The linear stability of a semi-infinite fluid undergoing a shearing motion over a fluid layer that is laden with soluble surfactant and that is bounded below by a plane wall is investigated under conditions of Stokes flow. While it is known that this configuration is unstable in the presence of an insoluble surfactant, it is shown via a linear stability analysis that surfactant solubility has a stabilising effect on the flow. As the solubility increases, large-wavelength perturbations are stabilised first, leaving open the possibility of mid-wave instability for moderate surfactant solubilities, and the flow is fully stabilised when the solubility exceeds a threshold value. The predictions of the linear stability analysis are supported by an energy budget analysis which is also used to determine the key physical effects responsible for the (de)stabilisation. Asymptotic expansions performed for long-wavelength perturbations turn out to be non-uniform in the insoluble surfactant limit. In keeping with the findings for insoluble surfactant obtained by Pozrikidis & Hill (IMA J Appl Math 76:859–875, 2011), the presence of the wall is found to be a crucial factor in the instability.

在斯托克斯流条件下，研究了半无限流体在充满可溶性表面活性剂且下方由平面壁界定的流体层上进行剪切运动的线性稳定性。虽然已知这种配置在不溶性表面活性剂存在下不稳定，但通过线性稳定性分析表明，表面活性剂的溶解度对流动具有稳定作用。随着溶解度的增加，大波长扰动首先稳定，为中等表面活性剂溶解度留下中波不稳定的可能性，当溶解度超过阈值时，流动完全稳定。线性稳定性分析的预测得到了能量预算分析的支持，该分析也用于确定导致（去）稳定化的关键物理效应。对长波长扰动进行的渐近扩展在不溶性表面活性剂限制中证明是不均匀的。与 Pozrikidis & Hill (IMA J Appl Math 76:859–875, 2011) 获得的不溶性表面活性剂的发现一致，发现壁的存在是不稳定的关键因素。