Force Balance at Contact Lines of Soft Substrates

We use coarse-grained molecular dynamics simulations to show that the force balance analysis at the triple-phase contact line formed at an elastic substrate must include a quartet of forces: three surface tensions (surface free energies) and an elastic force per unit length. In the case of the contact line formed by a droplet on an elastic substrate, the elastic force is due to substrate deformation generated by formation of the wetting ridge. The magnitude of this force f_el is proportional to the product of the ridge height h and substrate shear modulus G. Similar elastic line force should be included in the force analysis at the triple-phase contact line of a solid particle in contact with an elastic substrate. For this contact problem elastic force obtained from contact angles and surface tensions is a sum of the elastic forces acting from the side of a solid particle and an elastic substrate. By considering only three line forces acting at the triple-phase contact line, one implicitly accounts the bulk stress contribution as a part of resultant surface stresses. This “contamination” of surface properties by a bulk contribution could lead to unphysically large values of the surface stresses in soft materials.