Relating contact angles, drop size and Line Energy

The relation between drop radius, $r$, the force to slide it, and the advancing and receding contact angles, \textit{$\theta $}$_{A}$ and \textit{$\theta $}$_{R}$, has been studied. To keep the line energy (energy per 2$\pi r)$ independent of $r$, the modified Young equation predicts that \textit{$\theta $}$_{A}$ and \textit{$\theta $}$_{R}$ change considerably with $r$. As shown by many investigators, \textit{$\theta $}$_{A}$ and \textit{$\theta $}$_{R}$ change negligibly, if at all, with $r$. We show why the modified Young equation is correct and still \textit{$\theta $}$_{A}$ and \textit{$\theta $}$_{R}$ should hardly change with $r$. Our results suggest that the Laplace pressure is a significant parameter in inducing the line energy.