The relative contribution of solutal marangoni convection to thermal marangoni flow instabilities in a liquid bridge of smaller aspect ratios under zero gravity

Abstract

The effect of solutal Marangoni convection on flow instabilities in the presence of thermal Marangoni convection in a Si-Ge liquid bridge with different aspect ratios As has been investigated by three-dimensional (3D) numerical simulations under zero gravity. We consider a half-zone model of a liquid bridge between a cold (top plane) and a hot (bottom plane) disks. The highest Si concentration is on the top of the liquid bridge. The aspect ratio (As ) drastically affects the critical Marangoni numbers: the critical solutal Marangoni number (under small thermal Marangoni numbers (MaT As ≾ 1800)) has the same dependence on As as the critical thermal Marangoni number (under small solutal Marangoni numbers (400 ≾ MaC As ≾ 800)), i.e., it decreases with increasing As . The azimuthal wavenumber of the traveling wave mode increases as decreasing As, i.e., larger azimuthal wavenumbers (m = 6, 7, 11, 12, and 13) appear for As = 0.25, and only m = 2 appears when As is one and larger. The oscillatory modes of the hydro waves have been extracted as the spatiotemporal structures by using dynamic mode decomposition (DMD). The present study suggests a proper parameter region of quiescent steady flow suitable for crystal growth for smaller aspect ratios of the liquid bridge.