Dynamics of co-current gas-liquid film flow through a slippery channel

We consider a thin liquid film in a wide inclined channel being driven by gravity and co-current turbulent gas flow. The bottom plate with which the liquid is in contact with is taken to be slippery, and we impose the classic Navier slip condition at this substrate. Such a setting finds application in technological processes as well as nature (e.g., distillation, absorption, and cooling devices). The gas-liquid problem can be decoupled by making certain reasonable assumptions. Under these assumptions, we solve the gas problem to obtain the tangential and normal stresses acting at the wavy gas-liquid interface for arbitrary waviness. In modeling the liquid layer dynamics, we make use of the stresses computed in the gas problem as inputs to the interface boundary conditions. We develop the long-wave model and the weighted-integral boundary layer (WIBL) model to describe the thin film dynamics. We perform a linear stability of these reduced order models to scrutinize the effect of wall slip, liquid flow rate, and the gas shear on the stability of the flat film solution. It is found that the wall slip promotes the instability of the flat interface. Furthermore, we compute solitary wave solutions of the WIBL model by implementing Keller's pseudo-arc length algorithm on a periodic domain. We observe that the wave speed as well as the wave amplitude are attenuated on incrementing the liquid slip at the substrate. We corroborate these findings with the time-dependent computations of the nonlinear WIBL model.