Dynamics and emission of surfactant-laden sessile or pendant drops from an oscillating solid surface

Removal of sessile/pendant drops by causing the supporting solid to undergo forced oscillations is important in applications, e.g. self-cleaning coatings, heat exchangers, biomedical diagnostics, and inkjet printing. In such systems, the drops often contain surface-active species—as contaminants or surfactants—that can alter significantly their oscillatory response. Wilkes and Basaran and later others studied the forced oscillations and breakup of supported drops, but here we investigate the effects of insoluble surfactants on the dynamics. Surfactant adsorption at fluid interfaces lowers surface tension and can induce surface tension gradients (Marangoni stresses) due to spatial variations of surfactant concentration during oscillation. While both effects are expected to influence drop response, their combined and competing roles remain poorly understood but are resolved in this work by using a finite element-based algorithm. The Navier–Stokes equations and the convection–diffusion equation are solved in a non-inertial frame moving with the vibrating substrate to determine fluid motion and surfactant transport. We examine how surface tension lowering and Marangoni stresses together modify the oscillatory dynamics and the critical forcing amplitude required for drop emission.