The periodic instability of thermocapillary convection in cylindrical liquid bridges

Abstract

Thermocapillary convection (TC) in cylindrical liquid bridges (floating zones) of liquids with Prandtl numbers Pr=1, 7, and 49 is investigated experimentally. The zones have been heated from above or from below to study the influence of buoyant forces. Fourier analyses of temperature signals from zones covering systematically wide ranges of aspect ratios A and Marangoni numbers Ma have shown the existence of various forms of periodic and nonperiodic TC. This paper reports on periodic TC existing under certain conditions between the onset of time-dependent TC at the critical Marangoni number Mac and 7×Mac. From the measurements of the onset of periodic TC the dependence is reported for the threshold Mac and the period near the threshold τc on the aspect ratio. The development of periodic TC when further increasing Ma is shown by typical examples from measurements of the frequency and the amplitude of the oscillations. By correlation analyses from three temperature signals, different structures of periodic TC in the investigated A–Ma–Pr range were identified. Both the running waves with an azimuthal component (m≥1) and the axially running waves (m=0) were found and the findings of these and various other spatiotemporal structures of periodic TC were displayed in A–Ma/Mac state maps. These maps indicate as well the influence of the Prandtl number and of the buoyant forces on the preferred spatial structure of periodic TC, as discussed in the light of an already existing theory.