Droplet settling on soft layers

We study the gravitational settling of a droplet in air onto a soft substrate using a three-phase lubrication model. We consider for this soft substrate either a thin viscous film, a thin elastic compressible material, or an elastic sheet supported by a thin viscous film. We combine scaling analysis, analytical methods, and numerical simulations to describe the resulting dynamics. In particular, when the response of the soft layer is linear, we show that the air layer takes longer to drain as compared to the case of a droplet settling onto a rigid substrate. Our results provide new insight into the coupled interactions between droplets and solids coated by a thin film of a soft material.