Dynamics of an Electrified Multi-layer Film Down a Porous Incline

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.