| High quality single crystals can be grown in the micro-gravity environment of Space with a containerless process known as float zoning. Here, the large temperature gradients imposed along the interface of the melt produce thermocapillary or Marangoni convection in the bulk fluid. When this motion becomes unstable, the resulting crystal will contain undesired segregation bands. Thus, an understanding of the instabilities that occur in such flows is essential to the successful exploitation of this technology.;All existing analyses of surface-tension driven instabilities have assumed a motionless basic state from which convection develops. We begin the study of the instabilities of thermocapillary flows with dynamic basic states by considering such flows in two simple, planar geometries.;We find that these flows can become unstable in two distinct ways. The first instability is a two-dimensional surface wave that critically depends on the deformation of the interface. It is an instability of the particular velocity field associated with the flow, and surface-tension gradients are important only in that they drive this basic-state flow.;The second class of instabilities are driven by surface-tension gradients directly and appear in two forms. First, as a hydrothermal wave propagating obliquely to the basic-state flow and second, as a stationary longitudinal roll that is related to the classical Marangoni convection cell.;We document the mechanism of each instability and show how each behaves as a function of the system parameters. |
