Surfactant-induced stagnant zones in the Jeong-Moffatt free surface Stokes flow problem
Surfactant-induced stagnant zones in the Jeong-Moffatt free surface Stokes flow problem
复制标题
Jeong-Moffatt 自由表面斯托克斯流问题中表面活性剂引起的停滞区
DOI：
10.1063/1.4821137
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发表时间：
2013
影响因子：
4.6
通讯作者：
D. Crowdy
中科院分区：
文献类型：
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作者：
D. Crowdy
我们研究了表面活性剂对Jeong和Moffatt [J. Fluid Mech.241，1-22（1992）]提出的问题的影响，该问题是在粘性流体浴中无限界面下由两个辊引起的自由表面变形的模型。我们表明，表面活性剂的存在下显着影响的形状的稳态平衡的响应曲线。它还表明，有一个很好的定义，虽然不均匀，通道的清洁流量限制的表面活性剂的影响消失。我们的分析收益通过一个新的数学方法产生的混合边值问题在自由表面Marangoni流在无限Peclet数在二维Stokes流。这样的问题通常涉及与无滑移区和毛细管应力平衡保持的区域的混合物的界面。通过保角映射技术占的平方根奇异性固有的混合边值问题，它表明，后者可以转化为经典的修改…
We investigate the effect of surfactants on the problem introduced by Jeong and Moffatt [J. Fluid Mech. 241, 1–22 (1992)] to model the free surface deformation induced by two rollers beneath an infinite interface in a bath of viscous fluid. We demonstrate that the presence of surfactant dramatically affects the shape of the response curve for steady state equilibria. It is also shown that there is a well defined, albeit non-uniform, passage to the clean flow limit as the influence of the surfactant vanishes. Our analysis proceeds via a new mathematical approach to mixed boundary value problems arising in free surface Marangoni flows at infinite Peclet number in two-dimensional Stokes flows. Such problems often involve interfaces with a mixture of no-slip zones and regions where a capillary stress balance holds. By a conformal mapping technique accounting for the square root singularities inherent in such mixed boundary value problems it is shown that the latter can be transformed to the classical modified...