Vapour-film dynamics of Bird–Carreau Leidenfrost drops and operator-learning trajectory prediction

This work presents the first systematic computational study of shear-thinning Leidenfrost droplets governed by the Bird–Carreau model, using interface-resolved Volume-of-Fluid simulations with the Hardt–Wondra phase-change model in OpenFOAM. A five-dimensional parametric study spans the Weber ( 𝑊 ⁢ 𝑒 ), Jakob ( 𝐽 ⁢ 𝑎 ), Ohnesorge ( 𝑂 ⁢ ℎ ) and Carreau ( 𝐶 ⁢ 𝑟 ) numbers and the power-law index ( 𝑛 ), tracking the vapour-film thickness ( ℎ 𝑐 ), vaporisation rate ( ̇ 𝑞 𝑚 ) and vapour-neck radius ( 𝑟 𝑛 ). The model produces a heterogeneous viscosity field — highest in the droplet bulk, lowest in the high-shear neck — that modifies capillary oscillations relative to a Newtonian fluid at equal 𝑂 ⁢ ℎ . Elevated 𝐽 ⁢ 𝑎 intensifies evaporation and sustains thicker vapour cushions; increasing 𝑊 ⁢ 𝑒 amplifies film compression and post-impact amplitude; rising 𝑂 ⁢ ℎ damps the response toward aperiodic levitation; higher 𝐶 ⁢ 𝑟 lowers neck viscosity and amplifies oscillations analogously to decreasing 𝑂 ⁢ ℎ ; and lower 𝑛 yields the most vigorous oscillations and deepest basal dimples. A Spearman rank correlation analysis confirms a distinct dominant influence for each parameter: 𝑊 ⁢ 𝑒 on 𝑟 𝑛 , 𝐽 ⁢ 𝑎 on ̇ 𝑞 𝑚 and 𝐶 ⁢ 𝑟 on ℎ 𝑐 . A Deep Operator Network trained on 397 cases predicts trajectories across the { 𝑊 ⁢ 𝑒 , 𝑂 ⁢ ℎ , 𝐽 ⁢ 𝑎 , 𝐶 ⁢ 𝑟 } space, achieving 𝑅 2 = 0 . 9 8 0 , 0.965 and 0.867 for ̇ 𝑞 𝑚 , ℎ 𝑐 and 𝑟 𝑛 on a held-out test set. Because the trunk network parameterises a smooth basis over normalised time, the operator can be queried at any temporal resolution without retraining. Inference cost falls from 𝒪 ⁡ ( 1 ⁢ 0 2 ) CPU-hours to milliseconds, making parametric exploration and real-time control of Leidenfrost thermal-management systems tractable.