Effects of surface elasticity and surface viscoelasticity on liquid inclusions in solid materials

The effects of surface elasticity and surface viscoelasticity as well as surface tension on the deformation of solids with liquid inclusions are investigated using a finite element (FE) method. Both surface tension and surface elasticity stiffen the solids with liquid inclusions. The surface tension in elastic capillary number is replaced with surface Young's modulus to define the second elastic capillary number. The aspect ratio of the included liquids is used to indicate the stiffening effect for both numbers. A smaller aspect ratio corresponds to a larger stiffening effect. In a typical FE analysis, when either number is 1 and the applied strain is 4%, the aspect ratio decreases by 7.4% due to surface tension and 2.6% due to surface elasticity. Compared to surface tension, surface elasticity has a similar but smaller influence on the deformation of solids with liquid inclusions. Extensive FE calculations are performed to establish the fitting formula for the aspect ratio as a function of elastic capillary number, the second elastic capillary number, and the applied strain. Surface viscoelasticity is modelled in the FE method by converting surface viscoelastic properties into the viscoelastic properties of the equivalent shell. The time-dependent aspect ratio due to surface viscoelasticity is presented and FE results show the same trend as those calculated from the approximated theory. The internal pressure of the included liquid is obtained from FE analysis and is compared with the theoretical estimation employing the Young-Laplace equation.