WO2025005788A1

WO2025005788A1 - Apparatus, system and methods for high-frequency extensional rheology

Info

Publication number: WO2025005788A1
Application number: PCT/NL2024/050321
Authority: WO
Inventors: Yu-Fan Lee; Gabriel Marinus Henricus Meesters; Valeria GARBIN
Original assignee: Technische Universiteit Delft
Priority date: 2023-06-29
Filing date: 2024-06-19
Publication date: 2025-01-02
Also published as: NL2035219B1

Abstract

The present invention is in the field of an apparatus investigating or analysing materials by determining their physical properties, in particular rheological properties, a method of measuring extensional rheology of a material, in particular a high throughput method, and a computer program for carrying out the method of measuring extensional rheology of a material.

Description

APPARATUS, SYSTEM AND METHODS FOR HIGH-FREQUENCY EXTENSIONAL RHEOLOGY

FIELD OF THE INVENTION

RELATED APPLICATIONS

The present application claims the benefit of priority from Dutch Patent Applications NL2035219, filed on June 29, 2023, in the name of Technische Universiteit Delft, Netherlands.

The entire contents of the above-referenced application and of all priority documents as referenced in any present or future Application Data Sheet filed herewith are hereby incorporated by reference for all purposes.

BACKGROUND OF THE INVENTION

The present invention is in the field of rheology. Rheology relates to flow properties of matter, typically being a liquid. It may also be relevant for soft solids, materials with plasticity properties in that they flow rather than deforming elastically in response to an applied force. Rheology is considered to be a part of physics, and it is regarded to deal with the deformation and flow of materials. Rheological measurements can be performed on complex substances in view of their microstructure. Many of these substances find application in daily life, such as bodily fluids, biological materials, foods, and suspensions.

Liquids can be characterized, for instance in terms of viscoelasticity. Typically the terms “Newtonian” and “Non-Newtonian” are used. For a Newtonian fluid viscous stresses arising from a flow thereof are at every individual point of the fluid considered to be linearly correlated to a local strain rate, which relates to the rate of change of its deformation over time. Stresses are proportional to the rate of change of the fluid's velocity vector. Newtonian fluids therefore can be characterized by a single coefficient of viscosity; as the viscosity may also depend on temperature, this coefficient is for a given temperature. A class of fluids of which the viscosity changes with the strain rate or strain history is referred to as non-Newto- nian fluids.

Rheology characterization, or rheometry, can be used for non-Newtonian fluids. It is noted that rheological characteristics of such fluids may change, such as the viscosity of a fluid that may be reduced by mechanical agitation; such materials are shear-thinning materials, where an increase in relative flow velocity will cause a reduction in viscosity. Theoretical aspects of rheometry relate to a relation of flow/deformation behaviour of material and its internal structure, and the flow/deformation behaviour of materials that cannot be described by classical fluid mechanics or elasticity.

Formulated products that appear in daily life, such as detergents, shampoos, foods, and drinks, are often extremely complex multicomponent, structured, and multiphase materials, such as wherein a range of chemical compounds are blended, to obtain the desired texture and performance. Because of the complexity of formulated products, predicting the performance of the final product in application-relevant conditions from the current theoretical framework of physical chemistry is very difficult or impossible. Experimental determination and characterization is thus often necessary. The bottleneck, however, is a lack of any existing instruments available in the R&D phase to correctly replicate the realistic flow conditions during processing or use by the consumer. Currently, none of the instruments on the market can measure extensional properties at high-frequency flow conditions.

Some background art may be referred to. Akaki et al. (D01: 10.1039/C6SM02810A) characterised the resonant behaviour in ultrasound of isolated microbubbles embedded in agarose gels, commonly used as tissue-mimicking phantoms. Gels with different viscoelastic properties were obtained by tuning agarose concentration, and were characterised by standard rheological tests. Isolated bubbles (100-200 pm) were excited by ultrasound (10-50 kHz) at small pressure amplitudes (<1 kPa), to ensure that the deformation of the material and the bubble dynamics remained in the linear regime. The radial dynamics of the bubbles were recorded by high-speed video microscopy. Resonance curves were measured experimentally and fitted to a model combining the Rayleigh-Plesset equation governing bubble dynamics, with the Kelvin-Voigt model for the viscoelastic medium. The resonance frequency of the bubbles was found to increase with increasing shear modulus of the medium, with implications for optimisation of imaging and therapeutic ultrasound protocols. In addition, the viscoelastic properties inferred from ultrasound-driven bubble dynamics differ significantly from those measured at low frequency with the rheometer. CN 114 459 955 A recites a liquid field kinematic viscosity coefficient measurement method based on bubble elasticity characteristics. The measurement method comprises the following steps: 1) establishing a measurement system; 2) liquid injection; 3) releasing bubbles; 4) signal acquisition and processing; 5) calculating a kinematic viscosity coefficient; and 6) recovering the detected liquid. The design is scientific and reasonable, the kinematic viscosity coefficient can be rapidly measured, and the measuring system is simple in structure, convenient to measure and high in measuring precision. CN 112 033 858 A recites an ultrasonic suspension and liquid physical property measurement, in particular to an ultrasonic suspension type liquid viscosity measuring method and device. The method provided by the embodiment of the invention comprises the following steps: controlling a droplet state to be suspended and rotate around a shaft, the droplet state being realized by controlling a standing wave field formed by a fan vortex annular phased array transducer; measuring the rotational angular velocity and the major and minor semi-axes of the droplet to calculate the rotational inertia of the droplet; solving acoustic radiation torque according to the rotational inertia and known parameters; solving a sound attenuation coefficient of the droplet according to the sound radiation torque of the droplet; and solving the viscosity of the droplet according to the sound attenuation coefficient. The device provided by the embodiment of the invention comprises an ultrasonic generator, a pair of ultrasonic transducers or an ultrasonic transducer and a reflecting surface, a high-speed camera and a computer, and is characterized in that the ultrasonic transducers are fan vortex annular phased array transducers and are used for driving droplets to be detected to suspend and rotate around a shaft. The method and device are convenient to operate and high in precision. Saikat et. Al (DOI : 10.1016/jcis.2022.10.093) use ultrasound-driven bubble dynamics to probe the high-frequency rheology of a colloid monolayer used as model system with controlled interactions and simultaneous monitoring of the microstructure. By comparing the response of colloid- coated bubbles with that of a bare bubble under identical experimental conditions, it is possible to detect the non-linear response of the monolayer and use it to extract interfacial rheological properties at 10⁴s^-1. Using high-speed video-microscopy, the dynamics of colloid-coated bubbles were probed to study the micromechanical response of the monolayer to high-frequency deformation. Protocols analogous to stress-sweep and frequency-sweep were developed to examine the stress-strain relationships. A simple model, motivated by the observed non-linear responses, was developed to estimate the interfacial viscoelastic parameters.

