Ultrasonic properties

Ultrasonic Properties. Vitreous sihca of high purity, such as the synthetic type, has an unusually low attenuation of high frequency ultrasonic waves. The loss, is a linear function of frequency, up to the 30—40 MHz region and can be expressed a.s A = Bf, where B = 0.26 dB-MHz/m for shear waves and 0.16 dB-MHz/m for compressional waves (168). 

D. J. McClements, N. Herrmann, Y. Hemar 1998, (Influence of flocculation on the ultrasonic properties of emulsions theory), J. Phys. D Appl. Phys. 31, 2950. 

Parker KJ, Tuthil TA. 1986. Carbon tetrachloride induced changes in ultrasonic properties of liver. IEEE Trans Biomed Eng 33 453-460. 

Here to is the angular frequency ( = 2nf) and k is the wave number ( = ca/c + ia), which contains information about the ultrasonic properties of the material, i.e., the velocity and... 

In practice ultrasound is usually propagated through materials in the form of pulses rather than continuous sinusoidal waves. Pulses contain a spectrum of frequencies, and so if they are used to test materials that have frequency dependent properties the measured velocity and attenuation coefficient will be average values. This problem can be overcome by using Fourier Transform analysis of pulses to determine the frequency dependence of the ultrasonic properties. 

A simple relationship can be derived between the ultrasonic properties of a material and its physical properties by a mathematical analysis of the propagation of plane waves in a material. 

Here E is the appropriate elastic modulus (which depends on the physical state of the material and the type of wave propagating) and p is the density. By combining equations 3 and 4 the physical properties of a material (E and p) can be related to its ultrasonic properties (c and a). 

Thus a measurement of the ultrasonic properties can provide valuable information about the bulk physical properties of a material. The elastic modulus and density of a material measured in an ultrasonic experiment are generally complex and frequency dependent and may have values which are significantly different from the same quantities measured in a static experiment. For materials where the attenuation is not large (i.e., a ca/c) the difference is negligible and can usually be ignored. This is true for most homogeneous materials encountered in the food industry, e.g., water, oils, solutions. 

An ultrasonic experiment consists of two stages measurement of the ultrasonic properties of the material, e.g., velocity, attenuation or impedance interpretation of these measurements to provide information about the relevant properties of the material. These may either be fundamental physico-chemical properties (such as composition, microstructure or molecular interactions) or functional properties (such as stability, rheology or appearance). 

Once the ultrasonic properties of a material have been measured it is necessary to relate them to the physical properties which are of interest to the food scientist. There are two approaches commonly used to do this, these are the so-called empirical and theoretical approaches. 

For ideal mixtures there is a simple relationship between the measurable ultrasonic parameters and the concentration of the component phases. Thus ultrasound can be used to determine their composition once the properties of the component phases are known. Mixtures of triglyceride oils behave approximately as ideal mixtures and their ultrasonic properties can be modeled by the above equations [19]. Emulsions and suspensions where scattering is not appreciable can also be described using this approach [20]. In these systems the adiabatic compressibility of particles suspended in a liquid can be determined by measuring the ultrasonic velocity and the density. This is particularly useful for materials where it is difficult to determine the adiabatic compressibility directly, e.g., powders, biopolymer or granular materials. Deviations from equations 11 - 13 in non-ideal mixtures can be used to provide information about the non-ideality of a system. 

In non-ideal mixtures, or systems where scattering of ultrasound is significant, the above equations are no longer applicable. In these systems the ultrasonic properties depend on the microstructure of the system, and the interactions between the various components, as well as the concentration. Mathematical descriptions of ultrasonic propagation in emulsions and suspensions have been derived which take into account the scattering of ultrasound by particles [20-21]. These theories relate the velocity and attenuation to the size (r), shape (x) and concentration (0) of the particles, as well as the ultrasonic frequency (co) and thermophysical properties of the component phases (TP). 

The density of eHDA is 1.13 g/cm3, which is about 4% less than the density of uHDA [200], The different degree of structural relaxation should be evident when studying the thermal stability at 1 bar. The well-relaxed state is expected to be thermally more stable, and this expectation is confirmed experimentally At 1 bar, eHDA is stable up to 135 K, whereas uHDA is stable merely up to 115 K [190, 194, 196], Earlier, Johari [201] had noticed that HDA produced from LDA ( eHDA ) shows ultrasonic properties that differ from HDA produced from ice Ih ( uHDA ). 

