Hysteresis of Contact Angle of Sessile Droplets on Deformable Substrates: Influence of Disjoining Pressure

Liquid droplet placed on a deformable / soft substrate causes the substrate to deform. Combined action of capillary pressure and surface forces, which act in the vicinity of the apparent three-phase contact line and substrate's elasticity determine both the liquid shape and the substrate deformation. A theory of contact angle hysteresis of sessile liquid droplets on deformable/soft substrate is developed in terms of disjoining pressure isotherm, pi(h), which accounts for the action of surface forces in the vicinity of the contact line. Minimum of excess free energy of the droplet on deformable substrate results in two interconnected equations for droplet and deformed substrate shapes in terms of disjoining pressure isotherm. A simplified s-shaped disjoining pressure isotherm, which allows direct calculations of static advancing/receding contact angles on deformable substrates, is adopted. Elasticity of the substrate is assumed to obey a simple Winkler's model for elastic surfaces. The obtained results are in agreement with the contact angle hysteresis theory developed earlier for non-deformable substrates. Calculated values of both advancing and receding contact angles for droplets on deformable substrate depend on droplet volume (which has a direct experimental confirmation). Advancing and receding contact angles of droplets on deformable substrates are lower as compared with those on a non-deformable substrate. The results of the derived model on hysteresis of contact angle on deformable substrates qualitatively agree with known experimental observations.