The present invention relates to a rheological apparatus, and further aspects thereof, which overcomes one or more of the above disadvantages, without jeopardizing functionality and advantages.

SUMMARY OF THE INVENTION

The present invention relates in a first aspect to an apparatus 10, in particular for the characterization of at least one rheological property, in particular an acoustic bubble rheometer for extensional rheology measurement, comprising at least one microbubble generator 20 configured to provide at least one microbubble to a sample holder 30, the at least one microbubble with a diameter of 1-500 pm, in particular 10-400 pm, more in particular 80-300 pm, the at least one microbubble comprising 50-100 vol% gas, in particular 90-99.99 vol.% gas, more in particular 98-99.9 vol.% gas, even more in particular 99-99.5 vol.% gas, in particular wherein the at least one microbubble generator 20 is configured to provide the at least one microbubble with an internal over-pressure of 10²- 10⁵ Pa, more in particular with an overpressure of 10²- 10⁴ Pa, in particular wherein the microbubble generator 20 comprises at least one microbubble injector in fluidic connection with the microbubble generator 20 and with the at least one sample holder 30 for receiving a sample of a to be measured material and to receive at least one microbubble from the microbubble generator, in particular wherein the to be measured material is an opaque material, in particular wherein the at least one acoustic sample holder 30 is configured to contact the sample, at least one acoustic wave generator 90 configured to provide at least one acoustic wave to the at least one microbubble for physically interacting with said at least one microbubble, such as oscillating said at least one microbubble, in particular at least one acoustic wave generator in physical contact with the at least one acoustic sample holder or configured to be incorporated in the sample holder, and at least one sensor 40 configured for acoustic wave detection of at least one acoustic wave provided by the at least one microbubble. The present sample holder is in particular configured for the present acoustic bubble rheometer, and may therefore be considered as an acoustic sample holder. The microbubble may be used to characterize at least one rheological property. Thereto the microbubble has a particular size. The microbubble may be considered as a void in the material to be analysed. It may be provided as a bubble, and therefore comprising a gas, typically air or an inert gas, such as nitrogen, a noble gas, and mixtures thereof, or it may be formed in the material to be analysed; the material to be analysed typically partly evaporates in the void, providing a vapor therein; the microbubble typically does not comprise a solid material, whereas it may comprise another fluid, such as a liquid, but typically not. The microbubble has a certain internal over-pressure as described above. A suitable acoustic pressure range, provided by the present acoustic wave generator, for exciting bubbles without distorting their sphericity and introducing non-linear effects typically depends on bubble size and testing material rheology. If the acoustic pressure is too small, then the resultant signal will be too small to be detectable. If the acoustic pressure is too large, the acoustic pressure wave will essentially destroy the bubble and the testing materials. Inventors therefore recommend an external acoustic pressure range of 10-10⁵ Pa, particularly 10²- 10⁴ Pa for the most uses. The at least one microbubble generator may be an injector such as, a needle with a syringe, or may be a laser configured to form a microbubble in the material to be measured. At present the apparatus is in particular suited for measuring opaque materials, wherein an opacity is typically in a visible wavelength range of 300-800 nm, with 0%-70% transmittance, in particular 0.1- 50%, for the given sample holder, i.e. width thereof. The at least one acoustic sample holder 30 is in particular configured to contact the sample, that is being in direct contact therewith. In an embodiment the at least one acoustic wave generator is in physical contact with the at least one acoustic sample holder, and in another embodiment is configured to be incorporated in the sample holder. The at least one acoustic wave provided by the at least one microbubble typically relates to an emitted [acoustic] wave. The emitted wave may be considered as a scattered wave. Scattering is a term used in physics to describe a wide range of physical processes where moving particles or radiation of some form, such as sound, are forced to deviate from a straight trajectory by localized non-uniformities in the medium of the present material to be analysed, through which they pass. In conventional use, this also includes deviation of reflected radiation from the angle predicted by the law of reflection. The types of non-uniformi- ties which can cause scattering, sometimes known as scatterers or scattering centres, includes bubbles, and density fluctuations in fluids. The effects of such features on the path of almost any type of propagating wave or moving particle can be described in the framework of scattering theory. The present apparatus, in particular the acoustic bubble rheometer, is a state-of- the-art device capable of acquiring a product’s extensional rheology, in response to the in- creasing measurement demands found in many production processes involving fast fluid dynamics, such as spraying, fibre spinning, and ink-jet printing. Compared to an existing extensional rheometer, the present acoustic bubble rheometer features a high frequency oscillatory deformation, based on monitoring the dynamics of acoustic-driven microbubbles, enabling measurement in extensional rheological properties, in particular viscoelasticity, in the conditions that are relevant to production and use of formulated products. The acoustic bubble rheometer presented here provides a possible solution in response to the bottleneck of formulated product development. The present apparatus, such as the acoustic bubble rheometer, however, is able to acquire products’ extensional rheological properties at high frequency, meeting the realistic flow conditions of many production processes (pipe constrictions, spraying, fibre spinning, ink-jet printing) and end usages by customers. The present apparatus, e.g. the acoustic bubble rheometer, measures e.g. the viscoelasticity in a higher frequency range of 1 - 10⁴ kHz, corresponding to the typical frequency range of ultrasound. The method at the basis of the acoustic bubble rheometer consists in injecting a microscopic gas bubble in a sample, and recording the radius oscillation upon ultrasound forcing. As the measurement can be done within seconds, the device has the ability to measure changes in rheological properties over time. Additionally, the variation of the acoustic bubble rheometer can measure multiple samples simultaneously, such as for high-throughput screening processes. The device is small, portable, and cost-effective, making it suitable for at-line or in-line processes or on-line processes, in particular wherein the apparatus is place inside a production or process environment, or parallel line therein, such as in a sterile environment. The technique is based on the ultrasonic detection of a single oscillating bubble. Therefore, ensuring the existence of a single bubble at a fixed position without displacement induced by buoyancy is important for a successful rheological measurement. Thereto an automation is developed for reducing the measurement time down to less than a second. The variation of the acoustic bubble rheometer can measure multiple samples simultaneously for high-throughput screening processes. The device is designed to be small, portable, and cost-effective, making it suitable for at-line or in-line processes. The device has great potential to work as a sensor for measuring the in-line rheological properties to control the quality of the products. To provide detectable signals and avoid destruction of testing materials, it is preferred to operate in a pressure range of the at least one microbubble of 10-10⁵ Pa. In some example a suitable acoustic pressure range for exciting bubbles without distorting their sphericity and introducing non-linear effects may depend on bubble size and testing material rheology. If the acoustic pressure is too small, then the signal will be too small to be detectable. If the acoustic pressure is too large, the pressure wave will essentially destroy the bubble and the testing materials.

