Soft engines: Leidenfrost effect in elastic solids

Original article: Coupling the Leidenfrost effect and elastic deformations to power sustained bouncing

Have you ever wondered why a water droplet rolls around on a hot pan instead of evaporating instantly? The part of the droplet touching the pan does indeed evaporate. The resulting vapor forms a thin insulating layer that enables the drop to hover over the pan for seconds, even minutes. This is known as the Leidenfrost effect. Because they also produce vapor when heated, sublimable solids (solids that skip over the liquid phase and directly produce vapor) also exhibit the Leidenfrost effect. This effect has been studied extensively for both liquids and sublimable solids.

In their letter in Nature (2017), Waitukaitis et al. studied the Leidenfrost effect for the first time in soft elastic solids. They used hydrogels, polymer networks that can absorb water. Because they can contain up to 99% water by volume, hydrogels are deformable and bendy. Contact lenses, for example, are hydrogels. The large water content provides vapor, making hydrogels ideal soft candidates for the Leidenfrost effect.

Figure 1. Bounce height vs. number of bounces (nb) for a gel (A) dropped on the cold plate, (B) dropped from h>h0 on the hot plate, and (C) dropped from h<h0 on a hot plate. The gel on the cold plate successively bounced to lower heights before coming to rest, but on the hot plate it achieved the same steady bounce height (h0) irrespective of the initial dropping height (Figure adapted from original article).

In their experiment, the researchers dropped a hydrogel sphere ~1.5 cm in diameter on a hot plate and recorded its activity. As seen in Figure 1B, the sphere eventually bounced at a constant height h0~3.5 cm around 1000 times. The sphere finally came to a stop when it cracked due to heat and water loss. A sphere dropped from a lower height also eventually bounced at the height h0 (see Figure 1C). This was surprising when compared to the behavior of an identical gel bouncing on a cold plate. As seen in Figure 1A, the gel on the cold plate successively bounced at lower heights and eventually stopped, just like a tennis ball would. Existence of a constant bounce height on a hot plate suggested that the hydrogel gained kinetic energy during its collisions with the hot surface.

Figure 2. Red: Experimental data for energy gained on a hot plate vs. initial drop height. Blue: Experimental data for energy lost on a cold plate vs. initial drop height. The two lines cross at ~3.5 cm, the constant bounce height (Figure adapted from original article).

The authors repeated this experiment for different initial drop heights to obtain the kinetic energy gained as a function of the drop height (see Figure 2). Comparing the kinetic energy gained on the hot plate to the energy lost on the cold plate, the researchers found that there was a sweet spot where the energy lost and gained cancel each other out. This sweet spot was exactly at h0! Thus, once the gel reached the bounce height h0, it kept bouncing at the same height until it lost its elasticity due to cracking. 

Figure 3. Red: Model prediction for energy gained on a hot plate vs. initial drop height.
Blue: Energy lost on a cold plate vs. initial drop height due to inelastic collision. The prediction as well as the crossover point show good agreement with the experimental data. (Figure adapted from original article).

To understand the mechanism of bouncing, the researchers looked at the impact at a high resolution. During impact, a gap opened up between the hydrogel and the plate, and the thickness of this gap oscillated between 0 and 100 μm several times. The authors proposed the following physical process to explain the kinetic energy gain of the hydrogel. When the gel touches the hot plate, a small amount of water evaporates. The vapor deforms the gel bottom and gets trapped in a pocket between the gel and the plate. As the pressure builds up inside the pocket, the vapor eventually escapes. The gel bottom then elastically recoils towards the plate. This gap oscillation repeats itself several times. According to the authors, work is done on the hydrogel during each such oscillation. The gel therefore gains a small amount of energy from the hot plate, effectively acting as a tiny engine. The authors also numerically modeled the gel as a vertical chain of masses connected with springs between them and considered the forces acting on each mass. Despite being much simpler than the real system, the model’s predictions showed good agreement with the experimental results (see Figure 3).

In conclusion, the researchers studied the Leidenfrost effect in elastic hydrogels. Even though the experimental details were similar for the regular (liquids and sublimable solids) and the elastic (hydrogels) Leidenfrost effects, the mechanisms for the two phenomena are different. In the regular Leidenfrost effect, there is no transfer of energy between the hot plate and a liquid drop. However, for a soft hydrogel, the elastic oscillations of the gel bottom convert some of the heat energy from the plate into the elastic (and in turn kinetic) energy of the gel, enabling it to bounce at a steady height. According to the authors, the gel is “effectively a soft engine that harvests energy from the hot surface,” with water vapor acting as a fuel. This research may have exciting implications for robotics. Most conventional robots are made of hard materials, but it is desirable to have soft and bendy robots for performing human-like functions. This work with elastic hydrogels that can be energized with heat could lead to self-actuating soft robots. 

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