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A hybrid numerical method for interfacial fluid flow with soluble surfactant

机译:可溶性表面活性剂界面流体流动的混合数值方法

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摘要

We address a significant difficulty in the numerical computation of fluid interfaces with soluble surfactant that occurs in the physically representative limit of large bulk Peclet number Pe. At the high values of Pe in typical fluid-surfactant systems, there is a transition layer near the interface in which the surfactant concentration varies rapidly, and large gradients at the interface must be resolved accurately to evaluate the exchange of surfactant between the interface and bulk flow. We use the slenderness of the layer to develop a fast and accurate [`]hybrid' numerical method that incorporates a separate, singular perturbation analysis of the dynamics in the transition layer into a full numerical solution of the interfacial free boundary problem. The accuracy and efficiency of the method is assessed by comparison with a more [`]traditional' numerical approach that uses finite differences on a curvilinear coordinate system exterior to the bubble, without the separate transition layer reduction. The traditional method implemented here features a novel fast calculation of fluid velocity off the interface.
机译:我们解决了与可溶性表面活性剂的流体界面的数值计算中的一个重大困难,该困难发生在大体积Peclet数Pe的物理代表极限中。在典型的流体表面活性剂系统中,当Pe的值很高时,界面附近会存在一个过渡层,其中表面活性剂的浓度会迅速变化,必须准确解析界面处的大梯度才能评估界面活性剂与本体之间的表面活性剂交换流。我们使用该层的细长度来开发一种快速,准确的“混合”数值方法,该方法将对过渡层中的动力学进行单独的,奇异的摄动分析,以得到界面自由边界问题的完整数值解决方案。通过与更“传统”的数值方法进行比较来评估该方法的准确性和效率,该方法在气泡外部的曲线坐标系上使用有限的差异,而无需单独减少过渡层。在此实现的传统方法具有一种新颖的快速计算出界面流体速度的方法。

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