Transition of thermocapillary convection in a full-zone liquid bridge

Abstract

Themocapillarity is of fundamental importance in material processing. The floating-zone method is a material processing for producing and purifying single crystals of metals and oxides. It is widely known that, using this method, a transition to three-dimensional oscillatory thermocapillary convection takes place in the melt. The oscillatory convection causes detrimental striations in the crystal structure. In this study, flow transition points (critical Marangoni numbers) and flow structures were investigated in a thermocapillary convection in a model of floating-zone method (full-zone liquid bridge) of the high Prandtl number fluid (Pr =28.1) under the normal gravity condition. In the liquid bridge, the convection changes from two-dimensional steady flow to three-dimensional oscillatory one at a flow transition point. The convection was visualized by tracer particles in order to find the flow transition point and the shape of the modal structures in the oscillatory flow. The dominant modal structures near the flow transition point were estimated using the shape of the particle free zone on a horizontal plane of the liquid bridge and superposition of several waves with azimuthal wave numbers by the method of the least squares. In the present study, the critical Marangoni number of the full-zone liquid bridge was almost one-half of that of the half-zone liquid bridge in aspect ratio 0.45 to 1.3 (aspect ratio: half-height of liquid bridge over radius of rods). The dominant modal structures were combination of azimuthal wave numbers with 1, 2, and 3 in a range of the aspect ratio concerned. It was found that the azimuthal wave numbers of the dominant modal structures did not depend on the aspect ratio. The dominant modal structures were a standing or a travelling wave, and changed from one to another irregularly. Trade-off of a power and a phase locking between each modal structure were observed.