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Mechanical Spectrum of a Viscous Liquid
speciale, 3. modul, 2006/07, id:238
Vejleder:Jeppe Dyre, fysik og Jesper Larsen, matematik
Findes på RUb:Ja
English abstract
The goal of this thesis is to extend the newly developed narrowband picosecond laser ultrasonic technique to measure the acoustic properties of liquids in addition to solids and polymer films. The method covers a frequency window of roughly 1-400GHz and thus bridges a gap in the existing experimental methods. A sample holder to fabricate thin liquid films was constructed, where the liquid is confined between two metal coated substrates. The construction allows for both a Brillouin backscattering measurement as well as the picosecond laser ultrasonic measurement. This provides a cross-check of the results obtained as the two different measurements ususlly overlap in frequency. To validate the method, measurements are first carried out in the prototypical glass-former glycerol and compared to data in the literature. A series of measurements is then performed on the silicon oil (tetramethyl-tetraphenyl-trisiloxane) at temperatures ranging from 210-295K. The acoustic damping dtermined in the ultrasonic measurement on the silicon oil follows a parabola that seems to agree fairly well with the reference point determined by Brillouin scattering. However, the reproducibility of the results remains to be demonstrated. The prevalent method of data analysis of this type of measurement reveals the frequency dependence of the acoustic damping, but assumes a constant sound velocity. In order to analyze the data obtained with acoustically dispersive media (such as viscous liquids), the experiment is modeled mathematically. The sample construction consists of five layers (substrate-metal-liquid-metal-substrate) that are mechnically and thermally coupled. Each layer is modeled by two coupled partial differential equations for the temperature and displacement fields - the so called thermo-(visco)-elastic equations. Boundary conditions are matched at each interface of the inner layers, while the outer layers (two substrates) are assumed semi-infinite. The direct problem, i.e. assuming that the input and all parameters of the model are known, is formulated as a system of ordinary differential equations and solved algebraically. A comparison of model solutions to data is carried out in the frequency domain and shows that the model agrees qualitatively well with the data. Peak positions, widths of the peaks and the relative manitudes of subsequent peaks all agree excellently with the data. It is thus concluded that the model provides a good description of the experiment and can be a platform for a fitting routine to determine the liquid parameters from data.

Database opslag den: 25-01-2021