ICNPAA 2010: Mathematical Problems in
Engineering, Aerospace and Sciences

The process parameter considered in this paper is the pressure p, which incorporates the gas pressure in front of the free surface of the meniscus, the hydrostatic pressure of the melt column situated behind the meniscus, the hydrodynamic pressure associated to the thermoconvection in the meniscus and the Marangoni pressure associated to the Marangoni convection. The meniscus's shape and size are analyzed in function of the above parameter p. More precisely, for a meniscus having a given shape and size, the range of the values where p should be, is found. Furthermore, it is shown that if p is in a prescribed range, then a meniscus, having a given shape and the size (crystal radius) in a given range, is obtained. Finally, the (static) stability of the menisci is analyzed. For NdYAG microfiber numerical illustrations are given.