Creeping motion and pending breakup of drops and bubbles near an inclined wall

The gravity-driven motion of a three-dimensional deformable drop or bubble in the vicinity of an inclined wall is investigated for low Reynolds number by computational and experimental methods. The velocity, shape, and distance from the wall for a nonwetting drop moving due to gravity are examined for different values of the drop-to-medium viscosity ratio, lambda, the wall inclination angle from horizontal, theta, and Bond number, B, the latter which gives the relative magnitude of the buoyancy to capillary forces. The steady nondimensional velocity, scaled with the isolated settling drop velocity, is found to vary nonmonotonically with the Bond number for small inclination angles and intermediate viscosity ratios. For the same range of Bond numbers, the steady velocity was found to be an increasing function for bubbles and a decreasing function for highly viscous drops. Depending on the parameter values, steady motion of the drop may not exist. In particular, the critical Bond number, above which the droplet experiences unrestricted elongation and the possible onset of breakup, is found to be smallest at moderate inclination angles and to be a nonmonotonic function of the viscosity ratio. The underlying mechanism of breakup for this problem is described as a hydrodynamic "pinning" effect, through which the drop tail cannot move away from the wall as fast as the bulk or nose of the drop, which gives rise to the unsteady behavior. Experimental observations of drop shapes, velocity, and critical conditions for breakup show good agreement with the simulations.