Quasiequilibrium meniscus formation with hysteresis effects

Abstract

For many materials processing techniques, the meniscus of liquid bridging the crystal to the melt is critical in determining the properties of the solidified crystal. It is standard practice for existing theoretical models to use equilibrium meniscus shapes with specified contact angle to represent the behavior of the meniscus. It is shown here that with such boundary conditions, multiple solutions exist to the axisymmetric form of the Laplace–Young equation. Furthermore, these possible 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 implications of this observation on meniscus stability are explored. The effect of direction of pulling in relation to gravity is also investigated. It appears that for tall menisci, commonly adopted equilibrium shapes may be unstable and the consequent dynamic behavior must be considered. Quasiequilibrium dynamics of the meniscus is simulated using a simplified hysteresis model for the contact angle at the top of the meniscus. A variety of behavior is found to arise, which is not fully captured by relations governing meniscus behavior used hitherto in many theoretical simulations.