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

Abstract

AbstractWe 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.