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The dependency of the critical Marangoni number on the geometrical aspect ratio of the floating half zone is essential to predict the onset of oscillatory thermocapillary convection. The experimental studies in the microgravity conditions on floating half zones of several centimeters in diameter have predicted that the critical Marangoni number increases with the increasing aspect ratio, and the terrestrial experimental studies have predicted the contradictory conclusion for floating half zones of several millimeters in diameter. In the present work, terrestrial experimental studies were conducted on the floating half zones of 5 Centistokes (cSt) silicon oil and 10 cSt silicon oil. The experimental results show that the critical Marangoni number generally increases with the increasing aspect ratio of the floating half zone and then decreases. Moreover, a further increase of the critical Marangoni number with the increasing aspect ratio occurs for the slender floating half zones. [ABSTRACT FROM AUTHOR]

This study experimentally explored the fine structures of the successive period-doubling bifurcations of the time-dependent thermocapillary convection in a floating half zone of 10 cSt silicone oil with the diameter d =3.00 mm and the aspect ratio A= l/ d =0.72 in terrestrial conditions. The onset of time-dependent thermocapillary convection predominated in this experimental configuration and its subsequent evolution were experimentally detected through the local temperature measurements. The experimental results revealed a sequence of period-doubling bifurcations of the time-dependent thermocapillary convection, similar in some way to one of the routes to chaos for buoyant natural convection. The critical frequencies and the corresponding fractal frequencies were extracted through the real-time analysis of the frequency spectra by Fast-Fourier-Transformation (FFT). The projections of the trajectory onto the reconstructed phase-space were also provided. Furthermore, the experimentally predicted Feigenbaum constants were quite close to the theoretical asymptotic value of 4.669 [Feigenbaum M J. Phys Lett A, 1979, 74: 375-378]. [ABSTRACT FROM AUTHOR]