Surfactant-assisted spreading of a liquid drop on a smooth solid surface.

Axisymmetric spreading of a liquid drop covered with an insoluble surfactant monolayer on a smooth solid substrate is numerically investigated. As the drop spreads, the adsorbed surfactant molecules are constantly redistributed along the air-liquid interface by convection and diffusion, leading to nonuniformities in surface tension along the interface. The resulting Marangoni stresses affect the spreading rate by altering the surface flow and the drop shape. In addition, surfactant accumulation in the vicinity of the moving contact line affects the spreading rate by altering the balance of line forces. Two different models for the constitutive relation at the moving contact line are used, in conjunction with a surface equation of state based on the Frumkin adsorption framework, to probe the surfactant influence. The coupled evolution equations for the drop shape and monolayer concentration profile are integrated using a pseudospectral method to determine the rate of surfactant-assisted spreading over a wide range of the dimensionless parameters governing the spreading process. The insoluble monolayer enhances spreading through two mechanisms; a reduction in the equilibrium contact angle, and an increase in the magnitude of the radial pressure gradient within the drop due to the formation of positive surface curvature near the moving contact line. Both mechanisms are driven by the accumulation of surfactant at the contact line due to surface convection. Although the Marangoni stresses induced at the air-liquid interface reduce the rate of spreading during the initial stages of spreading, their retarding effect is overwhelmed by the favorable effects of the aforementioned mechanisms to lead to an overall enhancement in the rate of spreading in most cases. The spreading rate is found to be higher for bulkier surfactants with stronger repulsive interactions. With the exception of monolayers with strong cohesive interactions which tend to retard the spreading process, the overall effect of an insoluble monolayer is to increase the rate of drop spreading. Simulation results for small Bond numbers indicate the existence of a power-law region for the time-dependence of the basal radius of the drop, consistent with experimental measurements.