Solitary and transitional waves in gravity-driven two-layer microchannel flow

We consider steady-travelling solitary and transitional waves in a two-layer flow of immiscible viscous fluids in a vertical plane microchannel. To model the waves, we use evolution equations derived in Sisoev et al (2009 Chem. Eng. Sci. 64 3094-102). The problem is re-formulated in terms of a dynamical system to find homoclinic and heteroclinic trajectories in the phase space corresponding to solitary waves and transitional waves, respectively, in the physical space. Existence of such a rich set of solitary waves indicates that at real-life flow conditions, there are a variety of families of periodic waves which develop due to instability on the interface. In particular, shapes of the solitary waves given here can be used to identify observed periodic waves.