art.

[0088] The foamed medium 2 may comprise a cement blend, a plaster blend, a lime blend or a mortar blend. In this way, it is possible to control the median radius R.sub.0 of the bubbles 1 introduced into a blend so as to lighten the material formed by the solidified blend without degrading the mechanical performance of this material.

[0089] The foamed medium 2 can be produced by mixing water in a 3/7 proportion and gypsum in a 4/7 proportion in a mechanical mixer (e.g. a Tefal blender, model BL305801), adjusting the volume of water and gypsum relative to the total volume of the mixer so that the gas fraction is between 0.05 and 0.8.

[0090] The foamed medium 2 can comprise polyurethane foam and polyisocyanurate foam.

Cavity 3

[0091] The device 6 comprises a cavity 3 adapted to receive the foamed medium 2. The cavity 3 can have a width l. The width l can be measured along the direction of pulse propagation.

[0092] The transmitter 4 and receiver 5 can be arranged on either side of the width l of the cavity 3, so that the pulse propagates across the width l of the cavity 3, preferably into the foamed medium 2. The transmitter 4 may comprise a first transducer 11. The receiver 5 may comprise a second transducer 12. The first transducer 11 can be arranged to transmit a pulse towards the second transducer 12.

[0093] The width l can be less than 5 mm, in particular less than 2 mm, and preferentially less than 0.8 mm. In this way, it is possible to determine the median radius R.sub.0 by acquiring a signal representative of a ballistic portion of the transmitted pulse. Indeed, for widths l greater than 5 mm, the signal acquired by detector 5 is mostly representative of the superposition of several diffusion paths in foamed medium 2, which is driven by a gas volume fraction of between 0.05 and 0.8. This part of the transmitted signal can be called the coda. With a width l of less than 5 mm, it is possible to acquire a coda-free part of the transmitted signal. This part is also called the ballistic part of the signal. Only the ballistic part of the signal can be used to determine the median radius R.sub.0.

Ultrasound Pulse Transmitter 4

[0094] The device 6 comprises an ultrasound pulse transmitter 4 arranged to transmit an ultrasonic wave towards the cavity 3.

[0095] The transmitter 4 can be configured to transmit a longitudinal ultrasound pulse and/or a transverse ultrasound pulse. During the pulse transmission step 101, when the ultrasound pulse is longitudinal, the method 100 may comprise a step 103 of detecting the pulse propagated through the cavity 3. The detector 5 can then be arranged on the opposite side of the cavity 3 as the transmitter 4. When the ultrasound pulse is transverse, the method 100 may comprise a step 103 to detect the pulse reflected by the cavity 3. The detector 5 can then be arranged on the same side of the cavity 3 as the transmitter 4.

[0096] The transmitter 4 may comprise a voltage generator 10. The first transducer 11 may be an immersion transducer. The first transducer 11 may be focused to infinity. The first transducer 11 may be, for example, an Olympus V308-SU transducer.

[0097] The device 6 can be configured to measure a predetermined maximum median radius R.sub.0max of the collection of bubbles, and the first transducer 11 can extend along a length L in a direction perpendicular to a direction of pulse transmission by the transmitter 4. The length L can be greater than 30.Math.R.sub.0max and preferentially greater than 50.Math.R.sub.0max. In this way, it is possible to increase the proportion of the ballistic part in the detected pulse and reduce the proportion of the coda in the detected pulse. In fact, the long length L of the first transducer 11, compared with the maximum bubble radius R.sub.0max, enables signals to be averaged, each one driven by an individual bubble diffusion. The predetermined maximum median radius R.sub.0max may be equal to 300 m and the length L may be greater than 9 mm and preferably greater than 15 mm.

[0098] The voltage generator 10 can be a high-voltage electrical pulse generator, configured to transmit an electrical pulse with an amplitude greater than 50 V, in particular greater than 100 V and preferably greater than 400 V. The voltage generator 10 can be configured to transmit an electrical pulse with a negative mean voltage, so that the voltage of the electrical pulse is always negative. In this way, it is possible to counteract the attenuation of the pulse amplitude caused by transmission through the cavity 3 or reflection on the cavity 3, and thus enable detection of the pulse by the detector 5. The voltage generator 10 can be configured to transmit an electrical pulse with a duration of between 0.03 s and 10 s. The voltage generator 10 may be a JSR Ultrasonics DPR300 generator.

Ultrasound Pulse Detector 5

[0099] The device 6 comprises an ultrasound pulse detector 5 arranged to detect an ultrasound pulse. The detector 5 may comprise a second transducer 12.

