**3. Sensors suitable for studying media of which the physical properties evolve over time**

### **3.1 Monitoring changes in the physical state of the matter**

The analysis of the different stages in the formation of macromolecular networks is of major importance, since understanding the structure and properties (physical or chemical) of gels requires the understanding of the process of organization. In many physical, chemical or biological processes, the union of small separate elements to form aggregates of different sizes and further macroscopic phases makes connectivity an essential characteristic of this

Low Frequency Acoustic Devices for Viscoelastic Complex Media Characterization 217

extremely pointed ends that act as point sources was examined. The application of this technology using two near-field coupled sensors to explore the relationship between the physical properties measured during the evolution of the time of flight of the wave and the

The sensors were near-field coupled through the medium to be characterised. Such disposition privileges the Signal/Noise ratio and avoids the loss of acoustic pressure which is inversely proportional to the ray of the spherical wave. In a metal or ceramic solid all the waves are generated simultaneously, but in the media we are concerned with, the

The advantage of these sensors is that they can be adapted to the measurement configuration envisaged according to the nature of the wave and the appropriate resonance

The aim of the study was to define and develop optimal ultrasonic instrumentation to understand the phenomenon and quantify the viscoelastic properties of changing media. The usual ultrasonic characterization techniques are generally based on the use of a resonant piezoelectric transducer in thickness mode. As the resonant frequency of a transducer is inversely proportional to its size, it is greater for low frequencies around 100 KHz. Some researchers like Degertekin (Degertekin & Khury-Yakub, 1996a, 1996b, 1996c), Shuyu (Shuyu, 1996, 1997) and Nikolovski (Nikolovski & Royer, 1997) used this physical principle, but associated a tapered volume with the ceramic components to concentrate the mechanical

The aim of this part of the work was to obtain a low frequency acoustic point source to generate a spherical wave in the medium. To do this a different procedure from that traditionally used in classic sensor design was implemented. A new technique was used which consisted in setting in resonance the entire mechanical structure of a reduced-size unit through the contact of an extremely pointed end with the material to be analyzed. In order to behave like an acoustic point source, the size of the point was smaller than the

The first part presents a theoretical analysis of low-frequency ultrasonic resonators, beaming a spherical wave in the medium. The choice of a triangular shaped resonator and its mechanical behavior will be assessed and the study completed by a numerical approach based on the application of the finite elements method to characterize all the resonator vibration modes and visualize the corresponding distortions when the structure is excited. As the analytical results were in good agreement with the numerical results, they were applied to the whole triangular-shaped sensor to validate the findings experimentally. The resonance mode frequencies determined by the numerical calculation were then correlated

For a possible analytical analysis, the structure of a standard ultrasonic sensor is based on a

The propagation of longitudinal waves in the triangular part of the sensor was studied to determine the resonance frequency of the elongation mode and the velocity amplification

structural changes during matter formation (Figure 1) was investigated.

**3.2 Study of a low-frequency ultrasonic device** 

mode.

energy.

wavelength in the medium.

**3.3 Study and design 3.3.1 Analytical approach** 

simple triangle shape (Figure 2).

with the electrical impedance measurements.

dominating longitudinal wave is the fastest and is relatively simple to exploit.

type of process. Many models have been proposed to explain the phenomenon of aggregation. The most important ones are those of Flory (Flory, 1953), Stockmayer (Stockmayer, 1943), Case (Case, 1960), Gupta (Gupta et al., 1979), Eichinger (Eichinger, 1981), Allsopp (Allsopp, 1981) and San Biagio (San Biagio et al., 1990). In most cases the phenomenon is described by the classical theory as a "particular case of percolation" and the two-dimensional growth of the network according to Caylay's tree. Other studies including those of De Gennes (De Gennes, 1989) and Stauffer (Stauffer, 1981, 1985) describe the phenomenon of random aggregation and the problems of percolation and gelation. However, the different characteristics of the macromolecular chain-making system can be evaluated according to Clerc (Clerc et al., 1983), using for example a Monte-Carlo simulation, predicting the influence of the characteristics of the starting solution and the gelation conditions on the structure and the arrangement of the masses.

In fact, the gelation process is a transition from an entirely soluble system to a heterogeneous two-phase system: composed of an insoluble entity (infinite-size macromolecule) and a soluble phase. This transition is accompanied by radical changes in some physical properties of the medium. Below the gelation "point", the viscosity of the medium increases and the medium ceases to flow by developing an elasticity.

To study this phenomenon, several physical measurement techniques exist i.e. optical, thermal, rheological and acoustic (Nassar, 1997). However, sampling and sensitivity to a limited range of physical properties are often drawbacks. Consequently, different techniques are required to explore an entire process with the difficulty of bringing together the heterogeneous data provided by these techniques. This is, for example, the case of optical methods which are penalized by the opacity of the substances analyzed as well as the size of the molecules formed in relation to the wavelength. Thermal methods are insensitive to the mechanical characteristics of the medium. The fragility of some gels (milk gel) limits rheological techniques. In many cases, several analytical techniques exist, but they are only used in the laboratory.

Fig. 1. Basic principle

To develop further instrumentation in order to understand and to quantify the modification process of media in real conditions, a low-frequency ultrasonic technique using sensors with extremely pointed ends that act as point sources was examined. The application of this technology using two near-field coupled sensors to explore the relationship between the physical properties measured during the evolution of the time of flight of the wave and the structural changes during matter formation (Figure 1) was investigated.

The sensors were near-field coupled through the medium to be characterised. Such disposition privileges the Signal/Noise ratio and avoids the loss of acoustic pressure which is inversely proportional to the ray of the spherical wave. In a metal or ceramic solid all the waves are generated simultaneously, but in the media we are concerned with, the dominating longitudinal wave is the fastest and is relatively simple to exploit.

The advantage of these sensors is that they can be adapted to the measurement configuration envisaged according to the nature of the wave and the appropriate resonance mode.
