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 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 θ_r > 140°, the normalized F_d/πR is equivalent to the Young–Dupre work of adhesion γ(1 + cos θ_r).