Cost-Effective Characterization of Surface Tension in Surfactant-Laden Solutions via Splash Height and Drop-Based Methods

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Abstract

Surface tension governs key interfacial phenomena such as droplet formation, spreading, and splash dynamics, yet standard measurement techniques are often limited by costly instrumentation and restrictive setups. This study explores two simplified, low-cost diagnostic methods, the penny drop method and a newly developed splash-height method, for their ability to track surface tension (σ) as a function of surfactant concentrations (c). In the penny drop method, surfactant-laden drops are added to a coin’s surface until the liquid dome collapses, and the maximum supported volume is related to surface tension. In the splash height method, single droplets are released into surfactant-laden solutions, and the rebound height (cumulative jet) is quantified using high-speed imaging. Both methods are benchmarked against the established drop-weight method, based on Tate’s law. The drop weight method reproduces the expected σ(c) profile with an apparent critical micelle concentration (CMC). The penny-drop method and splash height method each show monotonic trends that correlate with surface tension over distinct concentration ranges. A Monte Carlo framework converts drops per 20 mL of water into mmol·L⁻¹ concentrations and propagates uncertainty in surface tension. Although less precise than standard tensiometers, the penny drop and splash height methods reliably reflect concentration-dependent changes in surface tension and interfacial elasticity. These results demonstrate that accessible optical and volumetric measurements can yield quantitative insight into surfactant-laden interfaces, enabling surface tension diagnostics to be extended to low-resource contexts.

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