On the peculiar bubble formation, growth, and collapse behaviors in catalytic micro-motor systems

Abstract

Bubbles often play a critical role in micro-systems involving Janus catalytic micro-motors (JCMs). Here, we examine some peculiar behaviors of the formation, growth, and collapse of the bubbles observed in recent experiments, in which JCM-laden droplets were dispensed on solid substrates and mixed with droplets of hydrogen peroxide solution. First, no oxygen bubble is visible near isolated JCMs when their size is smaller than a certain threshold, but bubbles can form and grow between a circular ring of small JCMs without touching any JCMs. Using analytical modeling and numerical simulations, we show that the lack of bubble formation near small, isolated JCMs originates from the low supersaturation of oxygen near their surface, which is caused by the efficient dissipation of oxygen molecules generated on their surface toward the bulk solution. In contrast, a cluster of small JCMs can collectively produce high enough oxygen supersaturation near the cluster to nucleate a bubble. Second, the radius of these bubbles grows following a power law of $R \sim t^{0.7}$, rather than the typical $R \sim t^{1/2}$ or $R \sim t^{1/3}$ laws for the growth of bubbles driven by simple diffusion or direct gas injection into the bubble. Our numerical simulations showed that this anomalous growth law is a result of the cooperative action of the oxygen supersaturation-driven bubble growth and the mutual motion between the JCMs and the growing bubble. Finally, once a bubble grows to its maximal size, it collapses far more rapidly than the time scale expected for bubbles that contain non-condensable gas and exist in bulk liquids. Our scale analysis and numerical simulations show that this rapid collapse can be explained by the coalescence of the bubble with the air–liquid interface of the liquid film.