Part 9

Part 9

FUTURE OUTLOOK

Most of the results described in this thesis concern numerical simulations of thermocapillary convection in so-called liquid bridge configuration, where the cylindrical liquid–gas interface is free surface along which temperature gradient is directed. Ultimately, all studies presented here, intend to increase our knowledge of both influence of different factors on the onset of instability and development of the flow with moving to far–supercritical region.

In four parts, cylindrical non–deformed interface is considered. For near–critical region of parameters, influence of dependence of the liquid viscosity upon temperature on the onset of instability and wave properties of the solution is considered. This is a new and important result proposing a kind of criterion for estimating the influence of this parameter on the stability boundaries. However, in reality only under full absence of gravity and when the liquid volume equal πR

d the free surface is cylindrical. Deformations of the interface and its deviations from cylindrical shape are among the factors capable to strongly influence the critical parameters. One part of the thesis is dedicated to the study of the onset of instability in deformed non-cylindrical domain. The importance of taking into account the free surface shape and of the liquid volume was confirmed by results of calculations. But this part of the study is not completely finished yet and only the first results are presented. In the non–cylindrical domain case, it takes much more efforts and time for finishing the investigation since there are still not much reliable published data to compare the results of calculations to. Computations for 0 − and 1 − g environment and for different liquid volumes are necessary for establishing benchmark computational results and fundamental confidence that the new software is capable of correctly resolving the problem for very thin and thick liquid bridges. Once such an option is available – it is forseen in the near future – one can be sure that the code works properly. Also, due to complicity of the governing equations written in a new co-ordinate system in which the initially deformed domain is cylinder, calculations are slower, algorithm is more sophisticated, and it is not easy to introduce the temperature–dependent viscosity into the model in this case.

The study of ambient conditions and heat flux on the convective flow stability and pattern formation needs to be extended. For some temperature distributions in the surrounded gas and intensive heat flux, that might correspond to intensive evaporation of the liquid through the free surface, we observed the onset of instability as very high frequency oscillations that occured in the near–interface region. Inside the domain, for r < 0.9, the flow stood steady two–dimensional.

With further increase of ∆T the three–dimensional oscillatory regime peculiar to the zero heat flux conditions on the free surface established, but these high frequency oscillations in the thin near–interface zone did not disappear. Since these results still requires further clarification, they are not included in the thesis.

A very interesting and amazing feature of the spatial organization of the oscillatory convective

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9 Future outlook

flow was found for P r = 4, 0 − g case. Two different solutions, one with m = 2 and the other with m = 3 symmetries, co-exist. Being absolutely independent, they reveal different behaviors.

The m = 3 solution passes through weakly temporally chaotic regime, but the m = 2 one is always periodic. It was discovered that from its very appearance the m = 3 mode is spatially non-symmetric (m = 2 always has absolute symmetry). It is possible that namely this feature of the solution is responsible for the chaotic regime onset in far supercritical region of parameters.

This problem is needed, however, to be investigated for 1 − g case since it could explain the onset of chaotic flow in P r = 18.8, 1 − g liquid bridge that was observed both experimentally [148] and via direct numerical simulations.

Starting in form of pure m = 1 wave, the flow then undergoes a transition to m = 1 + 2 mixed mode and later on the transition to chaos takes place. A suggestions made is that only one of the two modes reveals chaotic features (mostly probable, it is the m = 2 solution). It demands further clarification. The results of calculations obtained for P r = 18.8, 1 − g are in excellent qualitative agreement with the experiments, but it is of interest to investigate the same P r = 18.8 liquid bridge but under 0 − g conditions. The forthcoming results must clarify the importance of microgravity environment for the floating zone technique. At the time of writing this, the study of the onset of chaos in P r = 18.8 liquid bridge under absence of gravity is in progress.

As a perspective step for the future, coupling of soluto- and thermocapillary convections is considered. As in the real technological floating zone process one deals with dopants introduced to the melt, this complication of the model will definitely brings us closer to the real situation.

The studies of the thermodiffusion without Marangoni convection are carried out at the moment, but the results of calculations are not presented for they are not related to the subject of the thesis.

Numerical studies will continue to provide insight into the nature of the instability and various flow states.

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