Droplet detachment force and its relation to Young-Dupre adhesion

Area of Science:

• Fluid dynamics
• Surface science
• Materials science

Background:

• Droplet adhesion is governed by surface tension (γ).
• Understanding the detachment force (Fd) is crucial for technologies like inkjet printing and paint formulation.
• Previous studies have explored droplet detachment under various conditions.

Purpose of the Study:

• To numerically predict the vertical detachment force (Fd) of droplets on diverse surfaces.
• To derive an analytic solution for droplet detachment on highly hydrophobic surfaces.
• To validate numerical results against experimental data and theoretical models.

Main Methods:

• Numerical solution of the Young-Laplace equation.
• Simulation of droplet detachment under surface and body forces.
• Analysis of results across a range of droplet radii (R) and surface types (hydrophobic, lubricated, micro-/nano-structured).

Main Results:

• Numerical predictions of Fd align with previously reported experimental and theoretical results.
• Fd values ranged from nano- to milli-newtons for droplet radii from microns to millimeters.
• An analytic solution for Fd on highly hydrophobic surfaces was derived.

Conclusions:

• The derived analytic solution for highly hydrophobic surfaces shows that for receding contact angles (θr) > 140°, normalized Fd/πR equals the Young-Dupre work of adhesion γ(1 + cos θr).
• Numerical methods provide accurate predictions of droplet detachment forces across various experimental conditions.
• This work offers insights into droplet-surface interactions relevant to technological applications.