METHOD FOR DETERMINING THE RHEOLOGICAL PARAMETERS OF A FLUID

Description

[0001] The present invention relates generally to the determination of the rheological parameters of fluids, whatever their nature, and more particularly by means of a method using a continuous jet drop generator.

[0002] By determination of the rheological parameters of fluids, is meant, within the meaning of the present invention, the identification, for any type of fluid (whether Newtonian, shear-thinning, shear-thickening, viscoelastic or threshold, etc.) of all the rheological properties of the fluids to be analyzed, such as in particular the surface tension, the density, the dynamic viscosity and the kinematic viscosity, the relaxation time, etc.,

[0003] By continuous jet drop generator, we mean, within the meaning of the present invention, a continuous ink jet ejection device, which is usually designated by the acronym CIJ

[0004] Understanding fluid flow properties and measuring associated rheological and physical properties are crucial from both research and industrial perspectives.

[0005] The main quantities characterizing a fluid are its density, its surface tension and its rheological properties of viscosity and elasticity. To determine these quantities, different measuring devices are necessary. Depending on the devices used, couplings or disturbances make the measurement of these properties difficult. For example, the rheological properties of elasticity are disturbed by the surface tension and inertias of fluids and viscoelasticity measuring tools such as rotary rheometers commonly used in research and industry.

[0006] TIREL CHRISTOPHE ET AL ("Measurement of extensional properties during free jet breakup", vol. 61, no. 2 January 14, 2020) describes a method for determining the rheological parameters of a fluid, using a continuous jet drop generator.

[0007] In order to determine the physical quantities of fluids, the present invention is based on the development of a new method for determining the rheological parameters of fluids using a continuous jet drop generator of the CIJ type and using a so-called "Data-Science" approach based on a set of data obtained from the CIJ process as well as the numerical simulation of this process. During the ejection of a fluid by the CIJ ejection process, three forces, inertial, viscous and interfacial (surface tension) are in competition and significantly affect the morphology of the jet and the drops obtained. Under certain conditions, the morphology of the jet is thus unique (as illustrated by the figure 4) and directly linked to the rheological properties of the fluid. The length from which the jet breaks is called the breaking length. The broken jet presents drops and depending on the experimental conditions satellites (secondary drops of volume(s) smaller than the main drops).

[0008] In the present invention, the jet of fluid from the nozzle to the drops having a stabilized shape will be called a complete jet.

[0009] By ejecting a fluid using a suitable CIJ device, and comparing its morphology to a data set containing a wide range of jet morphologies using a "Data-science" approach, it is possible to precisely determine the rheological properties of the fluid, i.e. its dynamic viscosity, surface tension and density.

[0010] The present invention therefore relates to a method for determining the rheological parameters of a fluid which comprises the following steps: A) introduction of said fluid into a continuous jet drop generator comprising a reservoir maintained at a given pressure p 0 using a pump or any other pressurizing device and communicating via an inlet orifice with an ejection head whose temperature is controlled; B) periodic stimulation of amplitude A (in volts) and frequency F=1 / T of a piezoelectric actuator, so that said piezoelectric actuator disturbs the pressurized fluid in said ejection head; C) ejection from said ejection head, via an outlet nozzle, of the fluid thus disturbed, which is in the form of a jet; D) obtaining, using a stroboscope at a given time t, a fixed and illuminated image of the complete jet; E) recording one or more photographs of all or part of said fixed and illuminated image of the complete jet, using a camera or a photographic apparatus;F) exploitation of the photographs from step E to extract therefrom a descriptive data set of said jet; G) determination of the rheological parameters of said fluid (1) for a given ejection nozzle, a given stimulation amplitude A i and a given pressure p 0i, i being a natural integer at least equal to 2, said determination of the rheological parameters being carried out using a statistical method previously parameterized using as a training set a database containing the morphologies of known fluid jets.;

[0011] The method according to the invention is capable of determining the rheological parameters of any type of fluid, whether Newtonian or non-Newtonian.

[0012] The first step A) of the method according to the invention consists of introducing, into a continuous jet drop generator, a fluid whose rheological parameters are to be determined. The method according to the invention is suitable for any type of fluid, whether Newtonian, shear-thinning, shear-thickening, viscoelastic, threshold, etc.

[0013] The continuous jet drop generator used in the process according to the invention (also called a CIJ type device) comprises a reservoir maintained at a given pressure p 0 using a pump or any other pressurizing device and communicating via an inlet orifice with an ejection head whose temperature is controlled, as illustrated in the figure 1 .

