Convective instability mechanisms in thermocapillary liquid bridges

TLDR

The study calculates the primary instability of axisymmetric steady thermocapillary flow in a cylindrical liquid bridge using a mixed Chebyshev–finite difference method and analyzes the physical mechanisms through linear energy balance, comparing them with previous literature. For a unit aspect ratio the most unstable mode has azimuthal wavenumber m = 2; at low Prandtl numbers the bifurcation is stationary with the neutral mode amplified in the near‑surface shear layer, whereas at high Prandtl numbers the base state becomes unstable to nearly azimuthal hydrothermal waves.

Abstract

The primary instability of axisymmetric steady thermocapillary flow in a cylindrical liquid bridge with non-deformable free surface is calculated by a mixed Chebychev-finite difference method. For unit aspect ratio the most dangerous mode has an azimuthal wavenumber m=2. The physical instability mechanisms are studied by analyzing the linear energy balance of the neutral mode. If the Prandtl number is small (Pr≪1), the bifurcation is stationary. The associated neutral mode is amplified in the shear layer close to the free surface. For large Prandtl number (Pr=4), the basic state becomes linearly unstable to a pair of hydrothermal waves propagating nearly azimuthally. Both mechanisms are compared with those previously proposed in the literature.