Three-dimensional numerical simulation of spoke pattern in oxide melt

摘要

In order to reveal the mechanism of the well-known surface spoke patterns, three-dimensional numerical simulations of LiNbO_3 melt flwo in an open crucible (47 mm ×46 mm~h) were performed by menas of the finite differnece method, The crucible side wall was heated at constant the flux and the bottom was assumed to be adiaboatic. Radition heat loss from themelt surface to the ambient was at a temperautre of T_a. It was found that that the Rayleigh effect alone could not reproduce the spoke patern. However, if the Marangoni effect is taken into account, the numericla resutls could semi-quantitatively explain gthe spoke pttern. A skeries of simulaitns with varoius values fo the temperautre coefficient of surface tenison suggests that the spoke patterns are caused bythe Marangoni instability in the tin thermla boundary klayer near the melt surface. Incipience of the spoke pattern is kapproximately predicted by a critical Maranogi number value Ma_c肨ΔTΖ?μα=57.6 which correspondst of the critical Marangoni number for the incipience of the Marangoni instabiity in an adiabatic horizontal layer with a free slip bottom at a constant temeprautre, where γT=-γ/T is the temeporutre coefficient of surface tension, δ the depth of the thermal boundarylayer beneath the melt surface. ΔT the temperautre drop in the boundary layer, μ the viscosity and α the tehrmal diffusion coefficient of the melt, respectively. A series of simultions suggets that a constant temeprautre boundary condtion at the crucible side wall stabilizes the melt surfacde and the spoke pattern becomes very difficult to appear.