Self-induced flows enhance the levitation of Leidenfrost drops on liquid baths

The Leidenfrost effect, classically associated with drops levitating on their own vapor over hot solid surfaces, can also be observed over hot baths of nonvolatile liquids. In view of substrate fluidity, heat transfer through the bath to the drop should most certainly be dominated by convection and not by only conduction as in the solids, which may be instrumental for an efficient heat supply to the drop given typically poor thermal conductivity of the liquids. Here, we undertake an experimental and numerical study of the flow in a bath of silicone oil V20 induced by an overlying Leidenfrost drop, highlighting that a toroidal vortex is formed underneath the drop whose direction of circulation turns out to be different for drops of different liquids. We show that this is due to a shift in a delicate interplay between three mechanisms pulling in different directions: (i) shear stresses exerted by the vapor escaping from the gap between the bath and the drop, as well as (ii) buoyancy action and (iii) thermocapillary (Marangoni) stresses, both due to local evaporative cooling of the bath by the drop. Whatever the structure of this locally induced convection, its crucial heat transfer enhancing efficiency is readily confirmed in numerical simulations as favoring levitation.

Figure 1

(a) Leidenfrost drop of (dyed) ethanol of $R=1.2$ mm on a silicone oil V20 bath at $T_{\mathrm{bath}}=79{}^{\circ }\mathrm{C}$ ($\mathrm{\Delta }T=1{}^{\circ }\mathrm{C}$). (b) System sketch with various bath-flow mechanisms and (c) the typical vapor gap profile [20, 23]. (d) Experimental setup.

Figure 2

Flow and temperature fields in the bath in the cases of ethanol (a) and HFE-7100 (b) Leidenfrost drops, both of radius $R=2{\ell }_{\mathrm{c}}$ and subjected to a superheat $\mathrm{\Delta }T=19{}^{\circ }\mathrm{C}$ over the corresponding saturation temperature (given in Table 1). PIV images (a1 and b1), postprocessed experimental images (a2 and b2), numerical results in the same format with all effects included (a3, a4, b3, and b4), with only the thermal Marangoni effect included but the vapor shear stress and buoyancy excluded (a5 and b5), with the thermal Marangoni effect and vapor shear stress included but buoyancy excluded (a6 and b6). The dimensionless temperature is defined as $\tilde{T}=(T-T_{\mathrm{bath}})/(T_{\mathrm{bath}}-T_{\mathrm{sat}})$. Note that the laser sheet that illuminates the PIV particles comes from the right in (a1) and (b1), and is obstructed by the surface deformation under the drop.

Figure 3

Profiles of (a) the vapor shear stress and evaporation heat flux, obtained using the model by Maquet et al. [20], and (b) the surface tangential velocity and temperature, computed here with all effects included, for the two cases of Fig. 2. The stress and velocity are positive when directed outwards.