Modeling Leidenfrost Levitation of Soft Elastic Solids

The elastic Leidenfrost effect occurs when a vaporizable soft solid is lowered onto a hot surface. Evaporative flow couples to elastic deformation, giving spontaneous bouncing or steady-state floating. The effect embodies an unexplored interplay between thermodynamics, elasticity, and lubrication: despite being observed, its basic theoretical description remains a challenge. Here, we provide a theory of elastic Leidenfrost floating. As weight increases, a rigid solid sits closer to the hot surface. By contrast, we discover an elasticity-dominated regime where the heavier the solid, the higher it floats. This geometry-governed behavior is reminiscent of the dynamics of large liquid Leidenfrost drops. We show that this elastic regime is characterized by Hertzian behavior of the solid’s underbelly and derive how the float height scales with materials parameters. Introducing a dimensionless elastic Leidenfrost number, we capture the crossover between rigid and Hertzian behavior. Our results provide theoretical underpinning for recent experiments, and point to the design of novel soft machines.

Figure 1

Leidenfrost levitation of elastic solids enabled by soft lubrication. (a) A soft elastic hydrogel sphere of radius $R=7\mathrm{mm}$ hovers above a hot surface ($\mathrm{\Delta }T=115°\mathrm{C}$). The inset shows hydrogel in daylight. (b) Evaporative flux elastically deforms the soft solid. Competition between vapor pressure and elastic stress sets the shape of the solid’s underbelly and the gap height. Inset: we predict distinct height scaling laws in a contact region under the soft solid, an outer region, and a narrow neck region of width $\delta$.

Figure 2

Gap height scaling laws. (a) Profiles of the solid’s underbelly in the Hertzian limit $\lambda \to 0$ show the development of a neck region (orange triangle), with height scaling law distinct from the contact region (purple circle). (b),(c) Finite element simulations (markers) verify our analytically predicted gap height scaling laws (lines) for the contact ($h\sim E^{-1/3}{R}^{7/12}$) and neck ($h\sim E^{-7/24}{R}^{43/96}$) regions. Black lines show analytic predictions for a rigid sphere. We find three regimes: rigid ($\lambda \to \infty$), transition ($\lambda \sim 1$), and Hertzian ($\lambda \to 0$). In (b), $R=40\mathrm{mm}$. In (c), $E=50\mathrm{kPa}$. Remaining parameters as in [3].

Figure 3

Collapsing to the Hertzian limit. Nondimensionalized (a) height $\tilde{h}$ and (b) pressure $\tilde{P}$ profiles from finite element simulation. Both approach the Hertzian solutions (black dashed lines) as $\lambda \to 0$. Deviations are confined to the neck region $\delta (\lambda )$. Insets: our height scaling law in the contact region, ${\varphi }_c(\lambda )={\lambda }^{1/4}$, breaks down in the neck [(a), left]. Instead, our asymptotic theory predicts that profiles collapse in the neck when radius $\mathrm{\Delta }\tilde{r}\equiv \tilde{r}-1$ is rescaled by $\delta (\lambda )={\lambda }^{3/16}$, height by ${\varphi }_n(\lambda )={\lambda }^{9/32}$ [(a), right] and pressure by ${\psi }_n(\lambda )={\lambda }^{3/32}$ [(b) right].