Interfacial waves and the dynamics of backflow in falling liquid films

Abstract

AbstractBy studying the dynamics of the streamwise pressure gradient at the wavefront of travelling interfacial waves, we investigate the formation and evolution of backflow regions for the sinusoidal and teardrop-shaped surface wave regimes of laminar falling liquid films. The magnitude of the wavefront streamwise pressure gradient grows as the flow inlet disturbance increases in amplitude and steepness. At large enough values, the adverse pressure gradient induces flow separation and subsequently backflow at the large-amplitude wavefront. The backflow region evolves from a closed circulation to an open vortex as the wave grows to saturation. The dynamics of the streamwise pressure gradient at the sinusoidal wavefront approaches a stable fixed point at saturation. Thus, the open vortex retains its structure as the wave continues downstream. The streamwise pressure gradient at the wavefront of the teardrop-shaped pulse evolves similarly to a time-periodic function with multiple minima/maxima. This phenomenon is a consequence of the interaction between the teardrop-shaped wave and newly formed preceding capillary waves. The nature of the teardrop pulse–capillary wave interaction is such that a decrease in magnitude of the streamwise pressure gradient at the teardrop-shaped wavefront is followed by an increase at the capillary wavefront and vice versa. The increased adverse pressure gradient at the capillary wavefront induces a second open vortex backflow, while the teardrop-shaped wavefront’s open vortex reverts to a closed circulation. This interaction between the waves continues as the teardrop pulse–capillary wavetrain travels downstream, leading to multiple capillary waves and backflow regions.