Droplet detachment force and its relation to Young-Dupre adhesion

Abstract

Droplets adhere to surfaces due to their surface tension γ and understanding the vertical force Fd required to detach the droplet is key to many technologies (e.g., inkjet printing, optimal paint formulations). Here, we predicted Fd 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 |Fd| 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 Fd on highly hydrophobic surfaces and further show that for receding contact angle θr > 140°, the normalized Fd/πR is equivalent to the Young-Dupre work of adhesion γ(1 + cos θr).