Determination of diffusion and thermodiffusion coefficients in multicomponent mixtures. Numerical and experimental analysis of gravitational convective instabilities

Resumen

Thesis objectives were both, numerical and experimental analysis of the diffusion and thermodiffusion coefficient in binary and ternary mixtures associated with DCMIX campaign. First objective of the thesis was to develop numerical code within open-source project OpenFOAM regarding diffusion and thermodiffusion transport in multicomponent mixtures. This part have been conducted during the first year of the thesis. After that, second objective of the thesis was to understand better convective instabilities inside ternary mixture in sliding symmetric tubes techniques which is used to determine diffusion coefficient. Third objective related with thermodiffusion was to establish procedure for simultanous determination of thermodiffusion and diffusion coefficient through transient analysis of the signal in thermogravitational microcolumn for binary mixtures. And the last objective was regarding ternary mixtures, to introduce thermodiffusion steady-state measurements in microcolumn for the first time in literature. Structure of the work together with explanations for each section will be presented here. After introduction, the results related double diffusion covection instability in ternary mixtures are presented. The 1D diffusion problem will be solved along diffusion boundary for an initial step concentration function in two different ways. First solution related with semi-infinite domains is not valid for all times of the diffusion, second solution, more general, is applicable finite domains and is valid for all times. Theoretical limits related with these solutions for appearance of fingers and overstability, as two types of double diffusive convection motions will be established and further insight how different instabilities grow will be given. Graphs of stability for the ternary DCMIX1, DCMIX2 and DCMIX3 mixtures are given. Note that, graphs were not constructed for all possible concentrations, but for certain ones. Anyway, by applying initial conditions to proposed limits, one can easily obtain graph for each mixture with thermophysical and transport properties known. Different regions on the graph correspond with fingers, overstability, stable and unstable ranges. These regions are given as function of initial difference of concentrations ratio. Limits are applied for the mixture mentioned above with two different mean concentrations and with special care into experiments already conducted using Sliding Symmetric Tubes experimental technique (SST). SST technique is among others tehcniques that use step fucntion as initial conditions for the proccess of determining diffusion coefficients. This profile is prone to result in double diffusive convection, so it is necessary to very carefully design the setup of the experiment. To prove experimentally validity of our graphs in DCMIX1, five different compositions have been initially selected, three around the fingers-like type region and two around the over-stability region. Experimental results obtained during Sliding Symmetric Tubes (SST) based experiments have been compared with the analytical pure diffusion solution and also with a 3D numerical simulation which includes the buoyancy effects. For this purpose, a specific solver in the open source software OpenFOAM has been created. Predicted instabilities agree well with experimental results in most of the cases, confirming the accuracy of the obtained diffusion coefficients.In the next chapter, by using a parallelepipedic thermogravitational microcolumn, the temperature gradient influence on the stability of the flow has been examined, emphasizing mixtures with positive Soret coefficients. Experiments were conducted for DCMIX2 Toluene/Methanol and DCMIX3 Water/Ethanol binary subsystems because of their broad range of positive Soret values for high concentrations of methanol and ethanol, respectively. Two different mixtures have been studied here in order to confirm the thermogravitational stability of the mixtures. Experiments were compared with numerical simulations carried out again by using the open-source software platform OpenFOAM. Solver was upgraded with a boundary conditions that are related with thermodiffusion in comparison with solver from previous section.Fifth chapter contains information about interferometric transient analysis of the thermogravitational technique that is for the first time attempted in a microcolumn. In this way, the three transport coefficients, diffusion, thermodiffusion and Soret coefficients can be obtained in a single experiment. Two different models — one from the Furry-Jones-Onsager theory and the other with the ‘forgotten effect’ included — have been tested for six different binary mixtures. These mixtures are the three binary pairs of the Benchmark of Fontainebleau— tetrahydronaphthalene-isobutylbenzene (THN-IBB), tetrahydronaphthalene-dodecane (THN-nC12) and isobutylbenzene-dodecane (IBB-nC12), toluene-methanol, dimethyl sulfoxide-water (DMSO-H20) and dimethyl sulfoxide-deuterated water (DMSO-D20). The first three benchmark binary mixtures are used to validate the inteferometric technique and also to establish when it is reasonable to treat a mixture as ideal, without considering the forgotten effect. After that, the three remaining mixtures are deeply analysed. In the end, the isotopic effect in the Soret coefficient will be highlighted through the DMSO-H20 and DMSO-D20 mixtures.Sixth chapter covers transient analysis of the instabilities in binary mixtures inside microcolumn due to negative Soret coefficients. In particular, water/ethanol (DCMIX3) and toulene/methanol (DCMIX2) were considered, as they have significantly different thermophysical properties and relaxation times. Experiments were run with different temperature gradients in order to understand their impact on the stability of separation. Experimental results were compared with theoretical ones, predicted by Fury-Jones-Onsager theory, and by 3D numerical simulations. Correlations between the separation and the flow in the third dimension perpendicular to the thermal gradient of the thermogravitational microcolumn were analysed. Numerical simulations were also conducted in traditional cylindrical columns in order to compare the results with those previously reported. In these cases, the impact on separation stability was correlated with the azimuthal component of velocity. Thus, in both configurations, the disturbing convective current, always generated in the direction perpendicular to the thermal gradient applied, was shown to be vital for flow stability analysis. Difference between experimental and numerical results were justified by non-ideality of experimental setup, where one of the most visible causes could be inclination angle. Numerical simulations with very small inclination angle show the tendency of shorted stability window.In the last chapter, steady-state measurements in a thermogravitational microcolumn using optical digital interferometry are presented for the first time in the literature in the case of ternary mixtures. These measures enabled the subsequent determination of thermodiffusion coefficients of a ternary mixture once convection reaches the steady-state. The ternary mixture used was the benchmark one, Tetrahydronaphthalene (THN) – isobutylbenzene (IBB) and n-dodecane (nC12) with mass fraction of 0.8-0.1-0.1 respectively. Contrast factors due to the change in the concentration field were measured and compared with the corresponding ones in the literature. Uncertainty in the results was found to be of similar value like in the case of Selectable Optical Diagnostic Instrument (SODI), which means that the condition number of that contrast factor matrix is almost equal to the present one. Final values were compared with the results reported from other optical techniques, as well as with the results obtained by the traditional long opaque thermogravitational columns (TGC). Some proposals were then made in order to improve accuracy reducing the condition number of the contrast factor matrix.