Water balloons as macroscopic droplets: Effective surface tension and impact dynamics

Abstract

Water balloons provide a simple model system for studying the dynamics of membrane-confined liquids, yet their quantitative relationship to classical liquid droplets remains unclear. In this work, we experimentally investigate the mechanical properties and impact dynamics of water balloons and compare them with those of classical liquid droplets impacting superhydrophobic surfaces. Inflation–deflation experiments reveal a broad stretch-independent regime (1.5<λ<2.7) in which the membrane tension remains nearly constant at T≈122.7 N/m despite the nonlinear hyperelastic response of the latex membrane. Independent measurements of the equilibrium shape of water-filled balloons demonstrate that the pressure–curvature relation obeys a generalized Young–Laplace equation within this regime, validating the analogy between the membrane tension and the liquid surface tension. The membrane tension is then defined as the effective surface tension of the water balloon. Based on this result, an effective Weber number is introduced for water balloons. Impact experiments show that water balloons and droplets exhibit similar impact-induced wave, spreading, retraction, and rebound dynamics over a wide range of Weber numbers. Using the effective Weber number, the maximum spreading factor and normalized contact time of the two systems show similar trends over the entire Weber number range investigated and exhibit closely comparable capillary–inertial scaling behavior within their respective scaling regimes. The maximum spreading factors follow power-law dependences in the high Weber number regime with exponents of 0.26 for water droplets and 0.22 for water balloons, both close to the classical inertial–capillary scaling βmax∝We1/4, while the normalized contact times exhibit a common scaling in the low Weber number regime. These results demonstrate that water balloons can behave as macroscopic droplets governed by a surface-tension-like restoring force when the global membrane deformation remains within the stretch-independent regime, although local non-equibiaxial deformation may fall outside this regime. The present work establishes a quantitative connection between membrane-confined liquids and classical capillary systems, providing a unified description of impact dynamics governed by either the membrane tension or the molecular surface tension.