Modeling of two-layer fluid flows with evaporation at the interface in the presence of the anomalous thermocapillary effect

Stationary convective flows of two immiscible viscous incompressible fluids (liquid and gas) under action of the transverse gravity field and longitudinal temperature gradient along the interface are studied analytically. Mathematical model of the fluid flows with the effects of evaporation at the interface is based on exact solutions to the Navier–Stokes equations in the Oberbeck–Boussinesq approximation. The effects of the thermodiffusion and diffusive heat conductivity in the gas-vapor layer are taken into consideration. The obtained solutions are used to model the flows in the two-layer gas-liquid system in the case when a liquid exhibits the anomalous thermocapillary effect. Examples of the two-layer fluid flows are presented for various values of the gas flow rate, longitudinal temperature gradient at the interface and the gravity force acceleration.