Partial wetting of the soft elastic graded substrate due to elastocapillary deformation

Surface tension plays a central role in the mechanical behavior of soft materials such as gels. Elastocapillary deformation of elastic graded substrates is ubiquitous in soft materials. In this work, the effect of a partially wetting sessile liquid droplet on the elastocapillary deformation of a soft elastic graded substrate is studied. The modulus is assumed to have an exponential form along the thickness direction. By applying the Fourier transformation, a mixed boundary-value problem is reduced into a dual integral equation. The numerical results show that the surface displacement is strongly affected by the inhomogeneity of the material. The study of the wetting properties of gel substrates is essential for both understanding the wetting phenomena of gels and developing gels for applications as soft actuators and sensors that can be used in wearable electronics and soft robotics.