Thermocapillary flow regimes and instability caused by a gas stream along the interface

Abstract

We present the results of a numerical study of the thermocapillary (Marangoni) convection in a liquid bridge of $\mathit{Pr}= 12$ ($n$-decane) and $\mathit{Pr}= 68$ (5 cSt silicone oil) when the interface is subjected to an axial gas stream. The gas flow is co- or counter-directed with respect to the Marangoni flow. In the case when the gas stream comes from the cold side, it cools down the interface to a temperature lower than that of the liquid beneath and in a certain region of the parameter space that cooling causes an instability due to a temperature difference in the direction perpendicular to the interface. The disturbances are swept by the thermocapillary flow to the cold side, which leads to the appearance of axisymmetric waves propagating in the axial direction from the hot to cold side. The mechanism of this new two-dimensional oscillatory instability is similar to that of the Pearson’s instability of the rest state in a thin layer heated from below (Pearson, J. Fluid Mech., vol. 4, 1958, p. 489), and it appears at the value of the transverse Marangoni number ${ \mathit{Ma}}_{\perp }^{cr} \approx 39\text{{\ndash}} 44$ lower than that of the Pearson’s instability in a horizontal layer ($48\lt { \mathit{Ma}}_{\perp }^{cr} \lt 80$, depending on the Biot number). The generality of the instability mechanism indicates that it is not limited to cylindrical geometry and might be observed in a liquid layer with cold gas stream.

The Stability of a Thermocapillary-Buoyant Flow in a Liquid Bridge with Heat Transfer Through the Interface

“…In the non-adiabatic cases, the mechanism, which leads to the generation of m ¼ 0 mode seems to be similar to the one reported in [33]. The interface is cooled down to a temperature lower than that of the liquid beneath and in a certain region of the parameter space the cooling results in an instability due to the temperature difference in the direction perpendicular to the interface.…”

“…10(b). In the case of cooling an interface by a parallel gas stream this unusual direction of the wave propagation was reported by Shevtsova et al [33]. It was attributed to the inverted radial temperature distribution in the liquid near the interface, which is developed due to its cooling.…”

“…The Biot number is a dimensionless parameter whose value depends not only on the properties of the media but also on the features of the flow. The flow structure and temperature distribution in the gas phase around the liquid bridge were studied experimentally [19,32] and numerically [33]. In the vicinity of the interface, the ambient air is entrained by the moving liquid, thus forming a vortex flow in the gas phase.…”

“…temperature disturbance. In that case, instability is developed, which results in a traveling wave moving towards the cold end [33]. At a large cooling rate, the liquid beneath the interface is uniformly cold, and the radial temperature gradient, required for the instability to occur, is either not sufficient or exists only over a short range, and perturbations with m ¼ 0 attenuate.…”

On the variety of particle accumulation structures under the effect of g-jitters

“…As mentioned before, due to typical limitations imposed by terrestrial gravity, experiments are being planned for execution onboard the ISS (Shevtsova et al, 2013). Albeit this environment makes possible extended liquid/gas interfaces (of the order of some centimeters) and the avoidance of undesired buoyancy effects, it, however, suffers from some degree of residual accelerations.…”