Oil droplet entrainment from bursting oil-coated bubbles

Compound bubbles with a liquid coating in another continuous immiscible bulk phase are ubiquitous in a wide range of natural and industrial processes. Their formation, rising and ultimate bursting at the air-liquid interface play a crucial role in the transport and fate of both natural organic matters and contaminants. However, the dynamics of compound bubbles have not received considerable attention until recently. Here, we investigate the entrainment of daughter oil droplets in bulk water during oil-coated bubble bursting, inspired by our previous work (Yang et al., Nat. Phys., vol. 19, 2023, 884-890). We document that the size of the entrained daughter oil droplet is determined by the oil coating fraction and the bulk liquid properties. We rationalize this observation by balancing the viscous force exerted by the extensional flow produced by bubble bursting with the capillary force, considering the end-pinching process of the daughter oil droplet formation. The proposed scaling law for the daughter oil droplet size well captures the experimental results for a wide range of oil coating fractions and Ohnesorge numbers of the bulk liquid. Our findings may advance the fundamental understanding of compound bubble bursting, as well as provide guidance and modeling constraints for bubble-mediated contaminant transport in liquids.