Droplet detachment force and its relation to Young-Dupre adhesion

Droplets adhere to surfaces due to their surface tension gamma 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 theta(r) > 140 degrees, the normalized F-d/pi R is equivalent to the Young-Dupre work of adhesion gamma(1 + cos theta(r)).