Unstable thermocapillary flow inside a NaNO3 float zone

We have numerically investigated the problem of the transition from an axisymmetric state to an unstable i,e. oscillatory state in a liquid float zone which is held suspended between a pair of coaxial disks. The system of governing equations corresponding to a time-dependent-3D model was successfully solved by employing the modified-SIMPLE method. For a low Marangoni number, the flow consists of a steady, axisymmetric and toroidal structure exhibiting a 'purely' axial fluid circulation on the free surface. The vortex center is observed beneath that surface near the hot disk. When the Marangoni number increases beyond the critical value Ma CR, Ma CR ≃9750, the transition to an oscillatory state occurs. The flow and the thermal field become clearly three-dimensional and time-dependent, with the existence of a distorted 'saddle-shape-like' torus which exhibits its 'rotating' and dynamic character around the circumference. The fluid flows following a curved pattern on the free surface. The frequency of the oscillations was evaluated to be ≃0.4Hz