Thermodynamic behavior of a stain

Abstract

A thermodynamic model is developed to explain the formation of a solid ridge of polystyrene spheres on the periphery of a sessile drop. The drop initially contains a uniform solution of water and polystyrene spheres. Evaporation creates a crater. The spheres leave the center and a ridge, whose width increases with increasing initial concentration, forms. For each equilibrium state, three contributions to the Gibbs free energy mainly control this process. One is related with the mechanical work of formation, the other with the spreading of the diameter and the last with the variation of the number of particles in the ridge. The model predicts, in agreement with the experiment, the initial and final value of the contact angles and the exponential diminution of concentration of particles with the ratio of the diameters of the ridge.