Schematic diagram of the acoustic near-field technique. 

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... resonator is composed of two metallic parts (A and B) of stainless steel, glued to a piezoelectric element (PZT) ceramic (Fig. 1). Part A is a cylinder and part B is a cylinder terminated by a conical horn immersed in the media. The resonator has the following ...

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... oscillations of the resonator are described by plane waves inside the cylinder and the conical horn. The wavelength being higher than the cone dimensions, we only consider unidimensional acoustic waves propagation [1]. The piezoelectric element (PZT) acts as a sensor for the two acoustical impedances applied on its two sides (Z 2 and Z 3 ) ( Fig. 1). Its electric impedance is given by ...

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... l = L PZT , β is the wave vector in the ceramic, C 0 the clamped capacitance of the PZT, k T the thickness coupling constant, ω the pulsation of the electrical signal, Z 1 the acoustic impedance at the interface between the conical horn and the lower cylinder of the resonator (see Fig. 1), Z 2 the acoustic impedance at the interface between the piezoelectric and the lower cylinder of the resonator (see Fig. 1), Z 3 is the acoustic impedance at the interface between the piezoelectric and the upper cylinder of the resonator (see Fig. 1) and Z c the characteristic impedance of the ceramic given by Z c = cβ/ω, where c is ...

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... clamped capacitance of the PZT, k T the thickness coupling constant, ω the pulsation of the electrical signal, Z 1 the acoustic impedance at the interface between the conical horn and the lower cylinder of the resonator (see Fig. 1), Z 2 the acoustic impedance at the interface between the piezoelectric and the lower cylinder of the resonator (see Fig. 1), Z 3 is the acoustic impedance at the interface between the piezoelectric and the upper cylinder of the resonator (see Fig. 1) and Z c the characteristic impedance of the ceramic given by Z c = cβ/ω, where c is the elastic constant of the piezoelectric. For a free piezoelectric, the thickness coupling constant k T is given by ...

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... impedance at the interface between the conical horn and the lower cylinder of the resonator (see Fig. 1), Z 2 the acoustic impedance at the interface between the piezoelectric and the lower cylinder of the resonator (see Fig. 1), Z 3 is the acoustic impedance at the interface between the piezoelectric and the upper cylinder of the resonator (see Fig. 1) and Z c the characteristic impedance of the ceramic given by Z c = cβ/ω, where c is the elastic constant of the piezoelectric. For a free piezoelectric, the thickness coupling constant k T is given by ...

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... kind of material that have been used to check the technique is common polymers. The common ploymers, an epoxy resin (Araldite ® ) and a polyurethane varnish (V33 ® ), are prepared by mixing the resin with a hardener. The advantage of this process is the homogeneous evolution of the properties of the bulk material. Fig. 10 shows the curves corresponding to the polymerization of araldite for various ratios resin/hardner of polyurethanne varnish (5% and 7%). Impedance at resonance displays a maximum for a time of 1 2 h for 7% of resin/hardner ratio and after 2 h for 5% of resin/hardner ratio. This maximum of (1/Z) is related to an increase of viscosity in ...

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... of the complex shear modulus) [11]. The change of shapes after 1 h for 7% of resin/hardner ratio and 3 h for 5% of resin/hardner ratio indicate a change of physical behaviour due to the appearance of elastic properties. (1/Z) then remains quite constant after 2 h for 7% of resin/hardner ratio and more lately for 5% of resin/hardner ratio (see Fig. ...

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... + Z ) cos where l = L PZT , is the wave vector in the ceramic, C 0 the clamped capacitance of the PZT, k T the thickness coupling constant, ω the pulsation of the electrical signal, Z 1 the acoustic impedance at the interface between the conical horn and the lower cylinder of the resonator (see Fig. 1), Z 2 the acoustic impedance at the interface between the piezoelectric and the lower cylinder of the resonator (see Fig. 1), Z 3 is the acoustic impedance at the interface between the piezoelectric and the upper cylinder of the resonator (see Fig. 1) and Z c the characteristic impedance of the ceramic given by Z c = c β / ω , where c is the elastic constant of the piezoelectric. For a free piezoelectric, the thickness coupling constant k is given by ...

