Derived in this paper are evolution equations for the thickness and surface surfactant concentration pertaining to a thin liquid layer that is laden with a soluble surfactant as it flows under the influence of gravity down a heated incline. These equations account for variations in surface tension with surfactant concentration and temperature. A linear stability analysis and numerical simulations are carried out and discussed. An expression for the critical Reynolds number has been obtained and includes both thermocapillary and solutocapillary effects. The linear stability analysis was found to be in harmony with the nonlinear numerical simulations. A comparison with a weighted residual model also revealed good agreement.

在这篇论文中推导出了厚度和表面表面活性剂浓度的演化方程，该方程与薄液层有关，该薄液层在重力的影响下沿着加热的斜坡向下流动时充满了可溶性表面活性剂。这些方程说明了表面张力随表面活性剂浓度和温度的变化。进行并讨论了线性稳定性分析和数值模拟。已获得临界雷诺数的表达式，其中包括热毛细管和溶质毛细管效应。发现线性稳定性分析与非线性数值模拟一致。与加权残差模型的比较也显示出良好的一致性。