Instabilities of shallow dynamic thermocapillary liquid layers

Results of experiments with thermocapillary flow in shallow liquid layers heated from the side are presented. The fluid has Prandtl number 17 and the main configuration investigated is an annular gap to avoid side-wall effects. The liquid depth d was d≤3.00 mm to have negligible buoyancy effects. Various instabilities have been observed. At a Marangoni number M≂6⋅102, a transition to steady multicellular flow occurred. The convection cells are longitudinal rolls embedded in the main flow all rotating in the same direction. At M≂3⋅103, a transition of the steady multicellular flow to time-dependent flow states (t) was observed. Two different t-flow states have been identified by thermocouple measurements and by visualization of the dynamic-free surface deformations of oscillatory flow. Both t states can be described by disturbances in the form of traveling waves. A short-wavelength t state with small surface deformations and with waves traveling in azimuthal direction is the preferred mode for d≤1.4 mm. A long-wavelength t state with larger surface deformations and with waves traveling in radial and in azimuthal directions is preferred for d≥1.4 mm. The stability diagram, wavelength, frequency, and phase speed of both t states are presented and the findings in comparison to an already existing theory by Smith and Davis J. Fluid Mech. 132, 119, 145 (1983) are discussed.