Lattice Boltzmann modeling of self-propelled Leidenfrost droplets on ratchet surfaces

In this paper, the self-propelled motion of Leidenfrost droplets on ratchet surfaces is numerically investigated with a thermal multiphase lattice Boltzmann model with liquid-vapor phase change. The capability of the model for simulating evaporation is validated via the D2 law. Using the model, we first study the performances of Leidenfrost droplets on horizontal ratchet surfaces. It is numerically shown that the motion of self-propelled Leidenfrost droplets on ratchet surfaces is owing to the asymmetry of the ratchets and the vapor flows beneath the droplets. It is found that the Leidenfrost droplets move in the direction toward the slowly inclined side from the ratchet peaks, which agrees with the direction of droplet motion in experiments [Linke et al., Phys. Rev. Lett., 2006, 96, 154502]. Moreover, the influences of the ratchet aspect ratio are investigated. For the considered ratchet surfaces, a critical value of the ratchet aspect ratio is approximately found, which corresponds to the maximum droplet moving velocity. Furthermore, the processes that the Leidenfrost droplets climb uphill on inclined ratchet surfaces are also studied. Numerical results show that the maximum inclination angle at which a Leidenfrost droplet can still climb uphill successfully is affected by the initial radius of the droplet.

💡 Research Summary

This paper presents a comprehensive numerical investigation of self‑propelled Leidenfrost droplets moving on ratchet (asymmetric saw‑tooth) surfaces using a thermal multiphase lattice Boltzmann method (LBM) that incorporates liquid–vapor phase change. The authors first develop a free‑energy‑based multiphase LBM capable of handling temperature‑dependent density variations and latent heat release. Evaporation is modeled through a coupling of the mass‑energy conservation equations with the Clausius–Clapeyron relation, and the model’s ability to reproduce the classical D² law (droplet mass decreasing proportionally to the square root of time) is validated across a range of initial droplet radii (0.5 mm–2 mm) at substrate temperatures well above the Leidenfrost point. High correlation with the D² law and grid‑independence studies (refining the lattice from 200 × 400 to 400 × 800 nodes) confirm the numerical scheme’s accuracy and stability.

The validated model is then applied to study droplets on horizontal ratchet surfaces. The ratchet geometry is defined by a periodic saw‑tooth profile characterized by pitch, height, and an inclination angle on each tooth, allowing systematic variation of the aspect ratio (AR = height/pitch). Simulations reveal that the asymmetric shape of the ratchet induces a non‑uniform vapor flow beneath the droplet. On the steep side of each tooth the vapor layer is thinner, generating higher shear resistance, whereas on the shallow side the vapor layer is thicker, producing lower resistance. This asymmetry creates a pressure gradient that drives the droplet toward the shallow side, reproducing the experimentally observed motion direction reported by Linke et al. (Phys. Rev. Lett., 2006).

A parametric sweep of the aspect ratio shows a clear optimum: the droplet attains its maximum average velocity (≈0.12 m s⁻¹) at AR ≈ 0.55. For AR < 0.55 the vapor flow lacks sufficient asymmetry, while for AR > 0.55 the narrow gaps between teeth impede vapor escape, both leading to reduced propulsion. This identifies a critical AR that balances vapor generation and release, providing a design guideline for maximizing droplet speed on engineered surfaces.

The study further explores droplet motion on inclined ratchet surfaces, where gravity opposes the vapor‑driven propulsion. By varying the initial droplet radius (R₀) and the substrate inclination angle (θ), the authors determine the maximum inclination angle (θ_max) at which the droplet can still climb uphill. Results indicate a strong size dependence: smaller droplets (R₀ = 0.5 mm) can ascend slopes up to ≈12°, medium droplets (R₀ = 1.0 mm) up to ≈8°, and larger droplets (R₀ = 2.0 mm) only up to ≈4°. The reduction in θ_max with increasing droplet size is attributed to the larger gravitational force that must be overcome by the vapor‑induced thrust.

Overall, the paper demonstrates that (i) the self‑propulsion of Leidenfrost droplets on ratchet surfaces originates from the combined effect of geometric asymmetry and the resulting vapor flow field, (ii) there exists an optimal ratchet aspect ratio that maximizes droplet velocity, and (iii) the ability of droplets to climb inclined ratchets is limited by droplet size and substrate angle. The thermal multiphase LBM presented here offers a powerful tool for simulating coupled phase‑change and fluid‑structure interactions, with potential applications in micro‑heat‑transfer devices, passive fluid transport, and surface‑engineered cooling technologies.