In non-scattering systems, ultrasonic properties and the volume fraction of the disperse phase are related in a simple manner. In practice, many emulsions and suspensions behave like non-scattering systems under certain conditions (e.g. when thermal and visco-inertial scattering are not significant). In these systems, it is simple to use ultrasonic measurements to determine 0 once the ultrasonic properties of the component phases are known. Alternatively, if the ultrasonic properties of the continuous phase, 0and p2 are known, the adiabatic compressibility of the dispersed phase can be determined by measuring the ultrasonic velocity. This is particularly useful for materials where it is difficult to measure jc directly in the bulk form (e.g. powders, granular materials, blood cells). 

Equation 9.13, where k =(o/c + is the wave number of the continuous phase, illustrates how the scattering coefficients of a single particle are related to the ultrasonic properties of an ensemble of particles. 

Multiple scattering theory also assumes that the particles are randomly distributed in the continuous phase ( . e. that they are uncorrelated). In some systems, this is not true and ultrasonic properties can depend on the radial distribution function of the particles. 

Particle interaction. Scattering theory does not take account of physical interactions between particles. In concentrated systems such as pastes or sediments, the particles are in contact with each other and different theories have to be used to describe their ultrasonic behaviour [64,65]. The ultrasonic properties can be affected, even in dilute systems, if flocculation occurs. The dependence of the ultrasonic properties of a material on the degree of particle interaction allows ultrasonics to be used to investigate this phenomenon. 

The frequency dependence of the ultrasonic properties of materials can be divided in a number of ways based on pulse-echo, transmission or interferometric measurements. The principal differences between them are the way ultrasonic energy is applied to the sample (Fig. 9.4) and the experimental set-up used to make the measurements. 

As with any analytical technique, it is important for US spectrometry users to have a thorough understanding of its underlying physical principles and of potential sources of errors adversely affecting measurements. The basis of ultrasonic analyses in a number of fields (particularly in food analysis) is the relationship between the measurable ultrasonic properties (velocity, attenuation and impedance, mainly) and the physicochemical properties of the sample (e.g. composition, structure, physical state). Such a relationship can be established empirically from a calibration curve that relates the property of interest to the measured ultrasonic property, or theoretically from equations describing the propagation of ultrasound through materials. 

Determining the droplet size distribution of an emulsion by ultrasonic spectrometry involves two steps. First, the ultrasonic velocity and (or) attenuation coefficient of the emulsion is measured as a function of the frequency — preferably over as wide a range as possible. Second, the experimental measurements are compared with theoretical predictions of the ultrasonic properties of the emulsion, and the droplet size distribution providing the best fit between theory and experiment is determined. 

Ultrasonics is in many ways the ideal measurement method for fat crystallization studies. The ultrasonic properties of a fat are strongly sensitive to solids content and can be measured in opaque fats and through container walls. In the present work I will describe the basic physics of ultrasonic waves, their interactions with matter (particularly with semi-solid fats), and their measurement. I will then describe ultrasonic studies of fat crystallization in bulk and emulsified fats. Finally I will use some measurements of the effect of applied shear on fat crystallization as an illustration of a study that could not be easily undertaken by other methods. 

Sound is transmitted through materials as mechanical waves in physical structure. Because the material is being mechanically deformed by the passing wave, its ultrasonic properties contain useful Information about its macroscopic and microscopic composition and structure. 

A wave can be characterized by an amplitude, frequency, and wavelength which may change with time or distance traveled from the source. We can express both the storage and loss properties of a sonic wave moving in a material concisely as the real and imaginary parts of a complex wavenumber k = co/c + ia, where c is the speed of sound, co is the angular frequency (=2 Jt/),/is frequency, / = V - 1, and a is the attenuation coefficient. Ultrasonic properties are often frequency dependent so it is necessary to define the wavelength at which k is reported. The dependency of k on frequency is the basis of ultrasonic spectroscopy. 

Ultrasonic properties Ultrasonic resonance method, Fokker Bond Tester A—>C 50,51... 

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