Coalescence of polymeric sessile drops on a partially wettable substrate

Abstract

Coalescence of sessile polymeric fluid drops on a partially wettable substrate exhibits a transition from inertial to viscoelastic regime at concentration ratio $c/c^* \sim 1$. Our findings unveil that the temporal evolution of the growing bridge height follows a power-law behaviour $t^b$, such that the coefficient $b$ continuously decreases from 2/3 in the inertial regime ($c/c^*<1$) to an asymptotic value of 1/2 in the visco-elastic regime ($c/c^*>1$). To account for fluid elasticity and characteristic time-scale in the viscoelastic regime, a modified thin film equation under lubrication approximation has been proposed using the linear Phan-Thien- Tanner constitutive equation. The temporal evolution of the droplet has been evaluated by solving the modified one-dimensional thin-film equation using a marching explicit scheme. The initial droplet shapes are obtained by re-sorting to energy minimization. A good agreement between numerical and experimental results is obtained.