In a second aspect the present invention relates to a method of measuring extensional rheology of a material, in particular a high throughput method, such as for an array comprising samples, in particular an n*m array, wherein n=[l, 32] and m= [1,32], comprising the providing apparatus according to the invention, providing at least one sample comprising a material to be measured, loading the at least one sample into the at least one acoustic sample holder, providing at least one microbubble to be in fluidic contact with the at least one sample, providing an acoustic wave to the at least one microbubble therewith obtaining an acoustic wave activated microbubble, sensing acoustic wave activated microbubble oscillation from the at least one microbubble in fluidic contact with the at least one sample, and processing the sensed oscillation and obtain at least one rheological characteristics of said material.

In a third aspect the present invention relates to a computer program for carrying out the method of the present invention, in particular wherein the computer program comprising instructions for measuring at least one of a radius of the at least one microbubble, in particular the time-dependent radius of the at least one microbubble, of a density of the material to be measured, of a pressure of the at least one microbubble, of an interfacial tension of the at least one microbubble, of an ambient pressure of the to be measured material, of a stress of the to be measured material, in particular the radial stress of the to be measured material, of the at least one acoustic wave frequency, of the at least one acoustic wave amplitude, of a reference frequency, of a reference at least one microbubble radius, of a to be measured material polytropic exponent, of a to be measured material damping coefficient, for determining the at least one microbubble dynamics, in particular by varying the at least one microbubble radius at a fixed frequency, and/or in particular by varying the frequency at a fixed radius of the at least one microbubble radius, and/or wherein the method comprises using at least two different materials to be measured, wherein at least one of said two different materials is a reference material, and measuring at least one of a radius of the at least one microbubble, in particular the time-dependent radius of the at least one microbubble, of a pressure of the at least one microbubble, and of an interfacial tension of the at least one microbubble.

Thereby the present invention provides a solution to one or more of the above mentioned problems. Advantages of the present invention are detailed throughout the description.

DETAILED DESCRIPTION OF THE INVENTION

The present invention relates in a first aspect to an apparatus.

