Marangoni flow and surfactant transport in evaporating sessile droplets: A lattice Boltzmann study

The circulatory Marangoni flow can alter the contact line deposition in evaporating colloidal droplets with pinned contact line. Marangoni flow can be induced by surfactants or thermal effects. Although both cases have been exclusively investigated, the combined effect of surfactant-induced and thermal Marangoni flows is still unknown. The lattice Boltzmann method is utilized to simulate droplet evaporation and corresponding Marangoni flow. Five equations for hydrodynamics, interface capturing, vapor concentration, temperature field, and surfactant transport are intrinsically coupled with each other. They are simultaneously solved in the lattice Boltzmann framework. A geometrical method is proposed to pin the contact line at the triple point. First, evaporation-induced and thermal Marangoni flows are successfully captured. By incorporating surfactant-induced effects, interesting flow patterns are observed. Considering the combined effect of surfactant and temperature gradient, maximum surfactant concentration and maximum temperature (local minima for surface tension) are found at the top and the edge of the droplet, respectively. The maximum surface tension is consequently located between them, and double-circulation flow is observed. If the thermal effect is eliminated, surfactant local concentrations intermittently converge to steady values so that the edge concentration becomes higher than the apex concentration. Until reaching the steady state, there are two patterns that the flow alternates between: one in the direction of the thermal Marangoni flow and the other in the opposite direction.