Effect of film viscoelasticity on the finite deformation of a spherical bubble

According to the strain energy density function for finite deformation of viscoelastic material, the relaxation function of the Maxwell mode, and the deformation gradient tensor of the bubble, a stress equation for finite deformation of a protein bubble is derived. By using the above stress equation and the dynamics equation of the bubble, an equation describing the relation between the relative deformation rate of the inner radius and time is developed for finite deformation. Based on this equation and the nonlinear properties of finite deformation, the effect of the pressure difference, the thickness and viscosity of the film, the initial size of the bubble, and the initial gas pressure in the bubble on the radial deformation of the protein bubble are analyzed by numerical simulation. The results show that during the contraction of the bubble, an oscillation with degressive amplitude is associated. The variation tendencies of vibration frequency and amplitude and the balance size of the bubble are closely related to the applied load, the viscoelasticity of the film, and the initial bubble size. Increasing the thickness and viscosity of protein film or decreasing the initial bubble size can counteract the vibration of the bubble wall and thus, can enhance the load-bearing capacity of the protein bubble.