Accuracy of Axisymmetric Drop Shape Analysis in Determining Surface and Interfacial Tensions

Axisymmetric drop shape analysis (ADSA) has been used in a broad range of applications for determining surface tensions of air-liquid surfaces and interfacial tensions of liquid-liquid interfaces. However, it is well-known that the accuracy of ADSA deteriorates upon the reduction of drop volume. Here, we systematically compared different criteria and parameters in evaluating the accuracy of ADSA upon reducing drop volume. By scrutinizing the dependence of ADSA accuracy on various parameters, including the capillary constant (c), the Bond number (Bo), the Worthington number (Wo), and the shape parameter (P_s), we concluded that the classical Bond number failed to predict the accuracy of drop shape analysis at very small drop volumes. Thus, we proposed a replacement of the classical Bond number, called the Neumann number Ne ≡ (ΔρgR₀H)/γ. The design rationale of this new dimensionless number lies in the use of the geometric mean of the radius of curvature at the drop apex (R₀) and the drop height (H) as the new characteristic length (L) to represent the drop size, that is, L = (R₀H)^1/2. It is found that the Neumann number is capable of evaluating the accuracy of ADSA. Moreover, we have demonstrated the usefulness of the local Neumann number, Ne_z ≡ (ΔρgR₀/γ)z, in evaluating the contribution of the local drop profile to the accuracy of ADSA.