Flow and thermal properties in full-zone thermocapillary liquid bridges

Properties of low Prandtl number flows are derived for slender cylindrical liquid bridges driven by interfacial thermocapillary forces. The theory and computation address the full-zone setting with both ‘outward’ (positive Marangoni number) and ‘inward’ (negative) flows along the liquid-gas interface. Three main results are found. The first concerns three-dimensional nonlinear mode interaction. Full numerical simulation reveals the unsteady three-dimensional nature of the flow solution beyond a cut-off value. Attention is paid to the case where the radius-to-height aspect ratio is 0.5, from which the nonlinearly-coupled azimuthal modes m = 1 and m = 2 are seen to dominate. Second is the behaviour for negative Marangoni number, where asymptotic analysis reveals that a critical value of the scaled Marangoni number exists, on approach to which the pressure gradient across the middle of the zone becomes large and negative. Computational solutions show encouraging agreement with asymptotic predictions (as well as slender-flow midzone computations) near that critical negative value. Third, both the negative and the positive critical Marangoni numbers are seen to correspond to the onset of ‘lemonheads’ (non-convex radial velocity profiles near the midzone) which directly promote three-dimensional instability.