[0014] The second step B of the method according to the invention consists of carrying out a periodic stimulation of amplitude A (in volts) and frequency F=1 / T of a piezoelectric actuator, so that the latter disturbs the pressurized fluid in said ejection head. Pressurizing the fluid makes it possible to control the flow rate of the fluid during its ejection.

[0015] Advantageously, the piezoelectric actuator is immersed in the pressurized fluid in said ejection head.

[0016] The third step C) of the method according to the invention consists of ejecting from said ejection head, via an outlet nozzle, the fluid thus disturbed in step B, which then appears in the form of a jet of given morphology.

[0017] The fourth step D) of the method according to the invention is a step of obtaining, using a stroboscope at a given time t, a fixed and illuminated image of the complete jet.

[0018] By image of the complete set, is meant, within the meaning of the present invention, an image of the jet of fluid from the nozzle to the drops having a stabilized shape

[0019] Then, using a camera or a photographic device, one or more photographs are recorded of all or part of the image of the complete jet, the position of which appears fixed thanks to the stroboscopic lighting of said complete jet (step E). These images are then used (step F) to extract a descriptive data set of said jet and compared to a database in order to extract the rheological properties.

[0020] In particular, this database consists of the morphologies of fluid jets with different viscosities and surface tensions. It is therefore necessary to obtain the morphologies of a large number of fluid jets with different and known viscosities and / or surface tensions. As the morphology of the jets also depends on the parameters of the CIJ device, it is necessary to constitute this database under the same ejection conditions of the CIJ device. Furthermore, the number of known fluids (i.e. of which all the rheological parameters, namely the viscosity(ies), the surface tension and the density) are known and available experimentally, is insufficient to constitute the dataset.Therefore, a numerical simulation approach is necessary: ​​for a given nozzle, the jets are generated numerically and validated experimentally using some known real fluids, including standard fluids, by comparing the numerical and experimental results. A faithful prediction of the numerical model is therefore absolutely necessary in order to have a reliable determination of the rheological properties.

[0021] Jet morphologies are defined by the geometric shape taken by the free surface of the jet. It is possible to extract, from the geometric shape of the jet (as illustrated in the figure 3 ) information such as the following properties (non-exhaustive): the diameter of the undisturbed jet, the break length (smallest distance between the nozzle and the first drop), the drop volume, the drop surface at a certain distance from the break, the volume of the satellite(s), the surface of the satellite(s) at a certain distance from the break, the dynamics of the satellite(s) (slow, infinite or fast), the wavelength.

[0022] The measurement of the rheological properties of the ejected fluid is done by comparing the morphology of the jet to those contained in a database mapping a wide range of rheological properties.

[0023] Thus, more particularly, the last step of the method according to the invention (step G) is a step of comparison and interpolation of the descriptive data set of the jet obtained in step F.

[0024] This comparison and interpolation step F being carried out using a statistical algorithm for an outlet nozzle, a pressure p 0i and a stimulation amplitude A i given with i being a natural integer at least equal to 3, so as to estimate / determine the rheological parameters of said fluid.

[0025] In other words, this step F is based on the statistical algorithm which is a machine learning algorithm making it possible to identify, from experimentally obtained information, the fluid present using databases grouping together a large number of known fluids.

[0026] Advantageously, the descriptive data set of the jet may be the geometric shape of the jet or data extracted from said geometric shape of all or part of the complete jet. Thus, the determination of the rheological properties of the fluids that are analyzed using the method according to the invention is based on the geometric shape taken by the jet and in particular on the fact that this shape takes on a unique character depending on the stimulation amplitude.

[0027] Advantageously, the database may include information obtained with real jets and / or obtained with jets generated by numerical simulation (which are previously and experimentally validated using standard fluids).

[0028] According to a first variant embodiment of step G of the method according to the invention, the statistical algorithm can be based on a linear regression type model. The parameters of the model will be determined beforehand using as training set the database containing the morphologies of known fluid jets.

[0029] According to a second variant embodiment of step G of the method according to the invention, the statistical algorithm can be based on an artificial neural network type model.

[0030] Preferably, the neural network type model may comprise at least one layer of neurons, which will be previously trained using as training set the database containing the morphologies of known fluid jets.

[0031] The comparison and interpolation at step G is thus based on statistical models whose coefficients have been determined beforehand.

[0032] According to a first embodiment of the method according to the invention, the procedure is as follows: steps B to G are carried out for two different stimulation amplitudes A 1 and A 2 ; if the rheological parameters of the fluid estimated for each of these stimulation amplitudes A 1 and A 2 do not converge, steps B to G are then repeated with an amplitude A 3 or several other stimulation amplitudes A i , i being a natural integer at least equal to 3, until a convergence of the rheological parameters of the fluid thus estimated is obtained.

