The nonlinear dynamics of gravity-driven two-layers flow through an oblique microchannel of porous walls subjected to an external electric potential is examined. The evolution equation governing the surface wave deflection is derived in the frame of long wave theory. The stability criteria of the linearized system are investigated. As permeability, inclination or dielectric constant increase, the disturbances become stronger. However, the viscosity ratio plays an irregular role on the stability. Resonant waves propagating on the fluid interface are introduced. The instability of the base flow is simulated. It is observed that the instability onset can be controlled by many physical properties related with the model. The effect of permeability as well as dielectric constant corresponds to linear processing expectations. Viscosity ratio improves stability in certain situations. However, the electric role is generally dominant in the current model. Such results may be useful in practical applications by designing a device in order to control the instability. Solitary waves propagating on the interface are studied. The presence of stable stationary solitons is shown in certain statuses of the model.

重力驱动的两层流体的非线性动力学流经多孔壁的倾斜微通道，并受到外部电势的影响。在长波理论的框架内推导了控制表面波偏转的演化方程。研究了线性化系统的稳定性准则。随着磁导率，倾斜度或介电常数的增加，干扰变得更强。但是，粘度比对稳定性起不规则的作用。引入了在流体界面上传播的共振波。模拟了基流的不稳定性。可以看出，不稳定性的发生可以通过与模型有关的许多物理特性来控制。磁导率以及介电常数的影响与线性处理的预期相对应。粘度比可以提高某些情况下的稳定性。但是，电模型通常在当前模型中占主导地位。通过设计设备以控制不稳定性，这样的结果在实际应用中可能是有用的。研究了在界面上传播的孤波。在模型的某些状态下，显示出稳定的固定孤子的存在。