Instabilities of thermocapillary convection in a half-zone at intermediate Prandtl numbers

Abstract

The stability of thermocapillary convection inside a cylindrical liquid bridge is studied using both a direct numerical simulation of the three-dimensional problem and linear stability analysis of the axisymmetric basic state. Previously this has been studied extensively for low and high Prandtl numbers. However, the intermediate range of Prandtl numbers between approximately 0.07 and 0.8 which joins the low and high ranges is quite complicated and has not been studied to the same extent. One striking feature is that the axisymmetric base state is much more stable in this intermediate range than at high or low Prandtl numbers. We identify four different oscillatory modes in this range, which have different qualitative features. Direct numerical simulations have been carried out for representative parameter values, and show that the bifurcations are supercritical.

Proper orthogonal decomposition of oscillatory Marangoni flow in half-zone liquid bridges of low-Pr fluids

“…Ref. [5], and direct numerical simulations, e.g. Refs [4][5][6][7][8], have confirmed that Marangoni flow in nonisothermal liquid bridges of low-Pr fluids becomes oscillatory via a two-step bifurcation; this implies that the flow is steady and axisymmetric when the imposed temperature difference between the liquid-bridge supports (DT) is small.…”

A Continuation Method Applied to the Study of Thermocapillary Instabilities in Liquid Bridges

“…The Hopf frequency ω has the same dependence on the Prandtl number as critical Reynolds pronounced than the dependence of ω on Pr since the correction by m. In the range of intermediate Pr (0.06 < Pr < 0.1), the basic flow exhibits a striking stability property. This feature is due to a competition between two different underlying instability mechanisms and a change of the most unstable mode (see also Levenstam et al 2001). …”

Effect of interfacial heat exchange on thermocapillary flow in a cylindrical liquid bridge in microgravity

“…Motivated by the experimental work of Chun and Wuest [2,3] and Schwabe et al [4,5], extensive theoretical studies (e.g. linear instability analyses [6][7][8][9], energy stability analyses [10,11] and direct numerical simulations [12][13][14]) have established that an axisymmetric (2D) stationary thermocapillary flow first loses its stability to an asymmetric (3D) stationary flow, then to an oscillatory flow in liquid bridges of low Prandtl number fluids (Pr 6 0.06), while it transits to oscillatory flow directly in liquid bridges of higher Prandtl number fluids. However, the corresponding critical conditions determined through the theoretical studies do not give quantitative agreement with the experimental results, especially for high Prandtl number fluids.…”