Sessile Droplet Profiles and Apparent Contact Angles Considering Gravity and Contact-Line Energy

The equilibrium shape of a finite-volume axisymmetric sessile droplet is governed by surface tension, gravity and the energy associated with the three-phase contact line. A variational model is developed to predict the profiles and apparent contact angles of droplets on horizontal, macroscopically flat hydrophilic and hydrophobic surfaces. In the variational model, the free-surface variation yields the Bashforth–Adams equation for the profile, and the contact-line endpoint variation gives the transversality condition for the apparent contact angle. A numerical algorithm is developed to determine the equilibrium profiles and apparent contact angles. Experiments are conducted to calibrate and validate the model. The effective contact-line energy parameters, q, of water on the hydrophilic, SiO2, surface and the hydrophobic polytetrafluoroethylene, PTFE, surface are calibrated using measurements from droplets with volumes ranging from 10 to 100 μL. The calibrated, q, values are then used to predict the profiles and apparent contact angles of water droplets on the hydrophilic, SiO2, and hydrophobic, PTFE, surfaces with volumes of 25, 35, 55, and 75 μL, which are excluded from the calibration. Across all validation cases, the mean relative errors in the predicted apparent contact angles are 0.36% for SiO2 and 0.49% for PTFE, with an overall mean relative error of 0.43%. The predicted droplet profiles agree well with the experimentally extracted profiles.