In an exemplary embodiment of the present apparatus the at least one sensor (40) is configured for acoustic detection of a variation in rheological properties of the to be measured material over time, in particular ultrasound detection. Therewith the rheological properties can be determined rather accurately.

In an exemplary embodiment the present apparatus is configured to measure multiple samples simultaneously, in particular wherein the apparatus comprises an array of n*m sample holders, and an array of p*q sensors, or an arrangement of sample holders and according arrangement of sensors. Therewith a high throughput is achieved.

In an exemplary embodiment the present apparatus is portable, in particular wherein the apparatus has a volume of < 10 dm³, in particular a volume of < 3 dm³, and/or a weight of < 10 kg, in particular < 3 kg. As such the use of the present apparatus is simple and easy. It can also be used at different locations, e.g. where needed, without problem. In an exemplary embodiment the present apparatus is configured to characterize a material selected from a viscoelastic material, in particular a viscoelastic material with a viscoelasticity (ISO 6721-1 :2019 or ISO 3104:2020) of 10³-10⁸ Pa, in particular 5*10³-2*10⁷ Pa, a material with a non-Newtonian viscosity, in particular wherein the non-Newtonian viscosity material is selected from a shear thickening material, from a shear thinning material, and from generalized Newtonian fluids, a material with a shear-rate-dependent viscosity, in particular wherein the material with a time-dependent viscosity is selected from rheopectic materials, and from thixotropic materials, A wide variety of materials, as well as a wide range of properties can be characterized with the present apparatus. The present apparatus is in particular designed for characterizing viscoelasticity, particularly the relaxation modulus in a range of 10³- 10⁸ Pa, with a specific range of 5*10³-2*10⁷Pa. Notably, viscosity is a component of viscoelasticity, and the present apparatus can measure viscosity with a well-characterized pressure field.

In an exemplary embodiment of the present apparatus the at least one sensor (40) is configured to operate at a detection frequency of 1-10⁴ kHz, in particular 10-10³ kHz. The selection of the operating frequency of the present apparatus is taken inversely proportional to the size of the microbubble, which typically ranges from 1 to 500 pm. The corresponding frequency range is than 1-10⁴ kHz, with a specific range of 10-10³ kHz for optimal instrument precision.

In an exemplary embodiment of the present apparatus the at least one sensor (40) is configured to measure an acoustic wave propagation from a bubble oscillation.

In an exemplary embodiment of the present apparatus the at least one sensor (40) is physically connected to said sample holder.

In an exemplary embodiment of the present apparatus the acoustic wave generator is configured to provide an acoustic wave with a frequency of 10-10³ kHz, in particular wherein the at least one acoustic wave generator is at least one transducer (90).

In an exemplary embodiment of the present apparatus the at least one acoustic wave generator (90) is configured to provide at least one acoustic wave to the at least one microbubble for oscillation in the acoustic sample holder.

In an exemplary embodiment of the present apparatus the acoustic wave generator is configured to provide an acoustic wave with a power [or amplitude] of 10'⁵- 100 W, in particular 10'⁴-10 W, such as 0.1-5 W.

In an exemplary embodiment the present apparatus comprises a waveform generator (50), in particular a programmable waveform generator, more in particular wherein the waveform generator is configured to provide a driving frequency to the acoustic wave generator (90).

In an exemplary embodiment the present apparatus comprises a power amplifier (60) configured to amplify the waveform, wherein the waveform generator is configured to provide input to the apparatus, in particular to the at least one acoustic wave generator (90). In an exemplary embodiment of the present apparatus the at least one sensor (40) is selected from hydrophones, and from pressure sensors.

In an exemplary embodiment the present apparatus comprises a differential pressure sensor, from piezoelectric sensors, from MEMS, from ceramic devices.

In an exemplary embodiment the present apparatus comprises a signal amplifier (70) configured for amplifying a sensor signal and optionally configured to provide said amplified signal to an output device (80), such as a data storage device, a data logging device, a computer, and an oscilloscope.

In an exemplary embodiment the present apparatus comprises a controller, in particular wherein the controller is configured to control in operational communication at least one of characterization of rheological properties, the microbubble generator (20), the acoustic wave generator (90), the microbubble sensor (40), the waveform generator (50), the power amplifier (60), the signal amplifier (70), and the output device (80).

In an exemplary embodiment the present apparatus comprises at least one data processor configured to analyse at least one rheological property of the at least one sample from the emitted acoustic waves detected by said acoustic sensor, in particular wherein the data processor is configured to process at least one of a radius of the at least one microbubble, in particular the time-dependent radius of the at least one microbubble, of a density of the material to be measured, of a pressure of the at least one microbubble, of an interfacial tension of the at least one microbubble, of a pressure of the to be measured material, of a stress of the to be measured material, in particular the radial stress of the to be measured material, of the at least one acoustic wave frequency, of the at least one acoustic wave amplitude, of a reference frequency, of a reference at least one microbubble radius, typically taken in equilibrium conditions, of a to be measured material polytropic exponent, and of a to be measured material damping coefficient.

