On Thermocapillary Flows in Containers with Differentially Heated Side Walls

Abstract

The problem to be investigated in this paper is that of a liquid layer in a rectangular container heated from one side and cooled from the other side. The lower wall of the container is insulated. The upper surface of the liquid is open to the ambiancy (Fig. 1). In this container, flow is driven by density differences in the gravitational field and by surface tension gradients. In a microgravity environment, surface tension gradients are the only cause of motion. Indeed, since surface tension σ is temperature dependent, it is clear that a steady surface tension gradient exists along the upper free surface. Usually surface tension decreases with temperature (∂σ/∂T ≈ - 0.15 mN.m^-1.K^-1 for water), but we do not like to restrict ourself to this usual case. Rather, we will concentrate on the less known case of systems for which surface tension increases with temperature (∂σ/∂T > 0). Indeed if one looks at the surface tension of e.g. the system MnO-SiO₂ in the temperature range 1300–1600 °C, one observes that surface tension may decrease or increase with T depending on the composition of this particular silicate¹, When the content in SiO₂ exceeds 30 %, then ∂σ/∂T > 0. It seems to be a general rule that, in binary SiO₂ systems, the temperature coefficient of surface tension increases with the percentage of SiO₂, becoming thus positive at a given percent of SiO₂.