Wettability of semispherical droplets on layered elastic gradient soft substrates

Research on the wettability of soft matter is one of the most urgently needed studies in the frontier domains, of which the wetting phenomenon of droplets on soft substrates is a hot subject. Scholars have done considerable studies on the wetting phenomenon of single-layer structure, but it is noted that the wetting phenomenon of stratified structure is ubiquitous in nature, such as oil exploitation from geological structural layers and shale gas recovery from shale formations. Therefore, the wettability of droplets on layered elastic gradient soft substrate is studied in this paper. Firstly, considering capillary force, elastic force and surface tension, the constitutive equation of the substrate in the vector function system is derived by using the vector function system in cylindrical coordinates, and the transfer relation of layered structure is obtained. Further, the integral expressions of displacement and stress of double Bessel function are given. Secondly, the numerical results of displacement and stress are obtained by using the numerical formula of double Bessel function integral. The results show that the deformation of the substrate weakens with the increase of the elastic modulus, also the displacement and stress change dramatically near the contact line, while the variation is flat when the contact radius is far away from the droplet radius.