Towards operating windows for pendant drop methods: tensiometry and rheometry of elastic interfaces

Abstract We numerically evaluate the performance of two pendant drop techniques — Capillary Pressure Tensiometry (CPT) and Stress-Fitting Elastometry (SFE) — based on their ability to calculate the interfacial stress and dilatational rheological properties of complex interfaces. Although both methods incorporate simultaneous shape and pressure measurements, CPT assumes a spherical cap shape with isotropic deformations, allowing the interface to be fully characterized by a single scalar value for the surface stress. On the contrary, SFE accounts for mechanically resistant interfaces that exhibit non-uniform tensorial strain and stress fields. To compare these methods, we numerically generate drops with perfectly elastic (non-dissipative) interfaces and subject them to step-strain compressions of varying magnitudes. The calculations span a range of dimensionless parameters representing realistic drop volumes, geometries, and physical properties. We show that the local strain and/or stress vary along the surface, depending on the relative magnitude of the shear versus dilatational moduli. We analyze the strained interfaces using CPT and SFE, quantitatively evaluating their ability to predict the interfacial strains, stresses, and dilatational moduli. We then identify the configurations and analysis methods that yield the most accurate results. Finally, we assess the robustness of these methods by introducing random Gaussian noise to the interface profiles, with a magnitude comparable to experimental errors from image acquisition and processing. The performance of both methods is compared under both idealized and experimentally realistic (noisy) conditions.