Daughter oil droplet entrainment by oil-coated bubble bursting

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, rise and ultimate bursting at the air-liquid interface play crucial roles in the transport and fate of natural organic matter and contaminants. However, the dynamics of compound bubbles has not received considerable attention until recently. Here, inspired by our previous work (Yang et al., Nat. Phys., vol. 19, 2023, pp. 884-890), we investigate the entrainment of daughter oil droplets in bulk water produced by a bursting oil-coated bubble. We document that the size of the entrained daughter oil droplet is affected 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 resisting the deformation of the oil coating, and considering the subsequent end-pinching process which finally entrains the daughter oil droplets. We propose a scaling analysis for the daughter oil droplet size that well captures the experimental results for a wide range of oil coating fractions and Ohnesorge numbers of the bulk liquid. In addition, we discuss the non-monotonic variation of daughter droplet size with the Ohnesorge number, and show the eventual absence of daughter droplets because of the strong viscous effect in the high-Ohnesorge-number regime. Our findings may advance the fundamental understanding of compound bubble bursting and provide guidance and modelling constraints for bubble-mediated contaminant transport in liquids.