Surface tension-driven flows in horizontal liquid metal layers

Abstract

The problem of surface tension-driven flows in horizontal liquid layers has been studied experimentally, and theoretically by direct numerical simulation and small perturbation analysis. We focus our attention on situations in which the depth of the fluid (liquid tin; small Prandtl number, Pr=0.015) is small enough to ensure the predominance of the surface tension forces over those due to the buoyancy. The surface velocity has been experimentally obtained for liquid tin layer with various aspect ratio (length to height) in the range 5<A<83. The thermal gradients are ranged from 5 to 40°K/cm. In the numerical study, the Navier-Stokes and energy equations are solved by an efficient finite difference technique. The parameters governing the flow behaviour in the liquid are varied to determine their effects on thermocapillary convection: the Reynolds number 10<Re<2104 and the aspect ratio 2<A<25; with Pr kept constant at Pr=0.015. The linear eigenequation resulting from small spatial disturbances of the Couette flow solution is solved using an Tau-Chebyshev approximation. A notable feature of the theoretical study is the totally different end circulations. In the region near the cold wall a multicell structure is evident. This agrees with the eigensolution which is of complex type, indicating spatial periodicity. In the hot wall region the flow is accelerated to reach the velocity value for the fully-developed Couette flow which is reached under conditions such as Re/A<20. The transition from viscous to boundary layer regime occurs for a critical value (Re/A)c of nearly about 200, as deduced from the numerical and experimental results.