NUMERICAL SIMULATION OF THE MOTION OF DROPS ON AN INCLINED SURFACE

The flow of two-dimensional drops suspended in an inclined channel is studied by
numerical simulations at non-zero Reynolds numbers. The flow is driven by the acceleration due
to gravity, and there is no pressure gradient in the flow direction. The equilibrium position of a
drop is studied as a function of the Reynolds number, the Capillary number, the inclination angle
and the density ratio. It is found that the drop always lags the undisturbed flow. More deformable
drops reach a steady state equilibrium position that is farther away from the channel floor. For
drops that are heavier than the ambient fluid, the equilibrium position moves away from the
channel floor as the Reynolds number is raised. The same trend is observed when the inclination
angle with respect to horizontal direction increases. The behavior agrees with computational
modeling of chute flow of granular materials. A drop that is lighter than the ambient fluid reaches
a steady state equilibrium position closer to the channel floor when the Reynolds number or
inclination angle increases. Simulations of 40 drops in a relatively large channel, show that drops
move away from the channel floor when the density ratio is larger than unity.