We consider the effect of a partially contaminated interface on the steady thermocapillary flow developed in a two-dimensional slot of finite extent. The contamination is due to the presence of an insoluble surfactant which is carried away by the flow and forms a region of stagnant surface. This problem, first studied in the classical theoretical paper by Carpenter and Homsy (1985, J. Fluid Mech. 155, 429), is revisited thanks to new experimental data. We show that there is a qualitative agreement between above theory and our experiments: two different regions simultaneously coexist on the surface, one of which is free from surfactant and subject to vigorous Marangoni flow, while the other is stagnant and subject to creeping flow with the surface velocity smaller about two orders of magnitude. We found, however, significant disagreement between theory predictions for the extent of a stagnant surface region and newly obtained experimental data. In this paper, we provide an explanation for this discrepancy demonstrating that the surface temperature distribution is far from suggested earlier. Another effect, not previously taken into account, is a possible phase transition experienced by the surfactant. We obtain a correct analytic solution for the position of the edge of the stagnation zone and compare it with the experimental data.

我们考虑了部分污染的界面对在有限范围内的二维缝隙中产生的稳定的热毛细流的影响。污染归因于不溶性表面活性剂的存在，该不溶性表面活性剂被流动带走并形成停滞表面区域。这个问题最初是由Carpenter和Homsy（1985，J. Fluid Mech。155，429）在古典理论论文中首次研究的，这得益于新的实验数据。我们证明上述理论与实验之间存在定性共识：表面上同时存在两个不同的区域，其中一个区域不含表面活性剂，并且受到强烈的Marangoni流动，而另一个区域则处于停滞状态，并且随着该区域而发生蠕变。表面速度较小约两个数量级。但是，我们发现 对于停滞表面区域的范围的理论预测与新获得的实验数据之间存在重大分歧。在本文中，我们为这种差异提供了一种解释，表明表面温度分布远不如先前建议的那样。以前未考虑的另一种作用是表面活性剂可能发生的相变。我们为停滞区边缘的位置获得了正确的解析解，并将其与实验数据进行了比较。是表面活性剂可能经历的相变。我们为停滞区边缘的位置获得了正确的解析解，并将其与实验数据进行了比较。是表面活性剂可能经历的相变。我们为停滞区边缘的位置获得了正确的解析解，并将其与实验数据进行了比较。