Elastocapillary morphing of self-encapsulated droplets floating at the oil-air interface

• A quasi-convex variational membrane model for self-encapsulated floating droplets. • A robust numerical scheme computes equilibrium shapes with tension relaxation. • The model fits contact-angle experiments and predicts evaporation-driven morphing. • Phase diagrams reveal an elasto-capillary-gravity crossover between crumpling and wrinkling. Self-encapsulated droplets floating at an oil–air interface undergo striking shape changes during evaporation, including flattening and localized loss of membrane tension leading to crumpling and wrinkling. Here we combine experiments, modeling and simulations to obtain predictive morphological maps. We perform contact-angle and evaporation experiments on water droplets coated by a hydrophobin protein film and floating in a fluorinated oil, providing reference profiles and volume-loss sequences for quantitative validation. We develop an axisymmetric mechanics framework in which equilibria follow from minimization of a total free energy combining surface energies, membrane strain energy and gravitational potential, subject to volume and contact-line constraints. A quasi-convex tension-relaxation rule accounts for compression-free states and enables coexistence of taut, wrinkled (one principal tension vanishes) and crumpled (both vanish) membrane domains. A finite element algorithm computes quasi-static morphing under volume reduction; key parameters are identified by fitting the reference contact-angle profile and then used without further tuning. The model reproduces the experimentally observed shape evolution and resolves the associated stress redistribution. Systematic parameter scans yield morphological phase diagrams governed by the Bond number, the oil–droplet surface-tension ratio and the density ratio. For buoyant droplets, crumpling relocates between exposed and submerged caps as parameters vary; for heavy droplets, a crossover to circumferential wrinkling along the immersed sidewall emerges. Wall-meniscus variations shift phase boundaries and can suppress bottom crumpling, consistent with wall-affected experiments.