Geometry of the vapor layer under a Leidenfrost hydrogel sphere

Abstract

A floating Leidenfrost droplet exhibits curvature inversion of its underside, due to the balance of vapor pressure and surface tension. Using interferometric imaging, we find different behavior for a levitated hydrogel sphere. Curvature inversion is observed briefly just after deposition, but quickly gives way to a steady state with no inversion. We show the essential role of vaporization on shaping the underbelly of the hydrogel, adding a new component to the interplay between vapor pressure and elastic force

Figures (4)

• Figure 1: Experimental setup and key observations. (a) We use a piezo motor to slowly lower a hydrogel sphere connected to a string toward a hot ($\sim$220$^\circ$C) sapphire window. A weight sensor at the top of the string allows us to determine how much of the hydrogel is supported by the vapor layer. The hot plate below the sapphire window has an aperture that allows an expanded, 633 nm laser to pass through. A high-speed camera records the interference pattern produced from reflections at the top of the window and the bottom of the hydrogel, while a second camera records from the side. (b) When a water droplet is placed on the window, we observe a steady state with a rim pattern and both saddle/minima features, indicating a curvature inversion beneath the droplet. (c) In contrast, the steady-state pattern for a hydrogel only has concentric rings, indicating the absence of curvature inversion. (d) View of the gap below the hydrogel as seen by the side-view camera, with truncated radius ($r_{\text{trun}}$) indicated.
• Figure 2: Time evolution of the interference pattern. (a) Weight of the hydrogel supported by the vapor as a function of time, with key points indicated (I-IV) and corresponding interferometric images. In region I, the weight is carried fully by the string, and no features are present in the interference pattern. At $t=0$, the hydrogel starts interacting with the vapor (region II), and the interference pattern shows a distinct rim with saddle/minima points, indicating curvature inversion. In region III, the rim destabilizes and the underside of the hydrogel enters into oscillations. On region IV, the oscillations disappear, resulting in stable floating of the hydrogel and a stable interference pattern without any curvature inversion. (b) Reconstructed height profile of the hydrogel underside in region IV at different times, indicating it is essentially flat over. As we show in the Supplemental Material, there is in fact a very slight upward curvature Supplemtental_Info.
• Figure 3: Temporary recovery of curvature inversion via elastic reloading. (a) To re-load the hydrogel elastically, and hence temporarily recover curvature inversion, we start by lowering it just beyond the point where all weight is carried by the vapor, leaving the string slightly loose (left). We then let vaporization occur until a small amount of hydrogel, $\delta z$, is removed, resulting in the string again becoming taut (middle). Upon lowering the hydrogel again, the vapor elastically deforms the hydrogel to recover curvature inversion, but only temporarily as vaporization quickly acts to take it away (right). (b) Weight vs. time during multiple iterations of the elastic reloading process. Region V corresponds to the recovery of the weight by the string (middle panel a). Region VI, within the red box, highlights the elastic interplay between the hydrogel and the vapor layer. Once again, evaporation overcomes the curvature inversion and the hydrogel reaches a stable floating regime without curvature inversion.
• Figure 4: Simple vaporization model. (a) Height profile underneath the sphere vs. time, calculated numerically by iteratively applying Eq. \ref{['eq:Evaporation']} to determine the evolution of the height/radius profile, Eq. \ref{['eq:PRL_Scott']} to determine the corresponding gap height, and FEM simulations to obtain the updated temperature profile. (b) Truncated radius obtained at each iteration of the numerical calculation, compared with the experimentally measured truncated radius and the model prediction. See Supplemental Material Supplemtental_Info for full simulation details.