In the present method of extracting rheological properties from the acoustic signal emitted by an ultrasound-excited microbubble an acoustic scattering theory and the Rayleigh- Plesset equation may be used. According to acoustic scattering theory, the pressure wave emitted by an oscillating microbubble can be represented as follows:

Here, the microbubble's time-dependent radius, R(t), describes its dynamics, r is the radial distance in spherical coordinate system, while p denotes the density of the surrounding material. The relationship between the bubble dynamic and the viscoelastic properties can be described by Rayleigh-Plesset equation,

where p_gas is the gas pressure inside the bubble, p is the pressure far from the bubble, c is the interfacial tension, and Trr is the radial component of stress in the surround material. Once the emitted pressure is detected by the sensor, the bubble dynamics in terms of R(t) can be calculated according the acoustic scattering theory. Then, rheological properties can be computed using the generalized Rayleigh-Plesset equation once R(t) is obtained. In particular, viscoelastic properties such as the relaxation modulus G can be obtained by solving the Rayleigh-Plesset equation under the assumption of Kelvin- Voigt model. The analytical solution provide the link between rheological properties and bubble dynamics as follows,

where coo is the natural frequency, co is the applied frequency, Ro is the bubble radius at equilibrium, K the polytropic exponent, and P is the damping coefficient. As long as the resonance behavior of the bubble dynamic can be measured, the key rheological property G can be extracted. There are three operation modes available on our device to examine the resonance behavior of the bubble dynamics:

Frequency sweep to measure rheological property

In frequency sweep mode, bubble dynamics will be scanned across a range of acoustic frequencies which cover the resonance frequency of the microbubble. Prior calibration e.g. using a hydrophone is essential to ensure a constant acoustic pressure during frequency sweep. Specifically, the degree of power amplification can be adjusted to compensate for the frequency-dependent response of the transducer. It is worth noting that the frequency sweep can be rapidly performed in few seconds, essentially operating at a fixed bubble radius without be affected by bubble dissolution. Once the frequency sweep profile is obtained, the results can be again fit to Equations (1) and (2) to extract rheological property.

Radius sweep to measure very precise rheological property

In radius sweep mode, a single microbubble is placed in the pretreated sample to trigger the bubble expansion or dissolution. The sample can be pretreated to be either undersaturated or supersaturated with gas such as by regulating the temperature before conducting any measurements. Laplace pressure often facilitates bubble dissolution, particularly in the absence of temperature control. To perform radius sweeps, a fixed-frequency acoustic signal is directed to the acoustic sample holder during the microbubble's shrinkage. The sampling time interval of the acoustic signals is determined by the dissolution rate of the bubble. By varying the bubble's equilibrium radius at a fixed frequency, the bubble dynamics can be measured, and the results can be fit using Equations (1) and (2) to extract very precise rheological property. The entire operating time of the radius mode highly depends on the rate of microbubble dissolution/expansion, typically within 10 to 200 mins.

Acoustic fingerprinting method

The ultrasound-driven microbubble emits unique acoustic features when immersed in different rheological medium. These unique features can be used as acoustic fingerprinting when a suitable reference sample is well characterized, and then a high-throughput screening process can be implemented to compare multiple samples with the reference sample. The technique has significant potential for various industries, such as food and cosmetics, where product reformulation can be expedited without compromising the target rheological properties.

To implement acoustic fingerprinting, the acoustic signal of the microbubble in the reference sample needs to be well-characterized. Specifically, the characterization may involve performing a frequency sweep and analyzing the dataset to extract a set of acoustic features.. These features can be analyzed, such as in either Fourier domain or time domain, and then indexed, and stored in a database along with their corresponding metadata.

When multiple samples are measured, their acoustic features are extracted and quantized, e.g. using the same techniques as the reference sample. The quantized features can then compared to those stored in the database, using algorithms, such as nearest-neighbor search. The similarity between the measured and the stored acoustic fingerprints can then be quantified to find the optimal sample with rheological properties closest to the reference.

In an exemplary embodiment the present method comprises determining the at least one microbubble dynamics, in particular by varying the at least one microbubble radius at a fixed frequency, also referred to as radius sweep.

In an exemplary embodiment the present method comprises determining the at least one microbubble dynamics by varying the frequency at a fixed radius of the at least one microbubble radius, also referred to as frequency sweep.

In an exemplary embodiment the present method comprises determining the at least one microbubble dynamics comprises using at least two different materials to be measured, wherein at least one of said two different materials is a reference material, and measuring at least one of a radius of the at least one microbubble, in particular the time-dependent radius of the at least one microbubble, of a pressure of the at least one microbubble, and of an interfacial tension of the at least one microbubble.

In an exemplary embodiment of the present method one microbubble is provided to the at least one sample.

In an exemplary embodiment of the present method the acoustic wave generator provides acoustic waves to the at least one microbubble during a time period of 0.1-10 sec, in particular during a time period of 0.2-1 sec. In an exemplary embodiment of the present method the acoustic wave sensor detects propagated acoustic waves of the at least one microbubble during a time period of 0.1-10 sec, in particular during a time period of 0.2-1 sec.

In an exemplary embodiment of the present method a measurement is repeated 1- 10 times.

