Instabilities of thermocapillary flows in large Prandtl number liquid bridges between two coaxial disks with different radii

Abstract

We explore the geometric effects on the thermocapillary flow instabilities in large Prandtl number ( Pr =  1.4) liquid bridges between two coaxial disks with different radii under microgravity, focusing on the impacts of radius ratio Γr and aspect ratio Γ. The static deformation of the free surface is concerned by the solution of the Young–Laplace equation, and the linear stability analysis based on spectral element method is conducted for accurate identification of the instability characteristic. We observe that the flow stability is generally improved with the decrease in radius ratio Γr or aspect ratio Γ, especially for the liquid bridge heated from the upper disk. The critical oscillation frequency experiences an abrupt drop around Γr = 0.56 as Γr decreases for the liquid bridge with the bottom disk heated. Moreover, three transitions between two-dimensional axisymmetric steady flow and three-dimensional oscillatory flow are observed within the interval 0.87 <  Γ ≤ 0.91 at Γr = 0.50 when the liquid bridge is heated from the upper disk. The energy analysis indicates that the instabilities for all cases are predominantly caused by the hydrothermal wave instability and the phenomenon of three transitions results from the variation of thermal energy transfer efficiency with the growth of the Marangoni number.