Dynamics of the wet granular Leidenfrost phenomenon

By event-driven molecular dynamics simulations, we study the Leidenfrost effect for wet granular matter driven from below. In marked contrast to all earlier studies on other fluids, the dense plug hovering on the hot gas cushion undergoes an undamped oscillation. The location of the Hopf bifurcation leading to this oscillation is strongly dependent on the inelasticity of the grain impacts. The vertical separation into a gas phase with a condensed plug hovering above it is particularly pronounced due to the cohesiveness of the granulate. For sufficiently large system sizes, the Rayleigh-Taylor instability terminates the oscillatory state at late times.

Figure 1

(a) Local volume filling fraction $\phi$ as a function of the height $h/d$ in the container. The snapshots shown in the inset are taken at different times during the simulation of $3\times {10}^4$ slightly polydisperse particles. The system exhibits a Leidenfrost effect with a dense plug hovering on top of a granular gas cushion. The color (grayscale) of an individual particle indicates its kinetic energy on a logarithmic scale (see legend). They represent the top and bottom turning point of the plug motion, respectively (See movie M1 in Ref. [23]). The shadow is generated digitally by illumination with parallel light from the left. (b) The local volume filling fraction $\phi$ is shown in grayscale and normalized with respect to the maximum packing fraction ${\phi }_{\max }$. $\phi$ is plotted as a function of the dimensionless height $h$ in the system and dimensionless time $t$. The plug oscillation and its stationary state is clearly visible. The mean force induced by the capillary bridge is $F_{\mathrm{cb}}/F_g=4$, where $F_g$ is the gravitational force and the capillary bridge ruptures at a surface separation of $s_{\mathrm{crit}}/d=0.0711$. The strength of the driving is $E^{*}=98.9$ and $\Gamma =60.0$.

Figure 2

Oscillation frequency of the dense plug hovering on a dilute gas cushion as obtained from simulations (symbols) as a function of the normalized mean height $h_0/d$ of the gas phase. The simulations were performed in three dimensions with $3\times {10}^4$ particles. The different colors and symbols indicate different driving energies $E^{*}$, while the driving acceleration was the same as described in the legend of Fig. 1. The theoretical prediction is shown as solid black curve.

Figure 3

Root mean square of the excursion ${\epsilon }_h$ plotted versus the driving energy $E^{*}$ for simulations of slightly inelastic particles colliding with a coefficient of restitution of $\epsilon =0.98$ for particle collisions and $\epsilon =0.99$ for particle wall collisions. Circles denote values obtained by simulations and the red curve is a fit of the form ${\epsilon }_h\propto {(E^{*}-E_{\mathrm{onset}}^{*})}^{1/2}$. The oscillation sets in at a large enough driving energy $E_{\mathrm{onset}}^{*}$. The insets show the local volume filling fraction as a function of height and normalized time $t/T_{\mathrm{driv}}$. The maximum acceleration of the driving is $\Gamma =60.0$. The driving energies are $E^{*}=344.6$ (top) and $E^{*}=4395.4$ (bottom), respectively. Top: the initially visible plug oscillation is damped and vanishes. Bottom: an oscillation of the plug appears again for higher driving energies of the wall; however, it is not as stable as in the elastic case.

Figure 4

The critical width of the plug, $L_c$, is plotted against the height of the plug, $h_p$, where the plug becomes unstable and shows the Rayleigh-Taylor instability in simulations (circles). The simulations were performed in a square-based box with side lengths $L_c$ and the number of particle layers was constant at 48 layers. The solid red line is the theoretical prediction of Eq. (13). Inset: successive snapshots of a simulation of $3\times {10}^5$ wet granular particles show a rising gas bubble similar as in water. This can best be seen in the shadow, where the bubble is most apparent (see movie M2 in Ref. [23] for the full animation of the snapshots displayed here). The box is $125d$ in width and $50d$ deep. The driving parameters are $\Gamma =60.0$ and $E^{*}=98.9$.