Line energy, line tension and drop size

The relation between drop radius, r, the force to move the three phase contact line and the advancing and receding contact angles θ_A and θ_R is studied. To keep the line energy (energy per 2πr, also named line tension) independent of r, the modified Young equation predicts that the advancing and receding contact angles, θ_A and θ_R, change considerably with r. As shown by many investigators, θ_A and θ_R change negligibly, if at all, with r. We quantify recent evidences showing that the line energy is a function of the Laplace pressure and show that this way the modified Young equation is correct and still θ_A and θ_R should hardly change with r. According to our model, the small surface deformation associated with the unsatisfied normal component of the Young equation results in higher intermolecular interactions at the three phase contact line which corresponds to a higher retention force. This time increasing effect is supported by recent experiments.