Droplet detachment force and its relation to Young-Dupre adhesion

Droplets adhere to surfaces due to their surface tension γ and understanding the vertical force F d required to detach the droplet is key to many technologies ( e.g. , inkjet printing, optimal paint formulations). Here, we predicted F d on different surfaces by numerically solving the Young-Laplace equation. Our numerical results are consistent with previously reported results for a wide range of experimental conditions: droplets subjected to surface vs. body forces with | F d | ranging from nano- to milli-newtons, droplet radii R ranging from tens of microns to several millimetres, and for various surfaces (micro-/nano-structured superhydrophobic vs. lubricated surfaces). Finally, we derive an analytic solution for F d on highly hydrophobic surfaces and further show that for receding contact angle r > 140°, the normalized F d /π R is equivalent to the Young-Dupre work of adhesion γ (1 + cos r ). We show that for hydrophobic surfaces, the normalized detachment force F d /π R is equivalent to the Young-Dupre work of adhesion γ (cos r + 1).