含活性剂液滴在倾斜粗糙壁面上的铺展稳定性

针对含非溶性活性剂液滴在倾斜粗糙壁面上的铺展过程, 应用润滑理论推导出基态和扰动态下液膜厚度和活性剂浓度的演化方程组, 基于非模态理论研究了液滴铺展的稳定性特征, 探讨了相关参数的影响及其内在机理. 研究表明: 液膜厚度和活性剂浓度扰动量均呈现双驼峰型变化, 且峰值位于液滴底部凹陷处; 随扰动波数k增加, 最易失稳区域由液滴底部右侧凹陷处移至左侧凹陷, 壁面结构的影响逐渐减弱, 液滴铺展历程趋于稳定; 增加壁面倾角θ 将导致液滴铺展不稳定性加剧, 增大壁面高度D和壁面波数k₀均导致液滴铺展稳定性先增强后减弱; 随毛细数C减小, 液滴铺展稳定性下降, 重力的影响逐渐突显, 扰动量最大值呈现先增大后减小的变化趋势.

Stability of surfactant-laden droplet spreading over an inclined heterogeneous substrate

For the spreading of a droplet covered with insoluble surfactant over an inclined random heterogeneous substrate, the base state and disturbance evolution equations for the film thickness and surfactant concentration are derived using the lubrication theory. Stability of the droplet spreading on the heterogeneous substrates, and effects of dimensionless parameters as well as the internal mechanism are investigated based on the non-modal stability theory. Results show that the disturbances of film thickness and surfactant concentration exihibit a double-hump shape and the crests lie in thinning regions at the bottom of the droplet. With increasing disturbance wave number, the stability of the droplet spreading is enhanced, but the maximal disturbance transfers from the right-side to the left-side of the droplet bottom. Increasing inclined angle leads to severe instability distinctly. Improving topographical height or increasing wave number of the substrate leads the spreading stability to firstly enhance and then to weaken. The droplet evolution displays an unstable spreading under smaller capillary number, with the maximum disturbance to be increasing before decreasing.