[0033] According to a second embodiment of the method according to the invention, the procedure is as follows: steps B to G are carried out for two different pressures p 01 and p 02; if the rheological parameters of the fluid estimated for each of these pressures p 01 and p 02 do not converge, then said steps B to G are repeated with a pressure p 02 or several other pressures p 0i, i being a natural integer at least equal to 3, until a convergence of the rheological parameters of the fluid thus estimated is obtained.

[0034] Other advantages and particularities of the present invention will result from the description which follows, given by way of non-limiting example and made with reference to the appended figures and to the examples: [ Fig. 1 ] - there figure 1 is a schematic cross-sectional representation of an example of a CIJ-type continuous jet drop generator implemented in the method according to the invention; [ Fig.2 ]- there figure 2 is an enlarged view of the ejector head of the CIJ generator shown in the figure 1 ; [ Fig.3] - there figure 3 is an example of a digital jet with the presence of drops and satellites; [ Fig.4 ]- there figure 4 shows the morphologies of jets of 2 fluids with the same surface tension, density and viscosity at low velocity gradient, for different stimulations, the data being obtained with an identical CIJ device in both cases; part a of [ Fig.4 ] shows the morphology of a fluid with Newtonian behavior (constant viscosity), while part b of [ Fig.4 ] shows the morphology of a fluid with shear-thinning behavior (viscosity decreasing with shear rate); [ Fig.5 ] - there Figure 5 shows the evolution of the results of the Reynolds numbers predicted (on the ordinate) by the neural network compared to the actual Reynolds number of the jet (on the abscissa).

[0035] THE Figures 1 and 2show the experimental measurement system used in the context of the present invention: it is a continuous jet drop generator 2 or CIJ type device. The fluid 1 whose rheological properties are to be determined is contained in a reservoir 20 maintained under pressure by means of a pump (not shown in these figures) to ensure the flow. The pump is either pressure or flow controlled. The fluid 1 to be analyzed reaches the ejection head 22 of the generator 2 and exits in the form of a jet 3. The ejection head 22 is temperature controlled via a thermostatically controlled bath or any other temperature control device. The ejected fluid 1 is stimulated using a piezoelectric actuator 23 before ejection, in order to increase the so-called Rayleigh-Plateau instability which is responsible for the breaking of the jet 3.The jet 3 ejected by the CIJ type device 2 and disturbed by the periodic stimulation of the piezoelectric actuator 23 generates drops at a fixed frequency close to the disturbance. Using a stroboscope, it is then possible to obtain a fixed and illuminated image of the jet. The latter is then photographed by a camera 5 (or a camera). Part or all of the jet 3 from the nozzle to the break (cf. [. Fig.3 ]), as well as the generated drops are obtained by moving the camera 5 (or the camera) along the jet. The morphology of the jet 3 is such as that shown by the figure 3 which shows an example of a digital jet with the presence of drops 31 and satellites 32 (only one satellite on [ fig.3 ]). In the example of the figure 3 , the dynamics of satellite 32 is slow because satellite 32 is caught up by the drop 31 which precedes it. EXAMPLES EXAMPLE 1 : use of the CIJ type device to generate continuous jets of drops of a Newtonian fluid and a non-Newtonian fluid ; study of their morphologies

[0036] In order to determine the rheological parameters of a Newtonian fluid 1 (noted A) with constant viscosity, we generate, using the continuous jet drop generator 2 illustrated in the Figures 1 and 2 , a continuous jet of drops of fluid 1 (noted A).

[0037] Then, we start again and generate, using the same continuous jet drop generator 2, a continuous jet of drops of a non-Newtonian fluid 1 (noted B), slightly rheofluidifying at a very high shear rate (greater than 300,000 s-1) with a view to also determining its rheological parameters.

[0038] Fluids A and B have the same surface tension, the same viscosity at low shear rates and the same density. Thus, the difference between these two fluids lies only in the shear-thinning character of fluid B.

[0039] Fluids A and B are ejected through the same CIJ-type devices at different stimulation amplitudes, with the voltage of the piezoelectric actuator 23 varying from 2V to 62V. A photo of jet 3 at the break is taken for each stimulation. Fig. 4 , for fluids A ( Figure 4a ) and B ( Figure 4b ).

[0040] Despite very similar rheological properties, the competition between the different inertial, viscous and interfacial forces (surface tension) brought into play during the ejection of the fluid makes it possible to discriminate between the fluids and we observe a strong difference in the geometric shape of the jet for high stimulation amplitudes. EXAMPLE 2 : determination of the viscosity of fluids by implementing the second variant of step G of the method according to the invention, according to which the statistical algorithm is based on an artificial neural network type model.

