We investigate the linear stability characteristics of a pressure-driven two-layer channel flow of immiscible Newtonian and Herschel–Bulkley fluids subjected to an applied electric field normal to the flow. The linear stability equations are derived and solved using an accurate spectral Chebyshev collocation method. It is found that the electric field can stabilise or destabilise the flow depending on the electrical properties of the fluids. We also observe that increasing the electric permittivity ratio and decreasing the electrical conductivity ratio, while keeping the rest of the parameters constant, enhances the growth rate of the disturbances. The “Reynolds stress” of the Newtonian layer and the work done by the velocity and stress disturbances tangential to the interface are found to be the mechanism of the instability observed due to the applied electric field. A parametric study is also conducted by varying the thickness of the bottom layer, Bingham number and flow index of the Herschel–Bulkley fluid. Increasing Bingham number is found to be stabilising or destabilising depending on the thickness of the non-Newtonian layer and the maximum disturbance growth occurs at an optimum value of non-Newtonian layer thicknesses. Increasing the shear-thinning and shear-thickening nature is shown to destabilise the flow. Our study is relevant in many microfluidic and electronic cooling applications.

我们研究了在与电场垂直的外加电场作用下，不混溶的牛顿流体和Herschel-Bulkley流体的压力驱动的两层通道流动的线性稳定性特征。使用精确的光谱Chebyshev配置方法导出并求解线性稳定性方程。已经发现，电场可以根据流体的电特性来使流动稳定或不稳定。我们还观察到，提高电导率比和降低电导率比，同时保持其余参数不变，可以提高干扰的增长率。牛顿层的“雷诺应力”以及与界面相切的速度和应力扰动引起的功被发现是由于施加电场而引起的不稳定性的机制。通过改变底层的厚度，Bingham数和Herschel-Bulkley流体的流动指数，也可以进行参数研究。根据非牛顿层的厚度，发现增加的宾厄姆数趋于稳定或不稳定，并且在非牛顿层厚度的最佳值处出现最大的扰动增长。剪切稀化和剪切稠化性质的增加显示出使流动不稳定。我们的研究与许多微流体和电子冷却应用有关。通过改变底层的厚度，宾厄姆数和Herschel-Bulkley流体的流动指数，也可以进行参数研究。根据非牛顿层的厚度，发现增加的宾厄姆数趋于稳定或不稳定，并且在非牛顿层厚度的最佳值处出现最大的扰动增长。剪切稀化和剪切稠化性质的增加显示出使流动不稳定。我们的研究与许多微流体和电子冷却应用有关。通过改变底层的厚度，Bingham数和Herschel-Bulkley流体的流动指数，也可以进行参数研究。根据非牛顿层的厚度，发现增加的宾厄姆数趋于稳定或不稳定，并且在非牛顿层厚度的最佳值处出现最大的扰动增长。剪切稀化和剪切稠化性质的增加显示出使流动不稳定。我们的研究与许多微流体和电子冷却应用有关。剪切稀化和剪切稠化性质的增加显示出使流动不稳定。我们的研究与许多微流体和电子冷却应用有关。剪切稀化和剪切稠化性质的增加显示出使流动不稳定。我们的研究与许多微流体和电子冷却应用有关。