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... + Z ) cos where l = L PZT , is the wave vector in the ceramic, C 0 the clamped capacitance of the PZT, k T the thickness coupling constant, ω the pulsation of the electrical signal, Z 1 the acoustic impedance at the interface between the conical horn and the lower cylinder of the resonator (see Fig. 1), Z 2 the acoustic impedance at the interface between the piezoelectric and the lower cylinder of the resonator (see Fig. 1), Z 3 is the acoustic impedance at the interface between the piezoelectric and the upper cylinder of the resonator (see Fig. 1) and Z c the characteristic impedance of the ceramic given by Z c = c β / ω , where c is the elastic constant of the piezoelectric. For a free piezoelectric, the thickness coupling constant k is given by ...

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... + Z ) cos where l = L PZT , is the wave vector in the ceramic, C 0 the clamped capacitance of the PZT, k T the thickness coupling constant, ω the pulsation of the electrical signal, Z 1 the acoustic impedance at the interface between the conical horn and the lower cylinder of the resonator (see Fig. 1), Z 2 the acoustic impedance at the interface between the piezoelectric and the lower cylinder of the resonator (see Fig. 1), Z 3 is the acoustic impedance at the interface between the piezoelectric and the upper cylinder of the resonator (see Fig. 1) and Z c the characteristic impedance of the ceramic given by Z c = c β / ω , where c is the elastic constant of the piezoelectric. For a free piezoelectric, the thickness coupling constant k is given by ...

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... signal at the transducer. In return, the study of the electrical resonance state provides information on the media in contact with the probe. The considered resonance characteristics are the resonance frequency f and the maximum Z of the real part of the electrical impedance Z elec of the transducer. Studies have been made on various geometrical shapes of resonators (cylindrical (stepped), conical, exponential, Gaus- sian, Fourier, . . . ) [1–5]. The shapes of the resonator and, more particularly, of the probe are adjusted to take into ac- count criteria like amplification and mechanical steadiness. The first results were obtained with the stepped cylindrical resonators which made possible the characterization of the density and the viscosity of liquids by relating them to the measured electric parameters [6–8]. Thus, the acoustic near- field technique showed its potentialities for the characterization of liquid environments [7,8] such as biphasic liquid media [9] and polymers [10]. It was then adapted to the characterization of the evolution of cement pastes [11]. Being concerned about the miniaturization of the probe in order to increase its resolution, our search was directed towards the conical geometry. Furthermore, this geometry has the advantage of keeping its rigidity in very small dimensions (a few mm) it is not the case for the cylindrical probe which presents the disadvantage of being very fragile because of the small cylinder which can be deformed in contact with more or less significant loads. In a previous work [12], we studied the interaction of the conical horn with different materials. Thus, densities and vis- cosities of analysed liquids have been related to measured electric parameters. Furthermore, the study of change of resonance features of this resonator permitted the characterization, without discontinuity, of the evolution of rheological properties of bitumen as a function of temperature and cement setting. In this work, we will study the interaction of this probe with bitumen as function of depth penetration and the evolution of rheological properties of polymers during their processing. The resonator is composed of two metallic parts (A and B) of stainless steel, glued to a piezoelectric element (PZT) ceramic (Fig. 1). Part A is a cylinder and part B is a cylinder terminated by a conical horn immersed in the media. The resonator has the following ...

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... tip of the conical probe is chosen very fine in order to obtain maximum amplification. Indeed, maximum amplification is obtained for an infinite ratio r 2 / r 1 [3] ( r 1 is the radius of the tip). The PZT-piezoelectric disc is excited by an electrical signal supplied by a low-frequency (60–110 kHz) sine-wave generator. The amplitude of this signal is 1 V to limit the motions of the tip to 10 nm [7]. A lock-in amplifier measures the complex electrical impedance of the piezoelectric element. The mechanical loading exerted on the probe by the media modifies the resonance features of the resonator: the resonance frequency f and the maximum Z of the real part of the electrical impedance Z elec . The measurement parameters are f and (1/ Z ) denoting variations of f and 1/ Z . The reference values are measured when the probe is unloaded. Axial oscillations of the resonator are described by plane waves inside the cylinder and the conical horn. The wavelength being higher than the cone dimensions, we only con- sider unidimensional acoustic waves propagation [1]. The piezoelectric element (PZT) acts as a sensor for the two acoustical impedances applied on its two sides ( Z 2 and Z ) (Fig. 1). Its electric impedance is given by ...