The effects of surface tension on spherical oscillatory indentation of viscoelastic materials

Abstract The oscillatory indentation has become an attractive approach to characterizing the viscoelastic properties of soft biological solids. However, the influences of surface tension on oscillatory responses are ignored, which might lead to an inaccurate measurement of mechanical properties. In this work, the influences of surface tension on spherical oscillatory indentation for viscoelastic materials are investigated through the finite element method. The viscoelasticity of solids is characterized by the standard linear solid model and a sinusoidal displacement is applied as the excitation signal. During an entire cycle at the steady state of oscillation, both the average value of contact radius and the dissipated energy decrease due to the presence of surface tension. For the oscillatory responses at various frequencies, the existence of surface tension results in an increase of average force but a decrease of phase angle. The force amplitude at low frequencies becomes higher when surface tension is considered. For the evaluation of the complex modulus, neglecting the surface tension would lead to a significant overestimation of storage modulus at low frequencies and an obvious underestimation of loss modulus when the normalized frequency approaches 1. Our results provide a comprehensive understanding of the effects of surface tension on the mechanical responses of oscillation and the determination of viscoelastic properties through oscillatory indentation.