Surfactant-Mediated Modulation of Thin Droplets Spreading on a Soft Substrate

The spreading dynamics of an insoluble surfactant-laden droplet on a soft viscoelastic substrate have important implications in biological fluid systems, coating technologies, and stretchable electronics. In this study, we employ lubrication theory to develop a reduced-order model that captures the spreading behavior of such droplets over soft substrates. Coupled nonlinear spatiotemporal evolution equations are derived to track both the liquid-air and liquid-solid interfaces. A parametric investigation is carried out to examine the influence of the Marangoni number and Péclet number on droplet spreading. For perfectly wetting droplets, the presence of surfactants slows down spreading compared to clean droplets, as opposing Marangoni stresses resist the motion. Increasing the Péclet number reduces both the rate and extent of spreading due to the dominance of advective transport over diffusion. In the case of partial wetting, higher Marangoni numbers result in lowering the equilibrium contact angle and thereby enhance the extent and rate of spreading. The wetting ridge height is found to decrease with increasing Marangoni number, leading to reduced viscoelastic braking and faster spreading on soft substrates. Overall, for partially wetting droplets, the primary mechanism driving enhanced spreading is the reduction in viscoelastic braking due to lowered interfacial tension, which outweighs the counteracting Marangoni stresses arising from interfacial tension gradients. The surfactant enhanced spreading in the case of partial wetting over soft substrate is in line with recent experimental observations.