The Onset of a Boiling Crisis as a Stochastic Three-Dimensional Off-Lattice Percolation Transition

Boiling crises are complex stochastic processes that are influenced by the physical phenomena of heat transfer and evaporation, as well as the shape and roughness of the boiling surface. When calculating the critical heat fluxes corresponding to the point of the first boiling crisis, it is important to know the numerical density of the formed bubbles per unit surface and volume. Most models consider only non-interacting bubbles. This greatly reduces their predictive accuracy. An analysis of the video footage of bubble boiling near the point of the first boiling crisis allows us to conclude that this is a typical picture for a continuum off-lattice problem of percolation theory. The main purpose of the work is to consider the point of the first boiling crisis as the percolation threshold for a three-dimensional problem. This threshold describes the transition from finite size inclusions (single bubbles and small groups of weakly interacting bubbles) to a percolation structure in which there is a macroscopic irregular bubble, the size of which is comparable to the size of the entire system. This hypothesis allows us to make estimates for the concentration of bubbles at the boiling point and to obtain estimates for critical heat fluxes at this point. The fundamental difference between the proposed approach and previous attempts to apply percolation theory to the description of boiling crises is the consideration of a three-dimensional problem in liquid volume, rather than a two-dimensional problem onto a hot boiling surface. It is shown, for the first time, that the proportionality constant in the Kutateladze–Zuber equation coincides with the percolation threshold for a three-dimensional continuum percolation problem on overlapping ellipsoids.