In an exemplary embodiment of the present method the size of the at least one microbubble is measured, and wherein based on the size of the at least one microbubble, and at least one of the amplitude of the generated acoustic wave, the frequency of the generated acoustic wave, the phase of the generated acoustic wave, the amplitude of the propagating acoustic wave, the frequency of the propagating acoustic wave, and the phase of the propagating acoustic wave, the at least one rheological property is characterized, in particular wherein the at least one rheological property is selected from an extensional rheological property, more in particular wherein the at least one rheological property is selected from viscoelasticity, in particular the relaxation modulus, more in particular in a range of 10³-l 0⁸ Pa, e.g. 5*10³-2*10⁷ Pa, from an increase of viscosity, from a decrease of viscosity, from a texture of the sample, from a phase or multiphase of a sample, and from a homogeneity of a sample

The invention is further detailed by the accompanying figures and examples, which are exemplary and explanatory of nature and are not limiting the scope of the invention. To the person skilled in the art it may be clear that many variants, being obvious or not, may be conceivable falling within the scope of protection, defined by the present claims.

EXAMPLE S/EXPERIMENTS

The invention although described in detailed explanatory context may be best understood in conjunction with the accompanying examples.

Various samples are tested. In particular an agarose gel, which is considered to be a reference material, a multiphase system, such as a shampoo, a detergent, and hand-sanitizer, are tested. For instance, hand sanitizer is chosen here for its transparency, which allows for the measurement of bubble size through a microscope calibration. Once calibration is done, the same setup can be applied for opaque materials with similar rheological properties

Before use, incidentally, the sample holder is tested in view of performance, such as in view of leakage. Typically this was not an issue.

1-10 gr of the material is taken and put into the sample holder.

A bubble, typically one, was provided to the sample. Care is taken to provide the bubble to the centre of the sample as much as possible, and for reproducibility.

The present microbubble sensor 40, in particular a hydrophone, is placed carefully at a height substantially in the middle of the sample (c.q. sample holder), and with a sensor 40 axis at an substantially perpendicular (90°) orientation with respect to the propagating axis of the incident acoustic wave provided by the acoustic wave generator (90). Then at least one measurement is carried out, providing an acoustic bubble to the sample with the bubble generator of a suitable size, typically 200 pm in diameter. The size of the bubble can be checked, e.g. with a microscope, if transparent material is present for calibration in order to provide reproducible results. If the bubble sizes did not vary that fast over time, frequency sweep can be applied for the measurement. Otherwise, radius sweep can be applied . An acoustic wave, provided by the acoustic wave generator, with a suitable frequency, e.g. of 26 kHz, and a suitable power, e.g. ~1W, is used. The detection frequency demonstrated here is within the range of 10-40 kHz. The measurement can be provided in a radius sweep mode, in a frequency sweep mode, or both, to activate the bubble dynamics. The resultant emitted pressure waves from an microbubble are recorded by hydrophone. In this example as shown in Fig. 4, the hand sanitizer is measured using radius sweep mode, and optical measurement is utilized to demonstrate the precise calibration of the device.

Received signals are processed, using the above model and further parameters in so far as needed. Data analysis, e.g. using Eq. (l)-(4) is performed in order to compute the rheological properties of the testing media. Typical results give a viscoelasticity varying between l* 10³-2* 10⁷ Pa, depending on the material. For example, by fitting the dataset obtained from the radius sweep mode to Eq. (3)-(4), we obtain the shear modulus of 3.8 ± 0.8 kPa for hand sanitizer as illustrated in Fig. 4.

SUMMARY OF THE FIGURES

Figs. 1, 2a-b, 3, 4a-e show details of the present apparatus.

DETAILED DESCRIPTION OF THE FIGURES

In the figures:

10 apparatus

20 microbubble generator

21 bubble

30 acoustic sample holder

31 sample

40 microbubble sensor

50 waveform generator

51 delay generator

60 power amplifier

70 signal amplifier

80 output device

81 camera

82 microscope objective

90 acoustic (sound) wave generator

Fig. 1 shows that the present rheometer is well suited for measurements in the ~ 1-10⁴ kHz operational region, for measurements detection in the ~ 10³- 10⁷ Pa detection region. For prior art systems, such as a rotational rheometer, a piezo rheometer, and a Diffusion Wave Spectrometer (DWS), operational frequencies are typically much lower as well as detection regions. Such makes the present rheometer especially suited for determining parameters of polymers, of polymer solutions, gels, inks, formulated products, such as detergents, shampoos, foods, and drinks, complex multicomponent products, structured products, multiphase materials, such as wherein a range of chemical compounds are blended, to obtain the desired texture and performance, amongst others.

Fig. 2a shows a schematic layout of the present apparatus. Therein an acoustic sample holder 30 is shown, for receiving a sample comprising a to be measured material, and for receiving a bubble generated by the acoustic wave generator 90. A waveform generator provides input to a power amplifier, if required, and the possibly amplified wave is provided to the acoustic sound wave generator. A microbubble sensor 40, such as a hydrophone, is provided for acoustic wave detection. Optionally a signal amplifier 70 is used to amplify the signal of microbubble sensor 40, which (amplified) signal is provided to an output device, such as a monitor, a smartphone, a computer, etc.

Fig. 2b show two experimental set-up options. In the top one a single in-line sensor is shown, e.g. for process control. In the bottom one an array is shown for measuring, e.g. in high-throughput screening.

