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根据薄膜流体特殊的几何特征,运用润滑近似理论简化描述薄膜流体运动的控制方程,结合薄膜流体运动的边界条件可以得到水平基底上薄膜流体自由液面形态变化的数学计算模型。以MATLAB为计算工具,采用傅立叶伪谱法计算数学模型中的高阶偏微分项,然后结合龙格-库塔法可以对薄膜流体自由液面形态随时间变化规律进行数值模拟。数值模拟结果表明:薄膜流体液面形态在前100s内剧烈变化,随后液面形态变化速率逐步变小,至500s左右时液面形态保持稳定状态而不再有明显变化;此外还印证了流体蒸发作用在液面形态变化中所起的重要作用。
According to the special geometrical characteristics of the thin film fluid, the lubrication approximation theory is used to simplify the governing equation describing the fluid motion of the thin film. By combining the boundary conditions of the thin film fluid motion, a mathematical model for calculating the free surface morphology of the thin film fluid on the horizontal substrate can be obtained. Using MATLAB as the calculation tool, the Fourier pseudospectral method was used to calculate the higher-order partial differential term in the mathematical model. Then the Runge-Kutta method was used to numerically simulate the change of the free surface morphology of the thin film fluid with time. The numerical simulation results show that the liquid surface morphology of the thin film changes drastically in the first 100s, then the liquid surface morphological change rate gradually becomes smaller, and the liquid surface morphology remains stable without significant change until about 500s. In addition, the fluid evaporation Role in the liquid form changes in the important role played.