Effect of Horizontal Vibrations on Thermo-Solutocapillary Convection and Free Surface of Liquid Bridge
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ORIGINAL ARTICLE
Effect of Horizontal Vibrations on Thermo-Solutocapillary Convection and Free Surface of Liquid Bridge Ruquan Liang 1,2 & Shuang Zhao 2 & Jungeng Fan 2 & Shuo Zhang 2 Received: 27 June 2019 / Accepted: 7 June 2020 # Springer Nature B.V. 2020
Abstract In this study, effect of lateral vibrations on the thermo-solutocapillary convection and surface behavior in a liquid bridge of toluene/n-hexane solution has been studied numerically under microgravity. The Navier-Stokes equations coupled with the concentration diffusion equation are solved on a staggered grid, and the level set approach is used to capture the deformation of free surface. Present results indicate the interface deformation is convex below the midheight of the liquid bridge and relatively complex at the upper height of the liquid bridge under different frequency vibrations. The lateral vibrations restrain radial and axial velocities on the surface under lateral vibrations with frequencies of 5 Hz and 10 Hz. While the radial and axial velocities on the surface increase under the lateral vibration with frequency of 15 Hz, which illustrates that the effect of lateral vibrations on the free surface has uncertainty. Keywords Horizontal vibration . Thermo-solutocapillary convection . Free surface . Liquid bridge . Microgravity environment
Introduction The floating zone method is a commonly used method in the industrial production of high quality crystals, and the oscillatory thermo-solutocapillary convection is found to be the main cause of micron-scale impurity fringes in the grown crystals using the floating zone. To suppress oscillatory thermosolutocapillary convection, external vibrations, magnetic fields, and shearing airflow have been adopted to control the oscillations. The liquid bridge is a simplified model of the floating zone method, therefore, studies on the influence of external vibration on the liquid bridge have been carried out through theoretical analyses, simulations and experiments. Sanz and Diez (1989) considered the linear nonaxisymmetric oscillations of a liquid bridge. The plateau technique was used to obtain the resonant frequencies of the liquid
* Ruquan Liang [email protected] 1
School of Mechanical and Vehicle Engineering, Linyi University, Linyi 276005, China
2
Key Laboratory of National Education Ministry for Electromagnetic Process of Materials, Northeastern University, Shenyang 110819, China
bridge when lateral perturbations were imposed. Zhang and Alexander (1990) found that the liquid bridge deviated from its initial equilibrium position when a single frequency axial vibration was applied to the liquid bridge. This action of deviation depended on the vibration acceleration, and an ideal method was found to judge the limits of the liquid bridge deviation. Anilkumar and Grugel (1993) investigated a novel end-wall oscillation model for thermo-solutocapillary convection in a semi-floating silicon-oil bridge under constant gravity. It was found that the surface flow velocity depended on the vibration amplitude,
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