Fig. 3 shows a measurement process flow layout. A visualization method (shown in figs. 4a-e) is used as time dependent input radius parameters (R(t), used for the rheological measurement. The present apparatus design involves an all-acoustic method, as described and claimed throughout the description, with an optional customized design for specific pur- poses/samples to be tested. For better results typically obtained and provided signals are optimized, e.g. in terms of frequency (range), amplitude, etc. The present bubble generator is part of the present apparatus. In order to process signals the present method is developed. Thereto, as represented in the lower right comer, the present acoustic rheometer is provided, representing fig. 2a.

Figs. 4a-e show details of an exemplary visualisation method. In fig. 4a basically the present apparatus, as also shown in e.g. fig. 2a is given. A waveform generator 90 gives input to a signal amplifier 60, and optionally to a delay generator 51. The power amplifier provides a signal to the bubble generator 20, which in an example is a transducer. A bubble 21 is generated in sample 31. The behaviour of the sample and bubble can be observed with a high speed camera 81 and/or a microscope through objective 82. Fig. 4b shows schematically a (time/location) series bubble, of which radius variations R(t) over time t between R_max and Rmin of which a frequency spectrum with x=AR/Ro for a given co is shown, and in fig. 4e the relation between co and R is shown.

Claims

1. An apparatus (10), in particular for the characterization of at least one rheological property, in particular an acoustic bubble rheometer for extensional rheology measurement, comprising at least one microbubble generator (20) configured to provide at least one microbubble to a sample holder (30), the at least one microbubble with a diameter of 1-500 pm, in particular 10-400 pm, more in particular 80-300 pm, the at least one microbubble comprising 50-100 vol% gas, in particular 90-99.99 vol.% gas, more in particular 98-99.9 vol.% gas, even more in particular 99-99.5 vol.% gas, in particular wherein the at least one microbubble generator (20) is configured to provide the at least one microbubble with an over-pressure of 10-10⁵ Pa, more in particular with an over-pressure of 10²-l 0⁴ Pa, in particular wherein the microbubble generator (20) comprises at least one microbubble injector in fluidic connection with the microbubble generator (20) and with the at least one sample holder (30) for receiving a sample of a to be measured material and to receive at least one microbubble from the microbubble generator, in particular wherein the to be measured material is an opaque material, in particular wherein the at least one acoustic sample holder (30) is configured to contact the sample, at least one acoustic wave generator (90) configured to provide at least one acoustic wave to the at least one microbubble for physically interacting with said at least one microbubble, such as oscillating said at least one microbubble, in particular at least one acoustic wave generator in physical contact with he at least one acoustic sample holder or configured to be incorporated in the sample holder, and at least one sensor (40) configured for acoustic wave detection of at least one acoustic wave provided by the at least one microbubble.

2. The apparatus (10) according to claim 1, wherein the at least one sensor (40) is configured for acoustic detection of a variation in rheological properties of the to be measured material over time, in particular ultrasound detection.

3. The apparatus (10) according to any of claims 1-2, wherein the apparatus is configured to measure multiple samples simultaneously, in particular wherein the apparatus comprises an array of n*m sample holders, and an array of p*q sensors, or an arrangement of sample holders and according arrangement of sensors.

4. The apparatus (10) according to any of claims 1-3, wherein the apparatus is portable, in particular wherein the apparatus has a volume of < 10 dm³, in particular a volume of < 3 dm³, and/or a weight of < 10 kg, in particular < 3 kg.

5. The apparatus (10) according to any of claims 1-4, wherein the apparatus is configured to characterize a material selected from a viscoelastic material, in particular a viscoelastic material with a viscoelasticity (ISO 6721-1 :2019 or ISO 3104:2020) of 10³-10⁸ Pa, in particular 5*10³-2*10⁷ Pa, a material with a non-Newtonian viscosity, in particular wherein the nonNewtonian viscosity material is selected from a shear thickening material, from a shear thinning material, and from generalized Newtonian fluids, a material with a shear-rate-dependent viscosity, in particular wherein the material with a time-dependent viscosity is selected from rheopectic materials, and from thixotropic materials,

6. The apparatus (10) according to any of claims 1-5, wherein the at least one sensor (40) is configured to operate at a detection frequency of 1-10⁴ kHz, in particular 10-10³ kHz, and/or wherein the at least one sensor (40) is configured to measure an acoustic wave propagation from a bubble oscillation, and/or wherein the at least one sensor (40) is physically connected to said sample holder (30).

7. The apparatus (10) according to any of claims 1-6, wherein the acoustic wave generator is configured to provide an acoustic wave with a frequency of 1-10⁴ kHz, in particular 10-10³ kHz, in particular wherein the at least one wave generator is at least one transducer (90), and/or wherein the at least one acoustic wave generator (90) is configured to provide at least one acoustic wave to excite the at least one microbubble for oscillation in the sample holder (30), and/or wherein the acoustic wave generator is configured to provide an acoustic wave with a power of 10’⁵-l W.

8. The apparatus (10) according to any of claims 1-7, comprising a waveform generator (50), in particular a programmable waveform generator, more in particular wherein the waveform generator is configured to provide a driving frequency to the acoustic wave generator (90), and optionally a power amplifier (60) configured to amplify the waveform, wherein the waveform generator is configured to provide input to the apparatus, in particular to the at least one acoustic wave generator (90).

