Electrohydrodynamics (EHD) instability of a vertical cylindrical interface is tackled in the present study. The interface separates two viscous, homogeneous, porous, incompressible, and dielectric fluids which totate about the common cylindrical axis with different uniform angular velocities. A uniform axial electric field acts upon the considered system. Additionally, the influence of heat transfer is incorporated into the buoyancy term as well as the surface tension parameter, giving rise to the thermo-capillary effect. In this context, the viscous potential theory as well as the standard normal modes analysis are employed. The distributions of temperature, pressure, and velocity fields are evaluated. The linear stability approach resulted in an exceedingly complicated transcendental dispersion relation. The non-dimensional analysis revealed some physical Ohnesorge, Darcy, Rayleigh, Prandtle and Weber numbers. Actually, the dispersion relation has no closed form solution. Consequently, a numerical technique is utilized to display the stability profile. The relation between the growth rate and the wavenumber of the surface waves is constructed. The influences of various physical parameters on the stability profile are illustrated. It is found that the Ohnesorge number plays a dual role in the stability configuration.

本研究解决了垂直圆柱界面的电流体动力学 (EHD) 不稳定性。该界面将两种粘性的、均质的、多孔的、不可压缩的和介电流体分开，它们以不同的均匀角速度围绕共同的圆柱轴旋转。均匀的轴向电场作用于所考虑的系统。此外，传热的影响被纳入浮力项以及表面张力参数，从而产生热毛细管效应。在这种情况下，使用粘性势理论以及标准正态模式分析。评估温度、压力和速度场的分布。线性稳定性方法导致了极其复杂的超越色散关系。无量纲分析揭示了一些物理 Ohnesorge、Darcy、Rayleigh、Prandtle 和 Weber 数。实际上，色散关系没有封闭形式的解。因此，使用数值技术来显示稳定性曲线。建立了表面波的增长率与波数之间的关系。说明了各种物理参数对稳定性曲线的影响。发现 Ohnesorge 数在稳定性构型中起着双重作用。说明了各种物理参数对稳定性曲线的影响。发现 Ohnesorge 数在稳定性构型中起着双重作用。说明了各种物理参数对稳定性曲线的影响。发现 Ohnesorge 数在稳定性构型中起着双重作用。