Droplet on an elastic substrate: Finite Element Method coupled with lubrication approximation

Abstract

Sessile liquid droplets deposited on soft substrates may cause substrate deformation. The substrate elasticity affects the apparent contact angle and the spreading dynamics of the sessile drop. In the present work, a model for description of a droplet on an elastic substrate is developed using the disjoining pressure concept. A Finite Element Method for the elasticity problem in a substrate is coupled with lubrication approximation for the modelling of droplet spreading. The disjoining pressure model allows an independent definition of contact angle and the thickness of the adsorbed layer. Simulations are performed to quantify the influence of mechanical properties, the substrate size and the parameters of the disjoining pressure model on the substrate deformation and apparent contact angle. It is shown that the dimensionless substrate deformation peak height scales with the dimensionless parameter σsinθ/(Ea), and the solid angle appearing in the deformed substrate near the apparent cotact line scales with σ/(Ea), where σ denotes the surface tension, E is the Young modulus, θ is the apparent contact angle and a is a width of the region in which the disjoining pressure plays an important role.