[0041] This example illustrates the determination of the viscosity of fluids using the method according to the invention, in the case where the statistical algorithm used in step G is based on an artificial neural network type model.

[0042] The ejection nozzle 24 is selected and identical for all numerical and experimental jets generated by a CIJ 2 type device as shown in the Figures 1 and 2 .

[0043] In this example, the average ejection velocity, density, and surface tension are also fixed. Only the fluid viscosity varies, and the Reynolds number is directly related to it.

[0044] 4005 Newtonian fluid jets are then generated using computational fluid dynamics simulation software: for a Reynolds number at the nozzle outlet varying from 100 to 900, in steps of one, five stimulation amplitudes are numerically simulated. The simulation results are rigorously compared to several real fluid jets to ensure the relevance of the result obtained.

[0045] From the geometric shape of the 4005 jets thus obtained, the following data are extracted for each jet, in order to constitute the database: the length of jet 3 before breaking, the surface area of ​​jet 3 before breaking, the volume of jet 3 before breaking, for the first 6 drops, the length, maximum height, volume and surface area of ​​the drop as well as the distance between it and the previous one (for the first drop we give the distance between it and the jet).

[0046] 80% of the data set is randomly selected to constitute a training set for learning the said artificial neural network and the remaining 20% ​​will constitute the test data set.

[0047] There Figure 5illustrates the results of neural network predictions from the test dataset. We observe an excellent correlation between the predicted Reynolds number and the actual Reynolds number, with a relative average error of less than 3%.

[0048] This result shows that the method according to the invention makes it possible to precisely determine the rheological characteristics of fluids.

Claims

1. A method for determining the rheological parameters of a fluid (1), said method comprising the following steps: A) introduction of said fluid (1) into a continuous-jet droplet generator (2) comprising a tank (20) maintained at a given pressure p0 using a pressurizing device and communicating via an inlet orifice (21) with an ejection head (22), the temperature of which is controlled; B) periodic stimulation, of amplitude A (in Volts) and of frequency F=1 / T, of a piezoelectric actuator (23), such that said piezoelectric actuator (23) disturbs the pressurized fluid (1) in said ejection head (22); C) ejection, via an outlet nozzle (24) and out of said ejection head (22), of said duly disturbed fluid (1), which takes the form of a jet (3); D) obtaining, using a stroboscope (4) at a given instant t, of a fixed and illuminated image of the complete jet (3); E) recording of one or more photographs of all or part of said fixed and illuminated image of the complete jet (3) using a camera or a photographic device (5); F) analysis of the photographs from the step E to extract therefrom a set of data descriptive of said jet (3); G) determination of the rheological parameters of said fluid (1) for a given outlet nozzle, and for a given stimulation amplitude Ai and pressure p0i, i being a natural integer at least equal to 2, said determination of the rheological parameters being performed using a statistical method previously parameterized by using as training set a database containing the morphologies of known fluid jets.

2. The method as claimed in claim 1, wherein the piezoelectric actuator (23) is immersed in the pressurized fluid (1) in said ejection head (22).

3. The method as claimed in claim 1 or 2, wherein the statistical method is based on a model of linear regression type.

4. The method as claimed in claim 1 or 2, wherein the statistical method is based on a model of artificial neural network type.

5. The method as claimed in claim 4, wherein the model of neural network type comprises at least one layer of neurons.

6. The method as claimed in any one of claims 1 to 5, wherein the dataset comprises the data on the geometrical form of all or part of the complete jet.

7. The method as claimed in any one of claims 1 to 5, wherein the dataset is based on parameters obtained from the geometrical form of all or part of the complete jet.

8. The method as claimed in any one of claims 1 to 5, wherein the database comprises information obtained with experimental fluid jets and / or obtained with fluid jets generated by digital simulation.

9. The method as claimed in any one of claims 1 to 6, wherein: - the steps B to G are performed with two different stimulation amplitudes A1 and A2; - if the rheological parameters of said fluid (1) estimated for each of these stimulation amplitudes A1 and A2 do not converge, said steps B to G are reiterated with one amplitude A3 or several other stimulation amplitudes Ai, i being a natural integer at least equal to 3, until a convergence of the duly estimated rheological parameters of said fluid (1) is obtained.

10. The method as claimed in any one of claims 1 to 6, wherein: - the steps B to G are performed for two different pressures p01 and p02; - if the rheological parameters of said fluid (1) estimated for each of these pressures p01 and p02 do not converge, said steps B to G are reiterated with one pressure p3 or several other pressures p0i, i being a natural integer at least equal to 3, until a convergence of the duly estimated rheological parameters of said fluid (1) is obtained.