Temporal and spatial elements of thermocapillary convection in floating zones

On the onset of multi-wave patterns in laterally heated floating zones for slightly supercritical conditions

“…Most surprisingly, although slightly supercritical conditions had been considered, the dominant modal structures was found to be a peculiar combination of disturbances with different azimuthal wavenumbers m = 1, 2, and 3 (a superposition of distinct waves with different spatial modes). In a rather unexpected way, these modal structures were observed to have the characteristics of a standing or a travelling wave, changing from one to another irregularly with the resulting dominant modal structures not depending on the aspect ratio (another important distinguishing feature with respect to earlier studies dealing with the classical liquid-bridge problem [1][2][3][4][5][6]35 ).…”

“…The amount of existing literature on such subjects is really impressive (especially if one considers what has been done for the so-called half-zone liquid bridge, a popular simplified model of the FZ process, Refs [1][2][3][4][5][6] and references therein). Here, due to page limits we limit ourselves to recalling the points still requiring attention, and recent (still unexplained) findings.…”

Experimental study on the transition process to the oscillatory thermocapillary convections in a floating half zone

“…All conclusions related to two bifurcation transitions were predicted only by theoretical approach and there has no experimental verification reported yet. As a matter of fact, Frank and Schwabe, based on their experimental observation, have noticed the time-independent but three-dimensional flow states and mentioned, "The broken symmetry was probably affected by a hydrodynamical instability" [24]. We have been using "axial asymmetric flow" to describe the three-dimensional flow.…”

Flight results on marangoni flow instability in liquid bridges

“…When the temperature difference exceeds a critical value, depending on the geometry, on the liquid properties and on the boundary conditions, the flow experiences a transition to an oscillatory and three-dimensional pattern. A number of experimental works on the subject have been performed, on ground and in microgravity conditions, by different investigators [2][3][4][5][6][7][8][9][10]. From the theoretical/numerical point of view oscillatory thermocapillary flows in liquid bridges have been investigated by the hydrodynamic stability theory [11,12].…”

“…From the experimental point of view, the traveling wave model was observed by different investigators on ground and in microgravity [2][3][4][5]. The standing wave model, instead, has been observed more recently in ground-based experiments [7,8] and during a Spacelab experiment [9]. On the other hand, the development of supercomputers and of efficient numerical methods allowed direct numerical solutions of the three-dimensional and time-dependent Navier Stokes equations.…”