Moderately low-Bond-number axisymmetric drop shape analysis and tensiometry for sessile drops
摘要
The shape of a liquid drop is governed by both the surface tension of the liquid and the gravity which introduces the hydrostatic pressure gradient inside the liquid. The two factors (along with a characteristic size of the drop) can be combined into one dimensionless parameter, known as the Bond number. The accuracy of asymptotic solutions of the Young–Laplace equation for relatively small drops drastically decreases with increasing the Bond number. To extend their range of applicability, an asymptotic modeling approach is applied leading to simple closed-form approximations for the drop shape profile in a parametric form with the meridian angle used as a parameter. A quantitative comparison with the numerical solutions available in the literature is performed. The developed mathematical modeling framework allows to unify and simplify the consideration of different methods for determination of the surface tension and estimating the contact angle from the axisymmetric drop-shape analysis.
Graphical Abstract