Onset of solutal convection in liquid phase epitaxy system

The onset of convective instability in the liquid phase epitaxy system is analyzed with linear stability theory. New stability equations are derived under the propagation theory, and the dimensionless critical time τ _c to mark the onset of the buoyancy-driven convection is obtained numerically. It is here found that the critical Rayleigh number Ra _c is 8000, below which the flow is unconditionally stable. For Ra>Ra _c the dimensionless critical time τ _c to mark the onset of a fastest growing instability is presented as a function of the Rayleigh number and the Schmidt number. Available numerical simulation results and theoretical predictions show that the manifest convection occurs starting from a certain time τ _o (> τ _c ). It seems that during τ _c ≤τ≤τ _o secondary motion is relatively very weak. This article is dedicated to Professor Chang Kyun Choi for celebrating his retirement from the School of Chemical and Biological Engineering, Seoul National University.