发表机构
International Institute of Information Technology; Vivekananda Mahavidyalaya（印度信息科学研究院; 维韦卡南达学院）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
针对可溶性表面活性剂降膜的加权残差模型，发现并修正了体相扩散中的质量不平衡，恢复局部守恒，并通过数值基准验证了修正的精确性。
AI 中文摘要
吸附与解吸过程在液膜及其自由表面之间重新分配可溶性表面活性剂，但在封闭周期域内无法改变其总量。我们在针对含可溶性表面活性剂降膜的非线性加权残差模型中审计了这一要求。尽管先前的一项修正恢复了非线性表面Marangoni通量的守恒性，但深度积分体相扩散中仍存在一个单独的不一致性。我们推导了由此产生的质量不平衡，并构造了显式的正周期浓度场以展示该不平衡。缺失的贡献源于倾斜界面处法向扩散通量中出现的流向浓度梯度。纳入该贡献可恢复耦合体-表面输运系统的局部守恒性，同时保持流体动力学方程、主导阶吸附-解吸闭合以及均匀平衡的线性稳定性性质不变。在使用早期行波研究参数进行的独立无滑移计算中，参考模型在t=4500时损失了初始表面活性剂质量的0.0228832%，而修正后的运行其绝对相对质量变化为1.2×10^-15。在t≈4500时，主驼峰和毛细波纹保持高度可比。因此，该基准表明，与行波计算的一致性本身并不能保证简化模型遵守从底层输运问题继承的守恒定律。尽管在此情况下漂移很小，但修正后的方程对每个光滑周期解都守恒约化的总库存。我们还将这一精确守恒性质与完整弯曲界面边界条件的高阶相容性区分开来。
英文摘要
Adsorption and desorption redistribute soluble surfactant between a liquid film and its free surface, but cannot change the total inventory in a closed periodic domain. We audit this requirement in nonlinear weighted-residual models for soluble-surfactant-laden falling films. Although a previous correction restores conservation of the nonlinear surface Marangoni flux, a separate inconsistency remains in the depth-integrated bulk diffusion. We derive the resulting mass imbalance and construct explicit positive periodic concentration fields that exhibit it. The missing contribution arises from the streamwise concentration gradient appearing in the normal diffusive flux at a sloping interface. Including this contribution restores local conservation of the coupled bulk-surface transport system while leaving the hydrodynamic equations, the leading-order adsorption-desorption closure, and the linear stability properties of the uniform equilibrium unchanged. In an independent no-slip calculation using the parameters of an earlier travelling-wave study, the reference model loses $0.0228832\%$ of its initial surfactant mass by $t=4500$, whereas the corrected run has an absolute relative mass change of $1.2\times10^{-15}$. The main hump and capillary ripples remain closely comparable at $t\approx4500$. This benchmark therefore shows that agreement with travelling-wave calculations does not, by itself, guarantee that a reduced model respects the conservation laws inherited from the underlying transport problem. Although the drift is small in this case, the corrected equations conserve the reduced total inventory for every smooth periodic solution. We also distinguish this exact conservation property from higher-order compatibility with the full curved-interface boundary conditions.
