The occurrence of mass diffusion caused by a local temperature gradient is known as Ludwig-Soret effect or thermodiffusion.
In this work, thermodiffusion is investigated in ternary mixtures of n-dodecane, isobutylbenzene, and 1,2,3,4-tetrahydronaphthalene by means of a two-color „Optical Beam Deflection“ (OBD) technique. A temperature gradient is applied across the Soret cell and gives rise to a refractive index gradient. The refractive index gradient contains two contributions, a thermal one caused by the change of temperature, and a concentration part, which arises from the partially separation of the components caused by thermodiffusion. A laser beam passing through the cell will be deflected due to this refractive index gradient. The deflection of the laser beam can be detected as a function of time and used to determine the transport coefficients. To investigate a ternary mixture, two laser beams with different wave lengths are needed, because there are two independent concentrations to describe the mixture.
First of all, the theoretical background is considered with respect to the properties of the diffusion matrix and its comparability to binary diffusion coefficients. After that, the experimental set up is explained in detail, where the lab-built temperature control is a crucial point.
To obtain the transport coefficients, the so-called contrast factors must be known. These are the partial derivatives of the refractive index with respect to the temperature and the independent concentrations. The contrast factors were determined by a polynomial approximation of the refractive index. Therefore, the refractive index was measured for different samples at several concentrations by means of commercial Abbe refractometers and an interferometer to determine the temperature dependence. Furthermore, the contrast factors can also be obtained using a linear mixing rule of the molecular polarizabilities of the pure substances according to Lorentz-Lorenz and Looyenga. The temperature and concentration dependence is then described by the density of the mixtures. The density was also measured with commercial density meters, which is much faster than a characterization of the mixtures using only optical methods. The major result of this investigation is, that the temperature dependence of the molecular polarizabilities must be taken into account to obtain correct thermal contrast factors. The concentration dependent contrast factors are resulting in the so-called contrast factor matrix, whose condition number can be used to estimate the relative errors of the calculated transport coefficients. To obtain reliable results, the condition number must be sufficiently small. Therefore, the rows of the contrast factor matrix have to be almost linearly independent. This can be achieved by a proper choice of the two wavelengths.
After these preliminary investigations, the results along the binary boundaries are presented, which are forming a reference frame for the ternary measurements. The very first measurements of ternary samples had shown, that a more detailed investigation of the ternary OBD-signal is needed to evaluate the data. Therefore, the ternary OBD-signal is discussed with the aim to identify the characterizing parameters. A detailed analysis is carried out, which of these parameters, or combinations thereof, can be reliably obtained and how they are related to the transport coefficients. Afterwards, the evaluation procedure is shown, where an analytical solution of the diffusion problem is fitted to the concentration signal, before the ternary results are presented. Thereby, one particular mixture is treated in more detail, which was chosen as a benchmark point. This benchmark mixture was investigated by several workgroups with different techniques and the results were in excellent agreement. Additionally, data of this mixture are available which were measured in a microgravity environment aboard the International Space Station (ISS) as part of the DCMIX project. The absence of gravity will eliminate convective instabilities which can be caused by a density gradient. The performed measurements in this work are verified by the results of the benchmark mixture and can also be used as ground based reference data. The binary and ternary results are summarized a rather complete picture of the transport coefficients of the ternary system of n-dodecane, isobutylbenzene, and 1,2,3,4-tetrahydronaphthalene.
|School:||Universitaet Bayreuth (Germany)|
|Source:||DAI-C 81/1(E), Dissertation Abstracts International|
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