The onset time of buoyancy-driven instability in a saline solution where evaporation proceeds through the solution-air interface is analyzed theoretically and numerically. Based on linear stability theory, new stability equations are derived and numerically solved. Also, nonlinear numerical simulations are conducted using FEM solver, COMSOL Multiphysics. ® It is clearly shown that as the evaporation proceeds, the height of solution continuously decreases with time. Moreover, as the evaporation proceeds, concentrated saline solution near the evaporating surface induces gravitational instability. The critical time determined from the linear stability analysis explains the numerical simulation results reasonably. The present theoretical and numerical studies present that evaporation-driven instability is governed by the dimensionless evaporation rate, α , and the initial salt concentration, Ra. The present numerical simulations explain the previous experimental plume dynamics in the evaporation-driven instability systems quite well.

中文翻译：

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盐溶液中蒸发驱动的重力不稳定性的开始

从理论上和数值上分析了盐水溶液中浮力驱动的不稳定性的开始时间，其中蒸发通过溶液 - 空气界面进行。基于线性稳定性理论，推导出新的稳定性方程并进行数值求解。此外，还使用 ​​FEM 求解器 COMSOL Multiphysics 进行非线性数值模拟。® 清楚地表明，随着蒸发的进行，溶液的高度随时间不断降低。此外，随着蒸发的进行，蒸发表面附近的浓盐溶液会引起重力不稳定性。线性稳定性分析确定的临界时间合理地解释了数值模拟结果。目前的理论和数值研究表明，蒸发驱动的不稳定性受无量纲蒸发率控制，α 和初始盐浓度 Ra。目前的数值模拟很好地解释了先前在蒸发驱动的不稳定系统中的实验羽流动力学。