Numerical simulation of Marangoni flow around a growing hydrogen bubble on a microelectrode

In this work, a numerical model for Marangoni flow around a growing hydrogen bubble on a microelectrode is developed and validated. The growth of the bubble is implemented using a body-fitted moving mesh method that moves the bubble interface based on the production of hydrogen at the cathode. The dissolved hydrogen that is produced at the cathode diffuses into the bubble. The geometry of the bubble is a spherical cap with a pinned contact line and a decreasing contact angle as the bubble grows larger. There are two cases: (1) a case in which the bubble grows on a microbubble carpet that grows during the evolution of the bubble, and (2) a case in which the carpet thickness is negligible. The purpose of this model is to simulate and investigate thermocapillary Marangoni convection during almost the entire bubble lifetime (nucleation and detachment are not included).We validate the model with data from two experiments reported in literature (Massing et al. 2019; Bashkatov et al. 2022; Bashkatov, 2022). The evolution of the bubble radius, the temperature profile around the bubble, and the profile of the Marangoni velocity, which is tangential to the bubble surface at 5 mu m from the bubble, near the lower half of the bubble are accurately predicted. For the case with a bubble carpet, we investigated models with a growing carpet and fixed carpet thickness.We found that for a given bubble size the Marangoni velocity reduces with increasing carpet thickness. Stagnant bubble models are less complicated and computationally cheaper than the growing bubble model. For the case without a carpet, we compare the growing bubble model with two stagnant bubble models: one using constant current and another one using a transient current. A stagnant bubble model is recommended if the growth rate dr(b)/dt < 0.05uM where dr(b)/dt is the instantaneous bubble growth rate and u(M) the average Marangoni velocity at the bubble interface. This is the case at a relatively late stage of the bubble evolution. At the early stage of the bubble evolution, the absence of bubble growth dynamics in the stagnant bubble models appears to have an effect on the velocity profile and the pressure part of the hydrodynamic force.

Automated summary

This work develops and validates a numerical model for Marangoni flow around a growing hydrogen bubble on a microelectrode. The model accurately predicts the evolution of the bubble radius, the temperature profile around the bubble, and the profile of the Marangoni velocity. Different models are recommended for different stages of the bubble evolution.