[0100] The transmitter 4 and the detector 5 may be arranged on either side of the width l of the cavity 3 so that the pulse propagates in the foamed medium 2 along the width l of the cavity 3. This configuration corresponds to pulse measurement through the cavity 3 via transmission. The first transducer 11 and the second transducer 12 may be identical. The second transducer 12 may be an Olympus V308-SU transducer. The second transducer 12 may extend along a length L in a direction perpendicular to a direction of pulse transmission by the transmitter 4. The length L can be at least greater than 30.Math.R.sub.0max and preferentially greater than 50.Math.R.sub.0max. In this way, it is possible to increase the proportion of the ballistic part in the detected pulse and reduce the proportion of the coda in the detected pulse.

[0101] The transmitter 4 and detector 5 can be arranged on the same side of cavity 3, so that the pulse is reflected by cavity 3. This configuration corresponds to pulse measurement through the cavity 3 via reflection. In a reflection measurement, the pulse does not propagate in the cavity 3, but the foamed medium 2 in the cavity 3 causes a change in the reflected signal to detector 5. In this configuration, the first transducer 11 and the second transducer 12 may be the same transducer. The transducer can be directly connected to the control unit 7.

[0102] The detector 5 may also comprise an array of second transducers 12. In this way, the pulse propagated through the cavity 3 can be imaged. The array of second transducers can be a linear array in which the second transducers are arranged in a direction perpendicular to the width l.

Control Unit 7

[0103] The device 6 comprises a control unit 7 configured to acquire at least one component selected from an amplitude of the pulse detected by the detector 5 and a phase of the pulse detected by the detector 5.

[0104] The control unit 7 is configured to determine, on the basis of a pulse detected by the detector 5 and a reference pulse, at least one feature selected from transmission T of the pulse through the cavity 3 and reflection R of the pulse on a surface delimiting the cavity 3. The control unit 7 can also be configured to determine the modulus of the complex transmission |T|.

[0105] The control unit 7 is configured to determine the median radius R.sub.0 of the collection of bubbles 1 from the determined element(s) and the predetermined gas volume fraction . To this end, the control unit 7 can be configured to calculate the median radius R.sub.0 from the previously described model. The control unit 7 may comprise at least one processor and at least one memory, enabling calculation of the component and/or the median radius R.sub.0. The memory may comprise data representative of the reference pulse(s).

[0106] The control unit 7 can be connected to the detector 5, in particular to the second transducer 12 of the detector 5. The control unit 7 can be configured to control the voltage generator 10 of the transmitter 4. The control unit 7 may comprise a multiplexer for acquiring a pulse-related signal from first transducer 11 and/or second transducer 12.

[0107] In determination step 104, the element can be determined from a signal representative of the start of the pulse up to a predetermined pulse duration. The predetermined duration can be less than 2.Math.(1/f.sub.t) and preferably less than (1/f.sub.t). In this way, it is possible to avoid taking any pulse echoes into account when determining the component. The control unit 7 can be configured to determine the median radius R.sub.0 from the component determined only from the start of the pulse to the predetermined duration.

Flow of Foamed Medium 2

[0108] With reference to FIG. 5, the device 6 may comprise a channel 8 adapted for a flow of the foamed medium 2. The channel 8 comprises the cavity 3. The channel 8 can be tapered along the main flow direction of channel 8, with a tapered portion of the channel forming the cavity 3.

[0109] During the transport 101 of the foamed medium 2 in the cavity 3, a flow of foamed medium 2 can be entrained into the channel 8. Thus, it is possible to control the median bubble radius R.sub.0 of a foamed medium 2 during its production by diverting a sample of this foamed medium 2 to channel 8. The flow of foamed medium 2 can be driven by a flow generator 9.

[0110] The flow of foamed medium 2 can be sequential. If so, the flow is distinct from the transmission 102 and detection 103 steps.

[0111] The flow of foamed medium 2 can be continuous. If so, the transmission 102 and detection 103 are implemented during the flow. In this way, it is possible to average the effect of bubbles on the diffusion of the pulse(s), thus increasing the accuracy of the determination of the median radius R.sub.0.

Calibrating the Device 6

[0112] With reference to FIG. 6, the device 6 can be calibrated on the basis of median radius measurements r.sub.RX implemented by X-ray tomography. FIG. 6 shows a calibration curve determined from median radius measurements implemented by X-ray tomography and from the determination of the associated median radii for the same liquid media 2. The median radii are determined using the model described by the formulas in equations (2) and (3) above.