ABSTRACT
Thermocapillary flows within a differentially heated rectangular cavity containing two
immiscible liquid layers are of considerable technological importance in materials
processing applications particularly under microgravity conditions where the influence
of buoyancy-driven convection is minimized. In the present study, for the first time, we
account the affect of normal and tangential forces that control the track of the moving
interface by using level set method (LSM). A 2-D numerical procedure for two
immiscible fluid systems on the basis of a single phase model and the level set
formulation is developed. The time dependent Navier-Stokes and energy equations are
solved by means of the control volume approach on a staggered rectangular grid
system. The numerical model interprets the tangential and the normal stresses by a
single-phase model using a heavy side function. The topological change of the interface
between the two immiscible flows is described by the level set method. According to our
background this is the first study of such cases using the single phase model and the
control volume formulation. Two cases have been studied: the first case contains a
system with only one liquid interface (melt/encapsulant) between the two immiscible
fluids. The second one has a system with encapsulant free surface opened to air (and
so, subjected to a second thermocapillary forces). Both the liquid-liquid interface and
the free surface are assumed to be initially flat, which is a valid assumption according to
earlier theoretical and experimental results. In later cases, the liquid-liquid interface is
allowed to deform. The numerical results are compared with the available analytical
models and experimental results. The comparisons showed an acceptable agreement
between the present predicted results and the available data shown in the available
references.