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A Detailed Treatment of the Measurement of Transport Coefficients in Transient Grating Experiments
(2007)
- This thesis treats the measurement of transport coefficients in transient grating experiments and is organized into 3 parts. Part 1 provides a brief review of the thermodynamic-phenomenological theory relevant for a correct description of the Soret effect. It comprises the formulation of the first law in open systems, the calculation of the entropy production, and the derivation of the phenomenological equations. This part is based on the books by de Groot and Mazur and by Haase and contains also some own results. We have explicitely derived a relation between reversible work and dissipation function, if heat and mass are exchanged reversibly and irreversibly between the two homogenous phases of a non-isothermal heterogenous system. Moreover we have discussed in detail, whether Onsager coefficients are invariant against shifts of enthalpy or entropy zero. Furthermore some comments on recent literature work have been made, since thermodynamic principles are not always correctly incorporated. In parts 2 and 3 we have treated the measurement of heat, mass and thermal diffusion in transient grating experiments. In part 2 we have presented a two-dimensional model to account for the role of heat conducting walls in the measurement of heat transport and Soret effect driven mass transport in transient holographic grating experiments. Heat diffusion into the walls leads to non-exponential decay of the temperature grating. Under certain experimental conditions it can be approximated by an exponential function and assigned an apparent thermal diffusivity D_{th,app} <D_{th,s}, where D_{th,s} is the true thermal diffusivity of the sample. The ratio D_{th,app}/D_{th,s} depends on only three dimensionless parameters, d/l_s, k_s/k_w, and D_{th,s}/D_{th,w}. d is the grating period, l_s the sample thickness, k_s and k_w the thermal conductivities of sample and wall, respectively, and D_{th,w} the thermal diffusivity of the wall. If at least two measurements are performed at different d/l_s, both D_{th,s} and k_s can be determined. Instead of costly solving partial differential equations, the unknown parameters can be obtained by finding the zero of an analytic function. For thin samples and large grating periods, heat conduction into the walls plays a predominant role and consequently the concentration grating in binary mixtures is no longer one-dimensional. Nevertheless, the normalized heterodyne diffraction efficiency of the concentration grating remains unaffected and the true mass and thermal diffusion coefficient and the correct Soret coefficient are still obtained from a simple one-dimensional model. All theoretical predictions have been tested by experiments on pure and binary liquids over a wide range of grating periods and sample thicknesses. Excellent agreement has been found in all cases. A new transient grating technique for the measurement of heat, mass and thermal diffusion in liquids has been introduced in part 3. Similar to holographic grating experiments, a temperature grating is created in the sample. Thermal expansion transforms the temperature into a refractive-index grating, which is read by diffraction of a readout laser beam. In a multicomponent mixture an additional concentration grating is formed by thermal diffusion driven by the temperature gradients of the temperature grating. Differently to laser induced dynamic grating experiments we use Joule heating instead of optical heating. For that purpose we have built cuvettes which have a grating of transparent conducting strips on the inner side of one of their windows. If heated by an electric current a temperature grating will build up in the sample. Both, the heat equation and the extended diffusion equation, have been solved in two dimensions to allow for quantitative data analysis. Our apparatus and method of analysis have been validated by measurements of heat, mass and thermal diffusion in pure and binary liquids. Heat diffusion can be correctly determined as was shown for pure toluene, pure dodecane and the symmetric mixture of isobutylbenzene-dodecane. Mass and thermal diffusion was studied in the three symmetric mixtures of dodecane, isobutylbenzene and tetralin. The obtained diffusion and Soret coefficients agree with the literature values within the experimental errors. Uncompensated transient heating effects limit the resolution of the experimental technique.
