Elastic deformation of soft membrane with finite thickness induced by a sessile liquid droplet.

In this paper, the role of vertical component of surface tension of a droplet on the elastic deformation of a finite-thickness flexible membrane was theoretically analyzed using Hankel transformation. The vertical displacement at the surface was derived and can be reduced to Lester's or Rusanov's solutions when the thickness is infinite. Moreover, some simulations of the effect of a liquid droplet on a membrane with a finite thickness were made. The numerical results showed that there exists a saturated membrane thickness of the order of millimeter, when the thickness of a membrane is larger than such a value, the membrane can be regarded as a half-infinite body. Further numerical calculations for soft membrane whose thickness is far below the saturated thickness were made. By comparison between the maximum vertical displacement of an ultrathin soft membrane and a half-infinite body, we found that Lester's or Rusanov's solutions for a half-infinite body cannot correctly describe such cases. In other words, the thickness of a soft membrane has great effect on the surface deformation of the ultrathin membrane induced by a liquid droplet.