The not-so-subtle flaws of the force balance approach to predict the departure of bubbles in boiling heat transfer

Abstract

We present a critical evaluation of the force balance approach in predicting the departure of rapidly growing bubbles from a boiling surface. To this end, we conduct separate effect bubble growth experiments in a carefully controlled environment. We use high-speed video to quantify experimentally all the external forces acting on a growing bubble through the profile of the liquid–vapor interface. Our experimental data show that the momentum conservation equation is always rigorously satisfied, as it should, if the various forces are precisely quantified. However, based on our analysis and our observations, we come to the conclusion that force balance models cannot be either robust or accurate for the purpose of predicting bubble departure. They are not robust because the rate of change of the bubble momentum, i.e., the key quantity that force balance models aim at evaluating as the sum of the external forces, is orders of magnitude smaller than each of the force terms in the momentum conservation equation throughout the entire bubble life cycle. Thus, the slightest error on one of the external forces leads to very different predictions for bubble departure. The approach is also not accurate because the analytical expressions used to estimate the external forces are riddled with questionable assumptions (e.g., on the bubble growth rate, added mass coefficient, contact line length, and contact angle) and uncertainties that are, once again, orders of magnitude larger than the rate of change of the bubble momentum itself.