Effect of viscosity ratio on the motion of drops flowing on an inclined surface

The flow of two-dimensional drops on an inclined channel is studied by numerical simulations at finite Reynolds numbers. The effect of viscosity ratio on the behaviour of the two-phase medium is examined. The flow is driven by the acceleration due to gravity, and there is no pressure gradient along the flow direction. An implicit version of the finite difference/front-tracking method was developed and used in the present study. The lateral migration of a drop is studied first. It is found that the equilibrium position of a drop moves away from the channel floor as the viscosity ratio increases. However, the trend reverses beyond a certain viscosity ratio. Simulations with 40 drops in a relatively large channel show that there exists a limiting viscosity ratio where the drops behave like solid particles, and the effect of internal circulation of drops becomes negligible. This limiting condition resembles the granular flow regime except that the effect of interstitial fluid is present. The limiting viscosity ratio depends on the flow conditions (80 for \(Re=10\), and 200 for \(Re=20\)). There are two peaks in the areal fraction distribution of drops across the channel which is different from granular flow regime. It is also found that the peak in areal fraction distribution of drops moves away from the channel floor as the inclination angle of the channel increases.