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

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 A_s 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 (A_s ) drastically affects the critical Marangoni numbers: the critical solutal Marangoni number (under small thermal Marangoni numbers (Ma_T A_s ≾ 1800)) has the same dependence on A_s as the critical thermal Marangoni number (under small solutal Marangoni numbers (400 ≾ Ma_C A_s ≾ 800)), i.e., it decreases with increasing A_s . The azimuthal wavenumber of the traveling wave mode increases as decreasing A_s, i.e., larger azimuthal wavenumbers (m = 6, 7, 11, 12, and 13) appear for A_s = 0.25, and only m = 2 appears when A_s 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.