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 0(A) and 0(R) is studied. To keep the line energy (energy per 2 pi r, also named line tension) independent of r, the modified Young equation predicts that the advancing and receding contact angles, 0(A) and 0(R), change considerably with r. As shown by many investigators. 0(A) and 0(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 0(A) and 0(R) should hardly pressure 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. (C) 2008 Elsevier B.V. All rights reserved.