BIFURCATIONS OF NUMERICALLY SIMULATED THERMOCAPILLARY FLOWS IN AXIALLY SYMMETRICAL FLOAT ZONES

Two-dimensional time-dependent flow in an axially symmetric liquid bridge of Si at zero g with flat ends at the melting temperature γMof Si driven by motions of the free, lateral surface is studied numerically. The system is energized by a ring heater H at temperature θ H>θMthat surrounds the midcircle m of the bridge. The radiation from H creates a ∇σSa5 (δS is surface temperature), which in turn creates a ∇σ (σ is surface tension) that drives oscillations of its free surface and thermocapillary flow in the bridge. For aspect ratios A of 1/2, 2/3 and 1 it is found that as the relevant control parameter Δθ≡ θH - θMis increased, the flow in the bridge bifurcates differently depending on A. For A = 1/2 and 2/3 the flow bifurcates from steady state to small-amplitude periodic oscillations, breaking symmetry, to large-amplitude, period-tripled ones, to their subharmonics, then becomes aperiodic, and finally chaotic. Toroidal cells in the bridge oscillate to-and-fro along its axis as a compound pendulum, and they change in shape, number, and strength of rotation over the period of an oscillation. For A = 1, the bifurcation is from steady state to asymmetric oscillations steadily growing in amplitude as Δθ increases and then directly to semiperiodic ones and thence to chaos. Agreement between the present results and recent experimental and numerical ones, are also described. © 1990 American Institute of Physics.