QUASI-EQUILIBRIUM MENISCUS FORMATION WITH HYSTERESIS EFFECTS

For many materials processing techniques, the meniscus of liquid bridg ing the crystal to the melt is critical in determining the properties of the solidified crystal. It is standard practice for existing theore tical models to use equilibrium meniscus shapes with specified contact angle to represent the behavior of the meniscus. It is shown here tha t with such boundary conditions, multiple solutions exist to the axisy mmetric form of the Laplace-Young equation. Furthermore, these possibl e meniscus profiles may, depending on the interaction of Bond number, pressurization, aspect ratio and contact angle, correspond to minima, maxima or nonextrema points, as far as energy is concerned. The implic ations of this observation on meniscus stability are explored. The eff ect of direction of pulling in relation to gravity is also investigate d. It appears that for tall menisci, commonly adopted equilibrium shap es may be unstable and the consequent dynamic behavior must be conside red. Quasiequilibrium dynamics of the meniscus is simulated using a si mplified hysteresis model for the contact angle at the top of the meni scus. A variety of behavior is found to arise, which is not fully capt ured by relations governing meniscus behavior used hitherto in many th eoretical simulations.