A Numerical Investigation on the Effect of Contact-Line Mobility on Sessile Drop Oscillation Dynamics

In the present study, the effect of contact-line mobility on the natural oscillations of sessile drops is investigated through interface-resolved simulations. A hyperbolic tangent function is employed to model the variation of contact angle (CA) with contact-line (CL) velocity. The range of CL mobility considered is sufficient to recover the free contact-line (FCL) and pinned contact-line (PCL) limits. For finite CL mobility between these asymptotic limits, the CL can move, and the CA varies with CL velocity. The equilibrium CA and CL mobility are systematically varied to investigate their effects on oscillation frequency, energy dissipation, and oscillation decay rate. The results show that the oscillation frequency increases monotonically with CL mobility, transitioning from the FCL to the PCL limit. The CL dissipation is zero at the FCL and PCL limits and exhibits a non-monotonic dependence on CL mobility. The oscillation decay rate generally decreases with increasing equilibrium CA. However, due to the non-monotonic variation of CL dissipation with CL mobility, the decay rate initially increases and then decreases as CL mobility increases.