9. The apparatus (10) according to any of claims 1-8, wherein the at least one sensor (40) is selected from hydrophones, from pressure sensor, in particular a differential pressure sensor, from piezoelectric sensors, from MEMS, from ceramic devices, in particular wherein the apparatus comprises a signal amplifier (70) configured for amplifying a sensor signal and optionally configured to provide said amplified signal to an output device (80), such as a data storage device, a data logging device, a computer, and an oscilloscope.

10. The apparatus (10) according to any of claims 1-9, comprising a controller, in particular wherein the controller is configured to control in operational communication at least one of characterization of rheological properties, the microbubble generator (20), the acoustic wave generator (90), the microbubble sensor (40), the waveform generator (50), the power amplifier (60), the signal amplifier (70), and the output device (80).

11. The apparatus (10) according to any of claims 1-10, comprising at least one data processor configured to analyse at least one rheological property of the at least one sample from the emitted acoustic waves detected by said acoustic sensor, in particular wherein the data processor is configured to process at least one of a radius of the at least one microbubble, in particular the time-dependent radius of the at least one microbubble, of a density of the material to be measured, of the excited acoustic pressure of the at least one microbubble, of an interfacial tension of the at least one microbubble, of the ambient pressure of the to-be-measured material, of a stress of the material to be measured, in particular the radial stress of the to-be-meas- ured material, of the at least one acoustic wave frequency, of the at least one acoustic wave amplitude, of a reference frequency, of a reference at least one microbubble radius, of a to-be- measured material polytropic exponent, and of a to-be-measured material damping coefficient.

12. A method of measuring extensional rheology of a material, in particular a high throughput method, comprising providing the apparatus according to any of claims 1-11, providing at least one sample comprising a material to be measured, loading the at least one sample into the at least one acoustic sample holder, providing at least one microbubble to be in fluidic contact with the at least one sample, providing an acoustic wave to the at least one microbubble therewith obtaining an acoustic wave activated microbubble, sensing acoustic wave activated microbubble oscillation from the at least one microbubble to in fluidic contact with the at least one sample, and processing the sensed oscillation and obtain at least one extensional rheological characteristics of said material.

13. The method of measuring extensional rheology of a material according to claim 12, wherein the method comprises determining the at least one microbubble dynamics, in particular by varying the at least one microbubble radius at a fixed frequency, and/or in particular by varying the frequency at a fixed radius of the at least one microbubble radius, and/or wherein the method comprises using at least two different materials to be measured, wherein at least one of said two different materials is a reference material, and measuring at least one of a radius of the at least one microbubble, in particular the time-dependent radius of the at least one microbubble, of an acoustic pressure of the at least one microbubble, and of an interfacial tension of the at least one microbubble.

14. The method of measuring extensional rheology of a material according to any of claims 12-13, wherein one microbubble is provided to the at least one sample, and/or wherein the acoustic wave generator provides acoustic waves to the at least one microbubble during a time period of 0.1-10 sec, in particular during a time period of 0.2-1 sec, and/or wherein the acoustic wave sensor detects propagated acoustic waves of the at least one microbubble during a time period of 0.1-10 sec, in particular during a time period of 0.2-1 sec, and/or wherein a measurement is repeated 1-10 times.

15. The method of measuring extensional rheology of a material according to any of claims 12-14, wherein the size of the at least one microbubble is measured, and wherein based on the size of the at least one microbubble, and at least one of the amplitude of the generated acoustic wave, the frequency of the generated acoustic wave, the phase of the generated acoustic wave, the amplitude of the propagating acoustic wave, the frequency of the propagating acoustic wave, and the phase of the propagating acoustic wave, the at least one rheological property is characterized, in particular wherein the at least one rheological property is selected from an extensional rheological property, more in particular wherein the at least one rheological property is selected from viscoelasticity, in particular the relaxation modulus, more in particular in a range of 10³-l 0⁸ Pa, e.g. 5*10³-2*10⁷ Pa, from an increase of viscosity, from a decrease of viscosity, from a texture of the sample, from a phase or multiphase of a sample, and from a homogeneity of a sample.

16. A computer program for carrying out the method of any of claims 12-15, in particular wherein the computer program comprising instructions for measuring at least one of a radius of the at least one microbubble, in particular the time-dependent radius of the at least one microbubble, of a density of the material to be measured, of a pressure of the at least one microbubble, of an interfacial tension of the at least one microbubble, of a pressure of the to be measured material, of a stress of the to be measured material, in particular the radial stress of the to be measured material, of the at least one acoustic wave frequency, of the at least one acoustic wave amplitude, of a reference frequency, of a reference at least one microbubble radius, of a to be measured material polytropic exponent, of a to be measured material damping coefficient, for determining the at least one microbubble dynamics, in particular by varying the at least one microbubble radius at a fixed frequency, and/or in particular by varying the frequency at a fixed radius of the at least one microbubble radius, and/or wherein the method comprises using at least two different materials to be measured, wherein at least one of said two different materials is a reference material, and measuring at least one of a radius of the at least one microbubble, in particular the time-dependent radius of the at least one microbubble, of a pressure of the at least one microbubble, and of an interfacial tension of the at least one microbubble.